About Mathophile

I strongly believe that the ability to do mathematics (at any level) is a skill whose rudiments we are all born with, and which we can then develop by practice and expand by learning. I was very fortunate to benefit from the best mathematics teachers and mentors I could wish for, starting with my dad and ending with my current postdoctoral mentor. Unfortunately, most people are not so lucky, so it is no wonder that so few go into mathematics even though so many have both an ability as well as an interest in it. It is my hope that, in addition to dispelling common myths about mathematics and showing my readers what real mathematicians do and how their work affects our daily lives, this blog will also provide a source of inspiration for aspiring mathematicians.

Teaching math, storytelling and beehives – an interview with Benadette Manning

Dear readers,

It is my pleasure to present to you an interview I did with Benadette Manning, an outstanding high-school mathematics teacher I met at the Boston Athenaeum last year. In addition to teaching math, Benadette is engaged in education research and has also been a dean at a high school in Cambridge. She also won an “educator of the year” award for being exceptionally resourceful, and she shared some of the resources with me during the interview. The recording of our conversation is available here – I hope you enjoy it as much as I did!

As usual, a transcript for this interview will appear later this year in a separate post. Meanwhile, stay tuned for another interview with a very unusual (former) math olympian.

Of socks, vacuum-cleaners and the Appalachian trail: an interview with Yasha Berchenko-Kogan

Dear readers,

I recently had the great pleasure of interviewing Yasha Berchenko-Kogan, an MIT graduate student in mathematics who became notorious on the Internet for his answer to a question on Quora about what mathematics graduate students do all day.

Yasha and I first met at the MIT Math recital, an annual music concert at which every participant is affiliated with the Math department (Yasha performed a piece on the piano). After this initial meeting we decided to find a time to talk more in detail.

In the interview we talked about a number of things, but the primary theme was explaining mathematical concepts to ourselves and others. A number of new insights came out of the interview, and I hope you will enjoy it as much as I did. The transcript is here, and this is the article Yasha mentioned towards the end of the interview.

Transcript of my interview with Richard Hoshino

Dear readers,

I’m finally completing the transcriptions of the part of my interview series I did in the first 12 months of the blog, by posting the transcript of the very first interview I conducted, the one with Richard Hoshino. It was very inspiring for me to listen to our conversation again while working on this transcription, and I hope it will be equally inspiring for you to read it if you haven’t listened to the interview yet, or even if you already have. Enjoy and stay tuned for my next post, tentatively entitled “What cats can teach us about math”.

MP: Richard, thank you so much for agreeing to talk to me again and I would like to start by asking you about the big picture. In your 2006 presentation at the CUMC [Canadian Undergraduate Mathematics Conference] at McGill you said that your career goal was to search for diverse opportunities to combine mathematics with public policy, and so I was wondering how your career goal has changed since then.

RH: Well, thank you Leonid and it’s so nice that we can touch base after so many years and you know when I last met you this was back in 2006, so over six years ago, I feel like I had too narrow a view and I realize that to say that my goal is to use math to influence public policy was too narrow because I realize now that I had skills beyond mathematics and I can apply them to causes that are more broad than public policy. And just to give you a couple of really quick examples, I used to work for the Canada Border Service Agency where in my last couple of years I worked for an exciting project that led to reduced waiting time at international airports. This would be the equivalent of folks like you and me traveling to Canada from abroad and clearing customs and before we would be waiting forty-five minutes or an hour, hour and a half, two hours, and now we typically wait about five, ten, fifteen minutes. And it was exciting because it involved not math but statistics, areas of math that I didn’t understand. I love it because reducing waiting lines at a customs queue is “not really policy” but I am grateful for it every time I come back to Canada because I can wait about half an hour less than I used to. And just to give another quick example, I live in Japan right now where we experienced the worst natural disaster in world’s history about a year and half ago. And after this tragic earthquake I felt so powerless and so desperate to want to help especially seeing the pictures of the Tsunami and seeing the fallouts from the nuclear radiation and so many people whose lives were changed forever and I found a Christian Relief Organization that did earthquake relief especially in the heart of key areas and what I ended up doing with this non-profit was building and working with an IT specialist to help her build a computer database to keep track of volunteers and I had a very simple role where I used the database to schedule volunteers and document for other volunteers how to use this database to keep track of what we were doing and reduce duplication of work. And I want to share that because it didn’t really have to do with mathematics or public policy but I realized that in my big picture and I feel this tremendous yearning to make a contribution that has an impact in the world. And I’ll quote this section by quoting a guy named John Wesley. This was from 200, 300 years ago. And this has kind of been my life motto: Do all the good you can by all the means you can, in all the ways you can, in all the places you can, in all the times you can, to all the people you can, as long as you ever can. And I think that’s kind of my big picture of where I want to go with the rest of my life.

MP: Oh wow OK that sounds much broader than the original certainly, and it’s great that you’ve got these opportunities to contribute in those ways and so I guess going back to your presentation again for me, one of the big takeaways from that was that you really wanted to see life as a service and that actually resonated quite a bit with me and certainly, you’ve been consciously seeking out opportunities for serving others but I guess another question that I had is what might be some of the unexpected ways in which you’ve put your mathematical and perhaps other skills to use?

RH: Sure, so I’m part of the Canadian Mathematical Society and every month or so they release a bulletin called the Notices or Notes of the Canadian Math Society and so the December edition came out this morning and so I wrote a two page article in that and it was based on a media company producing a TV game show where they needed help to schedule the contestants to reduce fatigue. It was an obstacle course, medieval-themed show called Spatalot which was in Canada, Australia, and Britain. A huge hit in all three countries among the teenagers and it was really interesting because it involved an area of math called graph theory which is what I did my PhD in, yet even though my PhD thesis was very theoretical, it was so interesting because I can apply some ideas for that in all the real-life problems for this game show that was seen by thousands and thousands of people in three countries and it was exciting because I could use my passion for graph theory and scheduling to help the executive producer of the game show create a schedule that was exactly what he was looking for to reduce rest and boredom among the contestants competing on his game show.

MP: Wow, that sounds fantastic.

RH: And Leonid, I’ll send you the link if you’re interested.

MP: Absolutely, that would be great and I’ll put a link to it when I post the interview. Thanks and let’s change gears a little bit and talk about one of the big topics I’m trying to address in the blog which is the negative stereotypes we have, at least in North American society, about mathematicians. So you’ve spent the last few years living in Japan and I’m wondering what your experience has been in dealing with these stereotypes and also if you notice substantial differences in people’s attitudes towards math between Canada and Japan?

RH: Sure, well let me start with Canada because I have more familiarity with the Canadian system. We have a tremendous stereotype among the Canadian public that mathematics can only be done by boys, nerds, and Asians. In other words, people like myself. But I believe so strongly that with inspired mentorship anyone can succeed in math and develop the confidence and creativity and problem-solving skills and critical-thinking skills so essential in life. A good friend of mine, a mentor named John Mighton, he’s a professor at University of Toronto who is the pioneer of the JUMP, Junior Undiscovered Math Prodigy Program and JUMP has been a tremendous success, originally started with low-income kids in Toronto and now there are one hundred thousand students across Canada from grade one to grade eight working on this program that takes the subject of math and instead of pounding kids with formulas to memorize and equations/techniques to regurgitate, this program looks at problem-solving in a holistic way, breaking problems into small parts and empowering students to develop their creativity and confidence skills and also a will to discover patterns for themselves and take ownership of the subject, and I feel like as we teach in a more creative and empowering way, we can break these stereotypes. This reminds me of an experience in Nova Scotia where I did my graduate school work where I started and founded the Nova Scotia Math League, a Saturday morning outreach program now in its 9th or 10th year involving thousands of students from the entire province in every school board and what I loved about this was that when I started this back in 2003 or 2004, we had about 40% girls and why this was so exciting for me was because we got to share math in a different way. Math wasn’t about speed and symbols. It wasn’t about manipulating algebraic symbols and memorizing formulas. What we ended up doing was presenting math in a really fun and recreational way, in a cooperative team-based event and also instead of focusing on the symbols of mathematics we focused on the visual or linguistic or conceptual types of recreational math problems that really appealed to a wide audience and through this program females in the various schools got to meet other females and realize hey, I’m not the only one who enjoys math! And this created a community of learners and I think by having outreach programs and teaching math in a very innovative way we can actually break some of these stereotypes. And I have seen some of that in Japan as well and in Canada those are the ways we can provide for students in a way that promotes the subject and encourages them to pursue further learning in math.

MP: That sounds fabulous actually. I am really impressed with the initiative that you described and I think that’s a very good point, actually, that as long as we present things in a different way, in an engaging and fun way, we are going to get a lot more people interested in math of all backgrounds and not necessarily those who are traditionally thought of as being perhaps good or predisposed for mathematics. So that’s definitely really inspiring and we definitely need more of these kinds of initiatives like the Saturday Math League and the JUMP program that you described. So another question that I wanted to ask about a related topic has to do with the attitude that people have towards mathematics. There has been some discussion in the press recently that this attitude is different between the East and the West, broadly speaking, and especially because mathematics can be seen as such a challenging subject. I guess I was wondering whether you’ve seen any differences in the way that Japanese and Canadian mathematicians approach the subject.

RH: Sure and maybe now I can answer the question I didn’t answer in the last part about Japan. So, you know, one of the things I have noticed about living in Japan for the last three years is Japan has realized, the Japanese educational system realizes, the importance of failing and struggling as a part of the learning process and subsequent potential for eventual success and this is engrained. This notion of perseverance and following through in the face of difficult challenges, this is engrained in Japanese culture. And for me having Japanese parents and I did a math program as a kid in Canada called Kumon, and this program, Kumon, focused on the importance of math, that it wasn’t good enough to get eighty percent or ninety percent or even ninety five percent. The way Kumon math program worked was that if you didn’t one hundred percent you couldn’t move on to the next worksheet, you couldn’t move on to the next level. And I really get that sense living here in Japan that the goal of every activity, even hobbies, is having an uncompromising commitment to excellence, the goal is mastery rather than just getting by and just doing the path of least resistance to getting as much as you can, enough so you can go on. And I feel like in Canada, sometimes I feel like we try really hard not to discourage young people and by having that as the frame of reference we end up creating a watered-down math curriculum where it’s all about covering the material in a superficial way rather than uncovering the material in a very deep way where we don’t do enough to encourage students to take ownership of the material and we try so hard to make math “interesting” even though math is already more interesting than any of us can ever imagine and so for me when I start my new career as a math professor back in Canada just in a couple of months I’ll have my students actually doing mathematics, in other words posing their own problems, making their own conjectures, trying something and feeling it, experiencing the despair of being stuck as well as the euphoria of then seeing the key insight and ensuring that they have periods of both creative frustration and creative breakthroughs. I feel like by creating a positive environment where students experience failure puts them in a position where they can eventually succeed. And I feel that, that’s something Japan does quite well and something that Canada can do better.

MP: OK, that sounds great actually. Yeah, I think I agree with the point that letting people fail sort of early on and as part of the process and then making sure that they actually get to the point where they master the material is a more rational approach then sort of just getting by. So, continuing on that topic of education, which is a very interesting topic to me both for the blog and personally, so you just said that you’re going to go back to Canada in a couple of months and start a career as a mathematics teacher so the university that you’re going to be doing that at is Quest University and from what I understand it has a very different model of teaching and learning, so I was wondering if you could tell me more about the model and also what you think makes it more attractive than the traditional model?

RH: Sure, well let me first start, Leonid, by talking about the traditional model and why that was absolutely not the place I wanted to work in, in the future. And so I went to a very traditional university, one of the top universities in Canada for math and I absolutely absolutely hated it, and I found that my professors squashed my curiosity and passion by monotonously lecturing at us to the paradigm viewing information transfer as the only method of learning rather than for example, speaking with energy and passion or incorporating multiple teaching strategies or empowering us to construct and create knowledge for ourselves and I found that my love and enthusiasm for math, even though I was a math Olympian who had done extremely well in high school, I found that my love and enthusiasm for math flattened and I was disempowered by so many professors who treated learning and teaching as a chore on how we could regurgitate theorems and memorize proofs and whose commitment to excellence and research did not extend to inspiring undergraduates to prepare them to be leaders of tomorrow. In other words, we have an educational system that essentially says that research is the only important thing and we have for example, a program called the Canada Research Chairs, where the bonus of being considered a star researcher is that as a bonus we have less teaching. There’s perhaps a reason why we use words like teaching load, research opportunity; even just the semantics of the words we use. So I found that traditional universities have tenure, for example, all based on the number of publications, the amount of research grants, money that you can bring in and I realize that having gone through a traditional university for my undergraduate and my graduate degree that I couldn’t flourish in that system because I am more passionate and have always been more passionate about teaching, administration, service, and outreach more than research. And then just about a year ago I learned of this place called Quest University Canada in British Columbia. I never knew that this place existed. It’s a startup university, that started five years ago, very recently, and just had their first graduating class in April 2011, just a year ago. As I learned about this university and saw their job posting I was shocked that their educational philosophy was not providing the right answers but empowering students to ask insightful questions, this really spoke to me because in my own development as a mathematician I have learned that the best mathematics comes not from me getting the right answer but by me posing the right question and the professors at this university, they’re part of the learning process, they are called tutors rather than professors. Every single person from the president to every student goes by their first name, and learning comes from a community rather than a hierarchical top-down approach. And so what I enjoyed about this university as I learned more, I found myself getting so excited and was so thrilled to be hired by this university. So at Quest all the classes are seminar-style, less than twenty students. They have a block plan style of learning in which students focus on just one subject at a time for a month. So for example, you and I would have taken five classes during a fifteen week period during our undergrad whereas at Quest students take one class at a time and do just that one class for there and half weeks. So it’s pretty much the same number of contact hours. But a block type system enables for both breadth and depth and pedagogically it’s so much better for empowerment, for retention, for achieving mastery of a subject. And what I loved about Quest especially was that each student at the end of their second year comes up with a unique question that directs the final two years of their work. In other words, the student can decide at the end of two years, this is what I want to study and then with their tutors, taking classes and doing their own independent studies, they get to own the material and create a final project that they work on over two years, where at the end they really become the expert at the subject because it’s their question. It’s not their professor’s answer, it started with them, with their question and it provides them with a much deeper and more meaningful learning experience. And this contrasts with a professor at the university that I went to for my undergrad. We had to sit next to each other at a dinner table a year ago and this gentleman told me he felt I was very naïve in thinking of education in this way because in his opinion it’s important for students, for young people in undergraduate and Master’s to know “content” before proceeding with difficult problem sets. According to this professor students need to be fed information for the first let’s say seven or eight years of their secondary education before they’re in a position where they can start developing their own mathematics, and I absolutely, completely disagree with that and feel that students, by providing them with the opportunity to own their own education from the outset, develop into much more mature and more developed mathematicians, more importantly critical thinkers, problem solvers, by availing themselves of the opportunity to take their own question and roll with it, right from the get go, right from their undergraduate experience, and so that’s what attracted me to Quest. They get this. And I am so excited to start there in February.

MP: Oh wow, that sounds extremely exciting. This is just a quick follow up question on that. It sounds like the model is quite different but are there some things that are still carried over from the traditional model, so for instance, are there such things are majors and minors?

RH: So no majors and minors, all students at the small liberal arts university, they just have a Bachelor of Arts and Science. So every single student when they graduate they receive a single degree called a Bachelor of Arts and Science. McMaster’s is the only other university in Canada that I know to offer this degree, so students have a rigorous foundation program where for the first two years they take a breadth of courses in both the arts and sciences and their last two years they can come up with their own question that combines elements of the arts and the sciences and so they just get this one combined degree, and another thing that is unique about this university is there is no tenure so to my knowledge, it’s the only university in North America that doesn’t worry about tenure where every year, every two years, professors are evaluated on their performance, heavy commitment to teaching and it’s really exciting because having a system where there is no tenure, It forces and encourages and empowers the tutors to be very innovative and creates a system of accountability where the tutors that are effective and good at their jobs get to keep their jobs and I feel that this is a much better approach than many universities, for example in the public sector where I work poor performance is not dealt with and this ends up hurting the students and they’re not able to get the education that they paid for.

MP: Absolutely. Great, well another question about Quest and maybe your quests as a tutor there which is that, you know, you’re about to start teaching your first course and you’re actually writing a novel that you plan to use as a textbook for that course, and so in my personal experience, I have always found that the stories behind the mathematics is what really fascinated me. Like you said that’s what really engages you; it’s not so much the covering of the content but the uncovering of the content, and so I guess the question that I wanted to ask you is that, do you actually think that a fictional novel like your novel or another novel could be a better source for learning math than a textbook?

RH: Yeah, absolutely. Just to provide some context for this, in March 2010 after my wife, Karen, landed her dream job teaching English at the University here in Japan, I ended up quitting my job with the Canadian government and moved to japan as an unemployed househusband and with no clarity of what I was going to do here in Japan I ended up getting all these ideas and realized that I wanted to write a book about math but I wasn’t sure if it was going to be a textbook. I knew it was going to be something with problem solving and one day I just had this idea that I should write a novel instead and I ended up writing or have begun to write and nearly completed a novel of a fictional Nova Scotia teenager who commits herself to the crazy and unrealistic goal of representing her country at the Math Olympiad and from that decision discovers Math and really enjoys it. In some ways a couple of years ago, I read Sophie’s World, a fascinating book dealing with Philosophy and I felt that the author did an amazing job of making Philosophy accessible and enjoyable, and it was so much more interesting to read Sophie’s World, in fact I felt that I learned more philosophy from reading this book than the thick textbook that I read during my first year philosophy course during my undergrad, and I felt like by writing a novel instead of a thick textbook, sharing beautiful mathematics with the general public through the medium of a novel I feel like I can reveal the surprising and unexpected applications of the math in everything in this world, in a very big picture way, so instead of a problem-solving book on techniques and ideas – there are plenty of them out there – by sharing a larger story could mean that our dreams are worth pursuing, no matter how unrealistic they are because they motivate us to reach our fullest potential by making contributions to society. And then if we pursue our dreams we inspire others to achieve theirs. If by writing a math book where that’s the main message I feel like it would reach more readers and that’s why I ended up choosing for a novel instead of a textbook, and I’m so excited to use this in my problem-solving course next year.

MP: Definitely, and so I think that sounds great and I really hope that this book ends up being successful at reaching a wide audience as I am sure you hope for too. My question then is, I guess, as far as I understand you haven’t’ done much creative writing before this so you probably have been facing a lot of the same challenges when you started doing this that I’m having right now with the blog and I was wondering if you could talk a little bit about some of these challenges and also how you managed to overcome them?

RH: Sure, well so I am a first-time author with no background or experience in creative writing. I didn’t take a single English course during my undergraduate. So the last English course I took was in grade 12 so that would be sixteen years ago, and so I ended up publishing my entire manuscript online and invited people to comment on the manuscript providing feedback and what’s been really exciting about this, sharing my work with hundreds of people and posting it on various websites and forums, I have received valuable, tremendously helpful comments from hundreds of people in many different countries. I have been able to take their advice, from students, male and female, to professors, to parents. I have been able to take comments and then create a better book, so not just fixing typos but really helping me with the story and developing characters and helping me explain certain things in a much more meaningful or clear, concise way. I feel that because of them the final product is going to be so much better and I feel especially for me, as a first-time author, if I didn’t do this and waited until the final product, or I had a final product before sharing it, it would have been nowhere near as effective as what I have been able to do now.

MP: Absolutely, that sounds terrific. It reminds me actually of the product development process where, you know, you always hear that it’s a good idea to show your prototypes early to potential customers and so you don’t end up developing something that nobody ends up using and I think the approach that you’ve taken is really great and I wonder if perhaps some of these ideas are things that I should also adopt for my blog. Well, anyway I also wanted to get back to this creativity idea and talk a little bit about another area of creativity, which is music. I saw among a dozen of your papers there’s one in particular that deals with an application to music and I’m pretty sure a lot of the readers of this blog have an interest in music so I was wondering if you could maybe give us a quick summary of what the application is and also what inspired you to look into this question?

RH: Sure, I have a fabulous PhD supervisor named Jason Brown at Dalhousie, and Jason became very famous a few years back for applying his mathematical talent to music, combining his two biggest passions, and about forty years ago there was a very famous song by the Beatles called a Hard Day’s Night and it starts with a very famous opening chord that lasts about three seconds and nobody could understand or nobody could reproduce this, so the sheet music that the Beatles eventually released didn’t match up to the actual song, no one could reproduce that song and Jason, using some fabulous techniques in math called Fourier analysis, was able to deduce that famous opening chord involved the producer playing a certain sequence of notes on a piano and if you take that combination of notes on a piano and combine it with a Paul McCartney playing notes on his guitar etc. it actually makes the sound absolutely perfect and then you can reproduce that chord exactly and he ended up getting a lot of media attention for this; in fact he wrote an amazing book that I’ll shamelessly plug called, ‘Our Days are Numbered: How Mathematics Orders our Lives’ and in this book Jason talks about the application and the connection of math to music, and so that’s where the interest came in that there is a connection between these two subjects. I have a very very good friend named Sachiko Nakajima who lives in Japan. She was the first and currently the only female Olympian who’s ever represented Japan and what she learned, as passionate as she was about math, her real passion was music and so she ended up giving up a potential career as a math professor, realizing that there was something that she wanted to do more and that was to become a professional jazz musician and that’s what she ended up doing. It’s really exciting to see the connections between math and music and seeing how these two subjects are intricately connected and for me to have had the opportunity to be mentored by my PhD advisor, who is an expert in both. So that was an awesome experience.

MP: Absolutely, that sounds fantastic. And so another, different area of application. I was very pleasantly surprised to see an article in the Japan Times recently featuring your work. This is the work that you have done scheduling the Japanese Baseball League. So I was wondering if you could talk a little bit about what motivated you to look into that and also what were the differences between the theory that you must have used for analyzing the problem and how it actually got resolved in practice.

RH: Sure, well I did my PhD in graph theory, writing a two hundred and sixty page thesis on a very technical problem which had multiple sub-problems, a very pure theoretical type of math, and so when I came to Japan and eventually landed a position doing research with a famous graph theory professor at the National Institute of Informatics in Tokyo, I ended up working on some very difficult theoretical graph theory problem and I was unable to solve it and one day, just in a state of tremendous discouragement, riding the train I ended up picking up the schedule for the Chiba Marine Baseball Team, this is the local baseball team where I live, one of the twelve professional baseball teams in Japan. And as I was looking at the schedule I noticed that there were tremendous inefficiencies; this team, instead of playing multiple games where the opponents were located geographically close to one another, it was an extremely inefficient schedule and I realized that using techniques in graph theory, I had a flash of insight that perhaps there are techniques that can be done by taking a scheduling problem and converting it into graph theory. I had a big sense of how that could be done. And I was inspired by that because while I was looking at the schedule I was also on my cell phone and every Japanese person on their cell phone has a computer program that tells them how to get from one train station to the other in the shortest amount of time and this is a very simple application of graph theory called the shortest path algorithm and I had this idea that I could model this difficult baseball scheduling problem as a shortest path problem by figuring out the shortest travel distance from the start of the season to the end of the season. It took me a while to work out the details, but eventually I was able to do that and I have become an expert in scheduling theory by combining it with graph theory just in the last couple of years. After writing multiple research papers and presenting them at conferences I realized that wasn’t enough because why I was motivated to do this project in the first place was to make an impact for the Japanese baseball league where we showed theoretically that we can reduce the total travel distance by 25%, that is almost 70,000 kilometers, four trips around the world, that’s huge. Currently the baseball league travels 280,000 kilometers so that’s four trips around the world so we could show that we could cut that by a quarter. We were in a small island country. We could reduce the total travel distance by 70,000 kilometers and that represents an enormous impact in terms of cost saving, time saving, energy reduction, greenhouse gas emissions cut, and especially after our tragic earthquake last year I wanted to do something specific to help the country that I live in by applying my skills in math and so I worked really hard to get a meeting with the Japanese baseball league. It took almost a year to get a meeting but once I did they were astonished that what they have been doing manually, a six week process done by hand, can be done in four minutes using some techniques in graph theory and applying a computer software program to figure out the optimal combination, so once we actually met with the Japanese baseball league we learned that there were various constraints that we didn’t know, for example, a balance in weekday and weekend games, ensuring certain constraints that were made for balancing between the various teams, so once we were able to put that into our model we were able to develop theoretical techniques and then once we combined it with the actual information of when certain stadiums were unavailable, we were able to propose some schedule that made things much better leading to reduced travel, cost, as well as greenhouse gas emission reduction.

MP: Fantastic.

RH: And so we got part of our schedule implemented for the 2013 season but our hope is to develop the full schedule for the 2014 season and beyond. All of the intellectual work has already been done and it’s just a matter of each year updating when certain stadiums aren’t available, when certain teams should play against each other to maximize revenue and once we get that, we can generate schedules in four minutes instead of six weeks.

MP: Right, that sounds like a tremendous saving overall and definitely a win-win solution for everyone involved, and it’s really exciting that it actually got at least partly adopted into the actual scheduling. Hopefully, next year and the years after it’ll actually be used as the main program for creating that schedule. So that being said I also wanted to go a little bit back in time, to your time in Canada before you moved to Japan; as you told us you worked for the Canada Border Services Agency so my question is, what was it actually like to work for the government after spending most of your career in academia? Was it the case that you had an important contribution to make, did politics get in the way, were you able to publish work, and did it actually end up making a practical impact? I guess you said that the waiting time in airports has been reduced so that sounds like there was definitely a practical impact, so maybe you can address some of the other questions.

RH: So yeah, I ended up working for the Canada Border Services Agency hired under a new recruitment initiative by the Government of Canada called the Recruitment of Policy Leaders. And it was exciting that through this program I was the first mathematician in a 13,000-person agency and it was so exciting because the president, what they called the deputy minister, of the Canada Border Services Agency, he was a meteorologist specializing in weather prediction and that was how he started his public service career and he was shocked that the mathematical models did a better job of predicting weather than everything he had done, through years of training and education. And what he realized was when his expertise as meteorologist would combine with mathematical modeling, better results were produced. Weather prediction is one of the best in terms of forecasting, the science and the mathematics of weather prediction and forecasting is so strong, so when this man became the deputy minister of the Canada Border Services Agency he wanted to hire a mathematician to take those ideas and combine with the ideas of the local customs officers to create a more efficient and a more secure border. It was exciting, and for a period of four years I got to develop a new risk-scoring algorithm for marine cargo containers coming in to Canada, develop a new system for biometrics for passenger identification of iris scans using techniques in probability theory and then also reduce wait times at border crossings using some statistical modeling, some queueing theory and integer programming and work on a whole bunch of small side projects as well. That was so exciting, and yes, working in the public service there were some tremendous inefficiencies but there was this tremendous joy that what you worked on, although the process was extremely frustrating, to know that what you were doing was making an impact for the entire country was a tremendous joy, something that a lot of mathematicians have never had the joy of experiencing, to know that what you do has a direct impact in your country on society as a whole. That was tremendously, tremendously exciting, but more importantly, during those four years at the Canada Border Services Agency I ended up hiring fifteen people, some as students and others as full-time employees, and together, we ended up building a math team, a team that still exists today, so one mathematician now became a large team. During these four years I got to supervise fifteen people, many of whom have Master’s degrees in statistics or math. What we have been able to do is change the culture of the agency in a very short amount of time from one that was all based on local knowledge and “I have thirty to forty years of experience as a customs service officer therefore I know how to do security” to a more statistical or evidence-based approach that looks at analysis of data so that we can produce more efficient and more effective methods for improving our national security and economic efficiency. In many ways what we’ve been doing has been Moneyball, not just Moneyball in the context of using evidence-based statistics to evaluate baseball players, taking that type of approach to change a culture of an extremely risk-averse, change-averse government agency and bring it into the twenty-first century using some very powerful and sophisticated ideas in statistics and math.

MP: Yeah, that’s extremely exciting. I’m actually going to make a quick plug hearing you speak about an evidence-based approach versus relying exclusively on people’s domain expertise. Not the following week, but the week after that I’m actually going to talk in a blog post about Nate Silver and his statistical predictions for the US elections and how he managed to predict things way more accurately than people with a tremendous amount of experience and understanding of politics but with very little knowledge of mathematics and statistics; that’s definitely something that we’ll explore, that topic, a little bit more. I think in general the power of math is that we actually can integrate both the domain knowledge that people have as well as the evidence from other sources in a single predictive model, so that should be exciting. Now I actually want to switch gears a little bit, and I want to ask you how you would describe the research area that you’re working in to somebody who is not a mathematician, and in particular, would you classify it as pure or applied mathematics?

RH: Sure, I think of myself as a hybrid mathematician, in other words, perhaps my area of math nowadays is called operations research, where I look at applied problems – whether it’s reducing border wait times or cutting carbon emissions for a professional baseball league – taking real-world applied problems and trying to model them into the language of mathematics, and using techniques in pure math to solve them to develop techniques and ideas and theories, but then I am always driven by a real problem, and this very much models my own approach to teaching called problems-based learning, where by providing students with meaningful, contextually-rich problems, and having students discover the techniques and theories motivated by the desire to solve that problem leads to a lot of great ideas, so this is the type of math I do as a researcher. This is how I approach research math as well and I think of myself as both a pure and applied mathematician – motivated by the application, but developing the theoretical, and generalizing ideas to develop theories, and so I’m kind of a mix between the two.

MP: OK, that sounds great, would it be fair to say then that you are just going to use whatever tools are necessary, whether they are tools from pure or an applied mathematics and that you’re really interested in solving the problem at hand?

RH: Absolutely, absolutely. Fantastic! And this is exciting, actually, because then I get to learn more math than speaking to this one narrow research area for four years. And by being motivated to work on a real problem, it structures me to learn math in a way that I’m not aware of, and that enables me to expand my own breadth of knowledge and depth of knowledge and therefore, make a bigger contribution to society.

MP: Absolutely, yeah that sounds great! Another question I wanted to ask you is going back to this idea of engagement with society. It clearly has been a guiding principle behind your career so far and I am sure it’ll continue to do so. Would you feel that – maybe this is not a fair question, necessarily, but I’m still going to ask it – would you feel that it’s the research you do or it’s the teaching that you do that has a larger impact on society?

RH: I think the question itself involves, in some ways you’re comparing apples and oranges, I feel like absolutely, both are important, but I’d definitely be a worse teacher if I didn’t do any research, and vice versa that I’d be a worse researcher if I didn’t do any teaching and so I feel, Leonid, through teaching I can affect people whereas through research I can affect organizations and systems, so through the teaching that I do be able to challenge and then inspire one student at a time as a tremendous blessing and a tremendous privilege and through my research I can tackle very difficult problems and actually compose solutions that lead to measurable and meaningful change in ultra-conservative baseball leagues in Japan or slow-to-change government agencies in Canada. It’s really exciting to know what we’re able to do, and I can take the passion that I have for mathematics for research and teaching and live a life filled with passion and purpose by being able to do both research and teaching.

MP: Definitely, I think that’s a great way of addressing a tricky question. I think I definitely agree with you that there are different kinds of impact, that this is not something that you can make a fair comparison with. You don’t have to choose one or the other because you’re able to integrate both, which is great. And so let’s go back to the first question, and this is actually going to be our last question for the conversation because we’re already getting close to an hour and it’s been really fantastic having this discussion. So the question I wanted to ask you about is, what would you advise to somebody who is you know, let’s say a young person is considering a career in mathematics but doesn’t have the confidence to know that they’re actually good enough for it, or committed enough to it, and are kind of at a crossroads, what would you say to a person like that?

RH: Sure, thank you Leonid. This is a great question. When I was in grade seven I wrote my very first math contest and I remember feeling so discouraged because I liked math, I enjoyed learning the subject but I ended up coming twenty fourth in my very first math contest, way back in grade seven. Now this was twenty fourth in Canada, it wasn’t twenty fourth in my province, it was twenty fourth in my class and I remember feeling so discouraged because I liked the subject, I just didn’t know how to do problem-solving. And as I got better and better and better, my results slowly improved to the point where five years later I was one of the top six in the country, and I share this story because it’s not about how good you are at the beginning or “how smart you are”, but if one has an excitement for mathematics and one feels the energy from doing the subject and appreciates the beauty in the subject then and by combining that with an ability to persevere through difficult struggles and failure, then by having that passion for the subject as well as persevere, then that means that person is good enough and is committed enough and will therefore succeed. In fact I can end by sharing a quote from a guy who wanted to play professional basketball but wasn’t very good. He ended up being cut from his high school basketball team and what he did was tried a bit harder, he just barely made the team the following year and the way he got so good was by being the last person to leave practice every day, the first person to arrive at practice. By simply having more desire than anybody else because he loved the sport and had the perseverance to see things through, through times of failure and disappointment. Anyway this guy ended up winning a scholarship to college, ended up being drafted in the NBA and when he retired, arguably became the greatest player in basketball history. So let me end with this quote from Michael Jordan who really was cut from his high school basketball team. He said this, “I have missed more than nine thousand shots in my career, I have lost almost three hundred games, twenty-six times I was trusted to take the game-winning shot and missed, I have failed over and over and over again in my life, and that is why I succeed” and I feel that if I close with that, to encourage young people in particular, that failure and disappointment is a natural part of the process of doing and learning mathematics, but if one is able to persevere through those difficult times and combine it with a passion for the subject, that combination of perseverance and passion will lead to a life of tremendous purpose and one that involves making a tremendous impact on society.

MP: Well, that’s a fabulous story! Thank you so much for sharing it, Richard, and thank you so much, once again, for joining me on this interview, the first interview of our series. We’ll definitely have to stay tuned and stay updated on how things go for you at Quest and I’m also really excited about your novel and all the other developments. So thanks again, and we’ll hope to hear from you again soon.

RH: Yeah, you bet, Leonid, thank you so much. I am so glad we were able to do this and great to hear your voice again after so many years.

MP: Definitely, same here, thanks a lot.

RH: You’re welcome, thank you so much, and take care. Bye.

MP: Thank you, bye-bye.

Transcript of my interview with Nilima Nigam

Dear readers,

I am finally back to blogging after a long hiatus! Today I’m sharing with you the transcript of an interview I did at the beginning of last year, with Nilima Nigam. I would like to thank my assistant for helping prepare the initial transcript. You can find the audio of our interview here.

Transcript: Interview with Nilima Nigam

MP: Hi Nilima, I am really glad that I get a chance to speak to you today. I know you just got back from travelling so I really appreciate the opportunity to speak with you and it’s also the start of a new year so happy New Year.

NN: Happy New Year Leonid, and thank you so much for this opportunity to chat.

MP: Thanks a lot! So I’d like to start by just asking you about your work as an academic mathematician; more specifically, what do you find to be the most rewarding aspect of the work, you know, whether it’s research or perhaps teaching or maybe the administrative work that you do.

NN: I think it’s easier to say what I dislike about the work and that is without a doubt, the administrative aspect of it. In terms of the work that I find most rewarding I would say that it’s hard to distinguish between how valuable and rewarding research is and how valuable and rewarding teaching is. For me they both work hand in hand in the sense that in the semesters that I don’t teach, I find that I don’t get very much research done either, and this is paradoxical because I imagine that a semester without teaching is such a wonderful thing that people plan these grand research projects for then. I find that unless I am engaging with students and try to communicate what I know in very clear terms I am not really thinking clearly or engaging in the mathematics at the research level either.

MP: Oh that’s really interesting. I know that a lot of professors really enjoy having the opportunity to take a semester or two off of teaching and I don’t think I ever realized that it was actually potentially an obstacle to research.

NN: I find it to be disorienting. So after I moved to SFU, I have been fortunate or otherwise blessed to have a Canada research chair and this comes with a reduced teaching responsibility, but I find myself not doing as much as I could unless I am teaching so I’ve been teaching much more than I am required to.

MP: Fantastic! And so I guess in that way, do you feel that teaching is then directly helpful in the research that you do or is it just the requirement to state things very clearly and really distill everything down to its essence?
NN: So there are some pragmatic benefits and then there are some indirect benefits. The pragmatic benefits of teaching include having a very structured day, which for me is important because I find that without structure I don’t actually have the necessary discipline to sit down at my desk and crank through a hard technical argument. I keep postponing it. And so when I teach I do have rather strict limitations on when I can work on my research so that forces me somehow to engage with the harder, more technical work right away.

MP: I see.

NN: In terms of the indirect benefits, yes there’s the mental exercise of trying to be clear and concise and also trying to anticipate questions. I think being able to write a good paper means that one should be able to anticipate questions and this is very similar to how preparing a lecture should be. Does this make sense?

MP: Absolutely I think that’s a really great insight and I feel that I haven’t had that insight before so that’s definitely helpful, thanks a lot for that! I wanted to address another topic now that I have tried to address in my blog so far, which is the way that math is permeating our daily lives. I remember once we had this conversation where you told me that being an applied mathematician gives you the opportunity to play in many other people’s backyards. I am not sure if I am quoting very precisely but I think that was the gist of it. So when you choose a problem to work on what is the primary motivation for you – is it the mathematics itself or is it actually the application to the real world?

NN: OK so I should begin my answer by correctly attributing the quote. So I got this wonderful quote from David Wolfson who is a statistician and he said that as a statistician he gets to play in everyone’s backyard and I thought that was a really wonderful way of looking at one’s discipline and it’s actually also true of applied math. In terms of what’s a primary motivator? That is an excellent question and I have pondered on this a few times. And sometimes it’s very clear when I am looking at a problem what the mathematics is that one needs to do and then one chooses to work on that problem or not depending on the mathematical content, but there are other times where it’s not even clear what mathematical tools are needed. And then one’s motivated to work on the problem more from the perspective of the application and along the way one discovers interesting mathematics or mathematics that is surprising in the context of the problem.

MP: I see; would you be able to give me an example of the latter kind of situation when it’s not clear what the tool would be and you kind of start discovering new mathematics, or potentially existing mathematics but not necessarily that you had thought of applying to this problem, along the way?

NN: Here’s one example: when I was working on my industrial postdoc, the original objective of the postdoc was to write an algorithm to optimize magnetic read heads. The physics of this is pretty clear. One essentially has a system of PDEs to discretize and then solve.

MP: And for those of our blog readers who might not know what a PDE is, could you explain?

NN: Oh, I am sorry it’s a partial differential equation.

MP: Thanks, great.

NN: So built into this physical problem was an interesting constraint and the constraint was that at each point along the read head, the amount of the magnetization wasn’t allowed to change. It can point up or down or sideways or north/south but the amount was not allowed to change. This is all good and fine but if you start trying to write a numerical algorithm for this constraint it’s really annoying and hard to work with. And it turned out there had been a considerable amount of work in studying similar mechanical systems with such constraints but never in the context of magnetization or at least not the way I was looking at it, so I was fortunate enough to encounter Debra Lewis who is an expert in Lagrangian mechanics and mathematical mechanics in general and I learned a lot from her and we discovered there was this very deep and interesting way of reformulating a problem as its representational Lie algebra and then we worked instead of with the original system of equations, with the reformulated equations in the Lie algebra, and that led to a nice algorithm. This was, for me surprising.

MP: Wow that is really cool.

NN: Yeah it was cool. And until then I had never really needed to work with a Lie algebra or ever tried to code up something that involved a Lie group.

MP: Well, that’s a fantastic example.

NN: That’s something that I have also encountered a couple of times in my own experiences but I think this is a much better example than any of the things that I have encountered where you start working on a problem thinking that maybe this kind of tool is going to work but then it turns out that what is actually needed there is a complete rethinking and reformulation of the problem in order to make it actually reasonable.

MP: So I guess since we are discussing the postdoctoral program that you had, if I remember correctly this was the postdoc with SeaGate Technology, the company which makes hard drives and other computer devices. I actually seem to have an external hard drive that was made by this company and that’s enough to remind me of the practical implications of the work. I guess maybe if you could tell me a little bit more about what it was like to work at SeaGate Technology, especially after spending most of your time previously in academia and whether you had a significant contribution to make to the company?

NN: So I think it’s helpful to perhaps provide context for the postdoc. I became an industrial postdoc through a really fantastic program at the Institute for Mathematics and Applications in Minneapolis. And as an industrial postdoc I was obliged to spend half my time working on the problem from industry but I had an academic mentor as well, and for the rest of the time I was encouraged to talk to people in the School of Mathematics and to pursue my own work. So it was not strictly speaking a move from academia into industry, it was more of a blend of the two and this was very useful for me because for two years, I got to compare and contrast what the working environment in the two places would be like. It was really interesting to work with people at SeaGate. And they had, at the time, a very large research division. The research scientists there were the people I interacted with the most and I felt that they were astoundingly smart people who worked incredibly hard and they all had PhD’s and they were all I really believe first-rate scientists. The difficulty with working in an industrial setting, particularly in a sector as fast-moving as IT, is that it’s all good and fine to have research plans that are long-term but you’re ultimately answerable to some sort of a company bottom line! And the division as a whole would get its priorities set about once a year, and so by the time this got soldiered down to all the individual scientists I think they would get between three to four months on any given project and then they’d have to switch focus. And this is attractive in some respect because then you don’t try for the perfect answer, you strive for an answer that’s good enough. It’s very vibrant, it’s very dynamic but I am not that fast myself. It takes me a while to understand. The application takes me a while to sink my teeth into the mathematics. As a consequence I felt that such a rapid environment was not the right one for me. But if I had not had that experience, I would not have understood that. It was not that the mathematics they were doing was trivial or uninteresting; far from it, but I just felt that the pace was too fast.

MP: Yeah I think it’s really important to sort of get a feeling for both kinds of environments before making a decision because any person is better informed if one has actually gotten the chance to compare.

NN: I completely agree, Leonid, and I think it’s wonderful that you yourself have actually tried both sides of this somewhat artificial divide.

MP: Absolutely. Yeah, I definitely felt that for me the experience of working in industry was also an enriching one. I think I would definitely agree with your conclusion that sometimes the interest of the more academically minded or even not necessarily academically minded, any researcher and the interests of the company itself in terms of making profits can be at cross-purposes, especially in terms of timelines because you never really get the chance to work on something in great depth.

NN: Right, right. It has to move really fast so I guess even though I was in a rather different industry I had a very similar experience to yours.

MP: So since we’re speaking about this distinction between pure and applied mathematics, pretty much since the beginning of the conversation, how do you feel about that distinction? Do you feel that it’s a helpful one and do you also feel that there is a shared background that pretty much anyone who works in Mathematics should have and do you perhaps feel that it’s an artificial divide or if there is a place for it?

NN: So I personally think that the distinction between pure and applied math is more an administrative organizing principle than any true intellectual divide. And by this I mean the following; journals tend to specialize in some areas or not and then a collection of journals get lumped together, in a larger collection of journals say, and if you coarse-grain enough, at some point you come to two categories and one is called applied math and the other is called pure math. And it’s not clear that mathematicians who publish in one category never publish in the other. In fact it’s far from true. And I think this is an artifact of there being a lot more mathematicians than there ever have been so you do need some sort of an organizational principle otherwise where would departmental politics come from?

MP: That’s a great point.

NN: Yeah! I mean you could be Gauss and then who knows if you’re a pure mathematician or an applied mathematician or a physicist? Everybody claims you.

MP: That’s true.

NN: But now you would be pigeonholed. So I think intellectually I don’t find it to be a helpful distinction. It’s hurtful to people who are starting their careers because it artificially puts strictures on the kinds of coursework you see. I think I would admire a more liberal education for mathematicians where they pick courses based on interest rather than on perceived value as a pure or applied math course.

MP: But that being said would you say that there is still some kind of, I guess, regardless of one’s interest if one is to call oneself a mathematician one should at least, you know, have a certain amount of background in some very basic things and what would those things be?

NN: That’s a great question Leonid. And I have pondered this question for a while because I have been at several different educational institutions as a student and now as faculty, and every single place I have been at there has been a different answer to that question. It leads me to believe that the only real shared background that one can ask of is the ability to write a clear proof.

MP: I see.

NN: It cannot be the case that five different really excellent math departments have a different view of a common background. Like if it were genuinely common than everybody should have the same view of it.

MP: Absolutely.

NN: There are schools in which competence in analysis is viewed as absolutely essential for everybody. There are schools in which analysis and calculus are viewed as less important and algebra is viewed as the more fundamental. So it’s really not obvious what it is that we’re looking for in terms of shared background. I think we’re looking for a shared competence and the competence itself is the ability to reason clearly.

MP: I see and that’s perhaps not necessarily something that’s even taught very much at the undergraduate level. Would you say?

NN: I would agree. I think we do teach our students some elements of proof. We don’t expose them to the great many tools of proof that one might have or the different flavors of proof. And we certainly emphasize memorization of proof far more than we do the construction of proofs of an issue.

MP: Right.

NN: One’s always tempted to present a very clear proof on the board leaving the student to believe that, that is how one’s thought of the proof to start with.

MP: Absolutely, yeah.

NN: But that’s not how math works, right? It’s a very messy business.

MP: Definitely.

NN: And I think you have to gain experience with the mess and cleaning up the mess before one becomes a mathematician.

MP: And do you think that it’s a matter of just trying to be concise that, you know, sort of is responsible for the situation where most mathematical papers and event textbooks don’t actually go into this math that you mentioned where we could maybe call it the intuition and the different steps that precede the actual construction of the proof as much, and there is this tendency to, you know, focus on the final product and not present any of the preliminary work that goes into it or is it just a matter of culture perhaps? What would you say is responsible for this situation?

NN: I don’t think it’s very dissimilar from how authors work, say, on a book. Good authors revise their drafts many many times and there are loath to have their work in progress become public because it reveals inconsistencies and it reveals plot jumps and leaps that should not actually be there. Likewise I think a mathematical argument under construction does have holes or detours that one might find perhaps embarrassing.

MP: Yes, that’s a cultural problem.

NN: Or just worry about them being inaccurate.

MP: Sure.

NN: And so by the time one’s done testing one’s argument enough, hopefully one’s boiled away everything that’s not essential and one’s left with a skeleton which looks very concise but also looks far too pristine to have arrived just so.

MP: Absolutely. OK I think that’s a very helpful analogy. I actually found it pretty interesting myself to explore this parallel between writing and doing mathematics. Not that I would consider myself a writer but, you know, I do have stuff that I post on my blog and it’s certainly the case that I would not feel particularly comfortable, you know, publishing an incomplete draft although I do try to get some early feedback from a couple of reviewers before putting something up. And I think it’s probably the case also with mathematics that, I guess, we just don’t like to see anything that’s not complete, especially because where the analogy breaks down is while you know a draft of a book or an article is still something that you can read and understand and it’s a sort of valid product even though it might not be a finished product, a proof, unless it has sort of the complete logical structure in place and makes the connection between the conditions and the conclusions very clear is not quite an actual proof.

NN: Oh yes, most certainly. We have very high standards for what a proof actually is I guess. And if one were to publish, say, an intermediate argument it would go something like this; theorem and then the first few steps and then the conclusion and in between there is a heck of a lot of “my experience tells me” or “my intuition tells me” and then it’s those steps that you really have to fill in and that’s where the hand-waving has to stop. Yeah, it would be embarrassing to publish that.

MP: So on that note what do you think about the project I think it’s called PolyMath where basically the poster presents the problem that they are working on and then there is a collaborative effort by many different mathematicians in different places to try to fill in these gaps or try to kind of follow a program for getting an actual result together. How do you feel about that?

NN: It’s interesting that you ask that. I am currently involved in one. It’s on the hotspot conjecture proposed by Chris Evans. It’s been a fascinating experience. It’s also an experience that requires a great deal of courage which I constantly find myself lacking because any mistakes one makes are very public and matters or record, so I feel like I have made a complete fool of myself on numerous occasions on the PolyMath project and one also sees the somewhat spurt-like nature in which mathematicians work, so on PolyMath there was a flurry of activities in June and then a whole bunch of work in July and then things have essentially been quiet all through the Fall. Now you never see that in a real paper. In a real paper you have no sense of how long it took to come up with the paper and certainly the author does not seek to reveal their ignorance. But on a PolyMath project you seek to reveal what you don’t know so that other people can help you. So it’s been a very interesting project. I am not sure how many mathematicians actually participate in it.

MP: This is something that was started by Tim Gowers if I remember correctly?

NN: This is my understanding, yes. I think the current moderators are Tim Gowers and Terry Tao and Gil Kalai, if I’m not mistaken.

MP: Right, I think that’s a fascinating kind of idea and I’m actually really curious to see how things evolve, but do you feel that in the time that you’ve been involved in this work so far, there has been a substantial amount of progress and that it’s really been more than the sum of the individual parts, that it has been more than would have been obtained by any individual contributor in isolation?

NN: I have learnt a lot and I think that certainly working with the people that I find myself working with, these are people that I would not ordinarily have worked with, so I think in that sense it’s a great idea because it brings people from very different backgrounds together and it’s an opportunity to talk between sub-disciplines so that’s good.

MP: Absolutely.

NN: So in that sense it’s certainly much bigger than the sum of individual parts.

MP: Great, well I hope that work continues to be fruitful and I’m really curious to see how those things evolve. I have been really curious about this PolyMath project and I think it could be a very different model for how math is done and I think it could be significantly more groundbreaking in some specific well-taken problems. I don’t think it would work for every problem but I think for some specific ones it might actually work.

NN: Yeah, they seem to have had considerable success in some big ones so yeah.

MP: Wonderful. So another thing that I wanted to discuss with you kind of related to proof a little bit is the idea of how we use computers and computer programs as mathematicians. So of course, nowadays there are several big results that have been obtained with the help of computer proofs, but that’s certainly not the case for all areas of mathematics. So do you feel that mathematicians nowadays can still get away with not learning how to program? I know some of my undergraduate colleagues decided not to invest the time and effort in learning that and it is a pretty steep learning curve so I certainly don’t blame them, but would you actually say that at this point in time we actually have to understand how computers work or how computer programs work in order to do mathematics?
NN: So there is a distinction to be made between symbolic computation and between approximation theory and algorithms in the sense of numeric analysis. So I actually don’t think everybody needs to understand discretization but I do think everybody needs to know how to work with some form of computer program and so if one’s of the belief that discretization or approximation is not important that’s fine but then in that case one should be prepared to learn a symbolic computational tool; like Sage has multiple things that are very very useful. And I think the risk of not learning such tools is that one just becomes much slower than one’s peers. I don’t see any particular glory in trying to convert one hypergeometric function into another by looking at Abrmovitz and Stegun if this is all done for you automatically. Yeah I just think it slows you down. And anybody that believes otherwise is probably working in category theory.

MP: I see, very well. So things like Sage or Maple you would say are an essential part of the modern mathematician’s toolkit.

NN: I think that there are very few mathematicians out there who know off the top of their head relationships between various derivatives of the gamma function and they shouldn’t need to have memorized any of this and a symbolic computation toolbox enables them to get this information quickly and accurately, and to eschew the use of this is just silly. It’s like saying there’s a section of the library I don’t want to go to.

MP: But then what do you think about the increasing use of symbolic computations or computer programs in order to actually obtain new results? And I guess the specific question I have here is, do you feel that there is a danger in mathematicians becoming a little bit too reliant on this kind of technology and not substituting insights for things that can be obtained by writing an extensive computer program and taking the large number of cases as for instance with, to mention a couple of examples, the Four Color Theorem or Kepler’s Conjecture, that were both essentially reduced down to a large number of cases and then each of those cases was checked by computer.

NN: Right, so there’s a couple of different things. One of the worries is that by relying on computers we will give up on our intuition or rely less on our intuition. I think that is not strictly speaking, accurate. So a chimpanzee sitting at a typewriter will produce something, right? But that’s attributing too much to the typewriter.

MP: OK, that’s fair.

NN: And likewise if the person working with the software is not thinking very hard about what it is that they want, the algorithm to the answer, then they are no better than a chimpanzee at a typewriter.

MP: I see.

NN: So I think that it’s almost the opposite. I think that when you try and break down the steps of a proof enough so that you can code it up, you have really understood the steps of the proof.

MP: Right.

NN: Because a computer, even for its given sophistication, it cannot divine what you want it to do.

MP: That’s true.

NN: And unless you have a very clear idea of the path you wish to take, you’re just banging keys on a keyboard. You’re not really doing anything. So I do think that people that work on computers just for proofs who are able to bring an argument to the stage where it becomes now a matter of checking of variety of cases that they have done the intellectual hard work and the rest of it is tedious and it’s important but it’s still not at the same level of intellectual sophistication as the work that went into constructing the argument till there.

MP: Sure, yeah.

NN: But for more on this really great question, do you know this blog by Scott Aaronson; it’s called Shtetl Optimized?

MP: Yeah.

NN: So he’s got a series of wonderful articles on computers just for proofs. In fact I think he was at some sort of a symposium on computer-assisted proofs.

MP: I was not aware of that. I have been following the blog on and off.

NN: So I think it’s called the Symposium on the Nature of Proof’ or ‘Symposium on Proofs’ or something like that somewhere on the East Coast. And there were some very interesting discussions around that so that’s something worth looking out for.

MP: Absolutely, I’ll definitely check it out. Thanks for pointing that out. Now I’d just like to switch gears a little bit and talk a little bit about mentorship. So I know that you have mentored a great number of students in the course of your career. I was, of course, one of them and I certainly benefited quite a lot from your mentorship and I know so have a lot of others. And so the question I wanted to ask you about is, would you say you’ve encouraged your students that you mentor to go on to an academic career or other opportunities, perhaps in industry and also how do you think about the impact that these different choices can make for the student that you mentor?

NN: So every student I’ve mentored has been different, right? And I have learned so much from them and it’s been a joy to work with every one of them. So there’s no standard advice to give, right? Because there is no standard student. And what I try to tell my PhD students is that you need to have a variety of projects during your graduate career so that should you desire to go into one direction or the other you have the competence and the credentials to go in that direction. So I encourage my students to participate in industrial problem-solving workshops even during the time when they’re taking coursework, and I push them to take courses in a large variety of math, as large a variety as they are able to and so I think that having options is the most important thing and not getting too hung up on an academic career or an industrial career. That said, I have to confess that all my PhD students have been really really fantastic mathematicians and so of course when two of them decided to move into finance despite having really wonderful post-doc offers, I did feel a pang and I did try to encourage them to come back to academia. And it’s not particularly rational because they are doing lovely work where they are and they are happy and they’re actually earning good money. For my Master’s students I encourage most of them on the basis of their own interests and their specific circumstances. The academic path is less easy these days than it used to be and it’s my sense that it will not change for the better for a considerable while.

MP: Right.

NN: And so I think it’s probably sensible for students to keep industrial options as a very very real option and to not regard it as a lesser option. It’s a different option. It’s not lesser.

MP: Yeah, I think your experience that we discussed earlier at Seagate supports the idea that different options have different benefits and I guess if I’m hearing this correctly, it all comes down to sort of each person understanding for themselves what it is that they enjoy doing the most.

NN: You see, at the same time that one as a graduate student or a post-doc there are other important life changes. It’s the average age at which people meet their partner. It’s the average age at which their partner tries to find a permanent position of some form or another and so we’re rarely talking about just one mathematician who has a plethora of choices and can cherry-pick what they want to do! More often than not, it involves more than one person, there’s geographical constraints, there’s monetary constrains, there’s temperament, there’s all this stuff.

MP: Absolutely, yeah. So it is a decision with occasionally more than one stakeholder as well.

NN: Oh yes, usually more than one stakeholder.

MP: Great, well then in addition to the undergrads and the graduate students that you’ve talked about a little bit. I know you’ve also been involved as a tutor with middle school students. What was, in your experience, these students’ attitudes towards mathematics and how do you see the curriculum in middle school for mathematics? Is it something that’s fine the way it is or are their specific changes that you would like to see and so on?

NN: So I used to tutor in middle school while I was in Minneapolis and the public school system in the States is very different from the public school system in Canada, so I should make that clear right off the bat. The school that I mentored at had a lot of kids from a large number of different countries. So for most of them their path to the United States had been a somewhat difficult one and so the problems that these kids brought into the classroom went far beyond their love of or their hate of mathematics. But of course it affected their interest in mathematics. And so it was interesting to see that the kids whose parents had come as refugees from Southeast Asia, they were very much into trying to learn more math and do much more than the class demanded. And I think that was cultural and aspirational. And there were other kids who came from other parts of the world who were trying to find a way to fit into American society at the time and they were trying to distinguish themselves from other kids and their entire attitude was anti-intellectual.

MP: I see.

NN: But that to me was less about the material they were learning and far more about them as people at that age.

MP: Yeah, it is a pretty difficult age.

NN: Yeah it’s a terrible age particularly if you’re from a community that has been historically oppressed in a country and then you show up as an immigrant in cold Minnesota and your parents have told you these horrible horrible stories of things that have happened to your family and then you start going to class and there’s kids in the class from the other community that back in your home country oppressed you, you really have to figure out ways to negotiate these things.

MP: Absolutely.

NN: So Eritreans and Somalis in the same classroom; how crazy is that? But they had them. But in Canada, or at least in British Columbia the curriculum can certainly be improved. I think the textbooks are atrocious! They are atrocious! They are riddled with errors and I think they are confusing and I have tried on several occasions to talk with the ministry of education to try and ascertain how we, from the public, can provide input into what’s wrong with the textbook. But the mechanism for this dialogue is not clear. And I think a simple way to change all of this is to just have more dialogue. Every province has good universities. Most universities have really good mathematicians.

MP: Yeah.

NN: And I wish that there were dialogues between math departments and ministries of education that set the curriculum and make the textbooks. And there isn’t really this back and forth. And I think that’s dangerous and it shows.

MP: Right, well I think that’s definitely a big problem to tackle and I think it’s wonderful that you’re trying to get that conversation started and I hope that works out and it’s definitely the case that as mathematicians, a lot of the times we could or we’d like to engage more with high school or middle school education and we don’t necessarily have a clear way to do that or at least on a systemic level. Speaking more about this topic of education, I guess I was hoping to ask you about the fact that we have, in relative terms, a lot fewer women in mathematics currently than we have men and I guess the two questions around that, that I was hoping to discuss with you is one, how has your own experience has been affected by gender, and I know this is not necessarily a very sort of good way into asking the question but I would like to explore that, and the other question that I wanted to explore a little bit is, do you think there is some systemic changes that we could make in order to attract more women into mathematics, especially professional mathematics?

NN: So I think the second question is a really hard one, in terms of systemic changes. So I can tell you what I think seems to work, at least in Canada. The fact that Canada has federally mandated parental leave policy which most universities enhance so that you can take parental leave and not see your pay go to zero, that’s important. And most universities in Canada, in fact all universities in Canada will stop your tenure clock.

MP: Right.

NN: And I think that’s hard to overrate how important such things are because this is not the case in the United States. It is not in
all universities.

MP: That’s correct.

NN: In fact in many places the stated policy is that yes, you can take time off, but the pressure in the department is that, no you really shouldn’t, whereas that is not the case in Canada. People, most people that I have spoken to do say that the departments are very supportive of people availing of their rights because that is a very big component of why women, particularly in the hard sciences, find that it’s just the wrong time. You’re trying to break into a profession that’s competitive. You’re trying to get grants. You’re trying to get papers out. You’re trying to train students. And you’re doing this when everybody around you is in their early thirties. You’re in your early thirties. You’re going to be having kids.

MP: Right.

NN: In other disciplines, there’s more variance in age, that’s my impression. So that’s one large component of it. I think parental leave policy in general, policies around families, they are much more friendly in Canada and I think this is reflected in how people see more women per math department here than they perhaps anticipate. But beyond that I honestly can’t say because the numbers of female graduate students are on the rise, the number of female postdocs has been on the rise.

MP: That’s true.

NN: But there’s this leaky pipeline problem and the leaky pipeline is only a problem if the individuals leaving the pipeline are doing so for worse careers. I don’t know where they go, right? I don’t have the data to say. Just like my own students, most women in mathematics aren’t leaving for lucrative careers in Wall Street. I genuinely don’t know where they’re going.

MP: That’s fair.

NN: So In terms of how has being a female affected my own experience. I would say not at all. Yeah and that seems counterintuitive but it’s helpful to remember where I come from. I come from India, where discrimination and bias against women is on a scale that we just cannot imagine, right?

MP: Absolutely.

NN: And so when I came to the West and I started going to school here I was just astounded at how easy it was as a female. I have always felt that I was taken on my own merit and that has been great.
MP: Absolutely.

NN: Yeah I have not experienced any setbacks to my career.

MP: Well, that’s fantastic and I think certainly reading about the state of things in India definitely has put things in perspective for me as well as I think that’s definitely something that, as much as we might have some unresolved issues in North America, there’s a lot more issues that need to be resolved elsewhere.

NN: Yeah, you have to grow yourself a very thick skin if you come from those countries and I guess by the time you arrive in North America, that thick skin makes you somewhat impervious to more subtle forms of discrimination.

MP: Well that’s fantastic and speaking on this topic I know you have two wonderful kids so how have you managed to combine your extremely productive career and your family life and especially have you ever felt that you were in conflict somehow?

NN: Oh so I definitely think that the demands of a family life take away from the demands of a career and vice-versa. I have been very lucky to be married to a fellow mathematician who understands the pressures of the career. It’s also a very caring profession. So I remember, for example in the summer when you did your summer research with me you would come and basically put up with me and my newborn baby.

MP: Oh yeah, I remember that very well.

NN: Yeah, so I remember that with great fondness and I’m very grateful to you because working with you helped me get out of the house and kept me sane. So if one has to have kids then being a mathematician is perhaps the best career to be in because you don’t actually need to be at your desk to be doing your work. And people are very nice, in general. Fellow mathematicians have been fantastic. So while I always wish I could work longer hours or spend more time at work I don’t think that these conflicting priorities are at war.
MP: Sure. Well that’s wonderful and so I guess the other aspect that I wanted to touch on briefly before we finish is the one about stereotypes which was the topic of the first post that I had in my blog, stereotypes about mathematicians, and while we both know these are very prevalent in our society, how would you say we can best convey what we actually do to society and how can we counter these stereotypes because we certainly suffer from a certain image problem, well I am not necessarily sure that suffer is the right word? There’s definitely this problem for mathematicians, which was one of the main reasons for me to start the blog in the first place.

NN: Right, I think we as mathematicians could perhaps do a better job of trying to articulate what it is we do to people that we know and by that I mean even our own families, I don’t think we necessarily give them enough credit or try and explain in clear terms what it is we do. And I think that when we make that attempt and when we find the words to describe what we do on a daily basis then we might find it easier to talk to other people. And I think that that’s important. So for example, trying to explain what I did to Paul’s parents helped me sort of put the work I do into a format that then I could walk into my son’s second grade class and then tell them about what I did.

MP: Sure.

NN: And then once they see a mathematician, they see someone who explains what she does and it doesn’t seem crazy and it doesn’t seem evil and it doesn’t seem nerdy and horrible, maybe this is a class that a few years from now will not see mathematicians as stereotypical mathematicians. So I think this is something we should do better at. Another thing we should do better is communicating with the press. We don’t. We’re terrible at it. And we should learn from physicists. If you think about it, physicists have done a marvelous job of conveying the excitement of their discipline to the population at large and so billions of dollars have been poured into large science on the strength of what physicists are able to say about their work to the media and it terms of lobbying at congress. We, as a profession, don’t do a whole lot of that and we should.

MP: I think that’s definitely true. Hopefully, there will come a point where there’ll be a more concerted effort to do that.

NN: I think the professional societies are trying but people need to be trained in how to do this stuff and we don’t train people systematically.

MP: True. That’s a great point and I think it would be really helpful to have a little bit more interest from the press in the first place because I think because right now any kind of media coverage that we’d get would be extremely sensational.

NN: Oh sure but you know the fact that we had a normal day and proved an interesting theorem isn’t going to be news so we better get used to that. So physics is able to say we had a great day and we proved this amazing result. So maybe we have to put aside our tendency to be strictly accurate and be a little more entertaining, if necessary.

MP: Definitely. Well, I think on that note now would be a good place for us to wrap up the interview. I think it was really helpful to discuss all these different issues that both affect your own life as a mathematician and your students and also society at large. I think this has been really helpful and I learned a lot.

NN: Thank you very much Leonid. This has been a fantastic set of questions – very very thoughtful, and thank you for a really interesting blog. I really enjoy your blog. Thanks so much. I really appreciate that.

MP: So we’ll definitely be staying in touch and hopefully get some interesting comments on this interview as well.

NN: Take care of yourself and a very Happy New Year to you.

MP: Thanks very much. Happy New Year to you, too.

Dancing empowers girls to pursue mathematics: an interview with Kirin Sinha

Dear readers,

I recently had the great pleasure of speaking with Kirin Sinha, who just completed her Bachelor’s degree in Mathematics and Electrical Engineering and Computer Science at MIT. I found out about Kirin through an MIT News article and was intrigued by her initiative to help middle-school girls gain confidence in mathematics that uses not only traditional tutoring, but also dancing.

Kirin may be my youngest interviewee so far, but her passion for making a difference in the way mathematics is taught and perceived in society comes through very clearly. In addition to being a mathematician and a dancer, she is also an accomplished musician and music composer, and we had a great discussion of the close relationships between artistic and mathematical pursuits. Here is our interview.

Kirin hopes to bring her program, SHINE, to more girls around the world, and I hope you will join me in supporting her initiative by making a donation to her non-profit.

Transcript of my interview with Melodie Mouffe

Dear readers,

I’d like to wish all of you a happy New Year, and I hope it’s off to a great start! Today I’m putting up the transcript of another interview I did last year, the one with Melodie Mouffe. Once again, I would like to thank my assistant for preparing the initial transcript. Stay tuned for more transcripts, more interviews, and more exciting posts!

Transcript: Interview with Melodie Mouffe

MP: Hi Melodie! Well, thanks very much for agreeing to speak to me today. I’m really glad to get this opportunity to talk to you. And the first question I was hoping to ask you to start our interview is about your transition from academia into industry. And specifically what I would like to know is what your main motivation for it was; was it because of better working conditions or perhaps the chance to make a bigger impact or was there something else?

MM: Well actually, the main answer is two-fold. One of first reasons I wanted to go to industry was really to work with people, to interact more with people because as a mathematician researcher you generally work a lot kind of alone let’s say. One of the reasons I really enjoyed going into industry was to work with more of a team let’s say – that was the first reason. And the second one was simply the real application and then the impact as you say in your question. Actually to see that what you are doing is really applied and used by a person – that’s something I really like.

MP: Fantastic! So I guess the impact was a big part of it but also just the ability to interact, to work with a team. That’s great! So then let’s talk more about your work. You’re currently working at the energy company, multinational GDF Suez. So can you tell me what it is that you do on a day-to-day basis, just generally and also how challenging do you find the work at GDF Suez compared to your academic work?

MM: Well actually my everyday work involves a lot of mathematics because I’m currently part of a team that handles the mathematical models of the group, let’s say some of them, and I think one of the main challenges here is really the interaction with the users and so I think we have non-mathematicians who have needs to have models let’s say represent what they are really doing in their life in the energy world. And so I think one of the biggest challenges is to make our mathematical models and all the math things that are inside their tools look simple and represent for you what they want.

MP: That’s right. I see, so how do you go about doing that? How do you take something that is very complicated, a mathematical model, and how do you make it accessible to somebody who is not a mathematician, somebody who doesn’t necessarily know what’s inside it and wants to get the results from it? What are some approaches to that?

MM: Well I think the first thing is to listen to them and try to pick up the vocabulary they use and try to, as mathematicians in an industry we really have to understand the needs of the final users and we have to adapt ourselves to make it look simple, so really hear what they have to say and try to translate our equations into everyday words.

MP: I see. Yeah, so how do you, for instance, deal with someone who says OK, how do I know that this model is actually doing what I need it to do and it’s somebody who is not very familiar with mathematics so they might not understand if you go into the technical details? What would you say to somebody like that who is really skeptical, let’s say, or is that something that happens at all that people are just not able to trust the models?

MM: Yeah, it may happen but we’re doing a lot of testing fortunately—we have to! But also the users, let’s say the output of the models are really user-friendly. We hope they are and we’re working on that. The final user can really test whether the model really acts like it should. I mean if the final output of the model is what it’s supposed to be at least in some simple cases.

MP: Sure. OK, I understand. So how do you feel about the impact that your work is attaining? Do you feel that it’s a significant impact that you’re able to make with what you’re doing?

MM: Yeah, well actually the model I am currently working on I think helps real impact for some people using it. It has been recently introduced in some parts of the company and well we have a nice return from the users saying it’s nice. And we’re trying to introduce it in another part of the company currently and I look forward to hear the critiques – positive and constructive critiques from them, because we know it can have a real impact on the everyday life of the users.

MP: So I guess the feedback that you’re getting is probably really rewarding, just being able to know that people are actually using the models that you’re building. I think that well, at least for me this is always something that has been a source of anxiety so to speak, where I don’t actually know if anything that I produce or anything that I publish is actually going to be used by other people. Like it’s nice to get a paper, but then you don’t actually know for sure if anybody is going to really take it to the next level.

MM: I totally agree with your concerns and I think that is one of the main advantages of being in industry. Industry cannot waste money into projects that they will not pursue until the end so you’re sure what you’re working on will be used. That’s really rewarding.

MP: Absolutely, but do you also feel that there is, I mean one of the commonly stated concerns that academics have about working in industry is that you don’t get a lot of freedom, you don’t get a lot of choice in terms of the kind of problems that you’re working on, the kind of models that you’re building, the kind of questions you’re addressing? Is that accurate?

MM: Yeah, it’s totally accurate. Yeah, I think everybody has to find a tradeoff between freedom and being sure that what you were doing will be used because, of course when you have a lot of freedom, it’s fun, it’s even extraordinary. I love that, but somehow sometimes it’s also important to skip part of the freedom to go lead a project until the end, let’s say, and ensure that. But that’s true—that difference between academia and industry—that’s totally true.

MP: And do you mostly work on independent projects or are most of your projects collaborative projects where you get to work with other people?

MM: I mainly work in collaborative projects but well, in general it’s small and collaborative for now. Maybe in the future I will have the opportunity to work on more independent projects but that’s not currently the case.

MP: Not for the moment, huh?

MM: No.

MP: And how long have you been working at your current position?

MM: It’s just six months.

MP: Oh, it’s just six months so it’s very recent for you?

MM: Yeah.

MP: And how do you like the corporate culture so far? How do you feel about the culture of the company?

MM: Well for the moment I kind of enjoy that. Well I’m a part of a very very nice team and so that helps a lot.

MP: Absolutely, having a good team is probably the most important determinant of enjoyment.

MM: Yes and for the rest I really enjoy, I mean I have not really felt yet the system of being in a big company, you know this corporate culture that much.

MP: I see, for instance, the kind of things I was referring to, based on my own experiences in the corporate world. For instance, you know I found that there were a lot more meetings that I was wasting my time on and maybe out of an eight hour work day I would spend two to three hours in meetings and only five to six hours actually doing work.

MM: Yes, I can see that around me but I have the chance to be in a team where we really really do a lot of technical work so I see that for sure there are more meetings than in academia where there’s nearly no meetings actually. But it’s still reasonable I mean. And those meetings have good sides too. Yes, you have less time to work on technical topics but still when you’re in teamwork, it’s kind of important I think.

MP: Great. OK, well let’s go back in time a little bit and talk a little bit about the experiences you had with teaching, so in particular I am really curious what some of your favorite subjects to teach were and also why?

MM: Well I have not taught a lot but I really enjoy teaching. So to answer your question about topic – it was nonlinear optimization which was actually my field of research and yes, I really loved to teach that specific topic in particular because for me it’s the opportunity to really give the love of what you’re doing as a mathematician to young people and maybe hopefully to influence them and to give them the will or the wish to continue in mathematics themselves someday.

MP: I was just wondering what level of teaching they were; were these undergraduate students? Were they doing their Bachelor’s degree or Master’s degree? It’s a bit difficult to compare the systems but sorry for that.

MM: No, of course I am so used to the system here. It’s kind of like Master’s; it could be compared to first year of Master’s, I think.

MP: OK so roughly speaking, Master’s students.

MM: Yes, it was engineering students, but I think it was after the Baccalaureate.

MP: Have you ever had to teach any younger people like either at school or maybe undergraduate?

MM: During the Bachelor; yes. I had the opportunity to give a few lessons to students in their bachelor and in private to give lessons to really younger, like secondary school or high school actually, but it was more private lessons. And that’s a very different way of teaching of course. But still it’s very interesting.

MP: So you were like a private tutor for those students then?

MM: Yes.

MP: OK I see. That’s fantastic. I know you have some background in acting so I was curious – has that been helpful at all for teaching or perhaps has teaching been helpful for acting? What was the interaction between those two things for you?

MM: Actually, acting is very useful for teaching because it’s just acting is nice and it’s really helpful to feel comfortable talking in front of people let’s say. And maybe to find words a bit easily, to not feel shy the first time you’re in front of a class or something. That can help a lot I think.

MP: Sure, sure. So basically you get to use those skills. Would you say there is a need to improvise sometimes?

MM: Not sure.

MP: You’re not exactly sure, huh?

MM: We hope it will never happen but at least you cannot anticipate all the questions from the students for example. Yes of course you have to improvise sometimes and yes it can probably be also helpful even if I have not done improvisation.

MP: Well, I remember for me I had this experience when I had to teach my own class, in 2007 I think it was, and you know, it was interesting because it was not a topic that I knew all that well so I really wished sometimes that I had more experience with acting, especially improvisation, because I had to, a lot of the times, make things up as I went. So that’s interesting. Maybe you can tell me a little more about acting that you have done how much you have had an opportunity to perform in the past.

MM: Well actually I have always been an amateur, but my father took me to the first diction classes when I was eight so I, let’s say, entered the field of public speaking really young and I continued with declamation like poetry, reading and so on, and so I finally ended in some theatre classes and so I continued that for I don’t know like seven years or something, and I stopped just because I moved and I went to Toulouse so that’s the reason why I stopped. But I hope to continue someday.

MP: That’s when you started your doctoral work, is that right?

MM: Exactly, exactly. I could not find the time at that moment to continue.

MP: I see and I know that you also have an interest in the music; I guess you have done some music in the past. Can you tell me a little bit more about that?

MM: My family really likes music a lot so you cannot escape music in my family, like my brother [is a classical guitarist], as you know, and my name is Melodie. So I did some music theory lessons for five years and then I have learned to play drums and so I was not in a band but I enjoy playing just for myself.

MP: So you played drums as a soloist. Is that right?

MM: Yeah.

MP: And did you find any interesting parallels between mathematics and music? I know a lot of people are really curious about those connections and especially in music theory, which is very mathematical in some sense. Have you found that was a helpful connection there?

MM: Yeah I guess my interest in music might be related to my interest in mathematics. Even if I don’t really think a lot about it, to be honest. I appreciate like when I recognize some really like mathematical patterns in some music. I enjoy that.

MP: Absolutely I guess that’s the thing that a lot of people don’t necessarily appreciate about mathematics but do appreciate about music, right? There is a lot of patterns and figuring out what the patterns are in a way. So yeah, wells that’s fantastic. So then I wanted to also ask you little bit of a different question, which is that, you know, what have your experiences been of being a female mathematician? Of course we have a very heavily male dominated profession, unfortunately still today so have you ever felt that you were either treated in a different way by your colleagues or maybe faced any challenges that were specifically because, you know, you’re a woman?

MM: Actually I’ve never felt any bad sides of being a woman in the mathematicians’ world. Of course you see it’s a man’s world, OK. The problems are tackled as men would do and yes the human relations are really like more in a man’s world, really. It’s kind of colder maybe, I don’t know. But personally I have never experienced anything bad. It has always been more of an opportunity to be a woman in that man’s world because it is actually appreciated because we sometimes as women have different points of views let’s say and that is in general appreciated. Well that’s how I experienced it.

MP: So you would say it was actually more of an opportunity than a challenge for you?

MM: Yes, totally true, and both in academia and in industry actually.

MP: I see. Has anything been different between I guess the way that other people have seen you in academia versus in industry, being a woman? Is that something that’s sort of changed with your transition or has that mostly stayed the same?
MM: Not really. I have not seen any changes especially as I told you in general people appreciate to have women in the mathematical field. The women around me are also really appreciated as women in addition to being appreciated as mathematicians. I mean the atmosphere is different when it’s more mixed, let’s say. And it’s the same in academia as industry.

MP: Would you say that there’s like in terms of proportions, would you say there’s more female mathematicians in the academic environment that you have experienced or is it more, proportionally speaking female mathematicians in the industrial side that you’re in right now?

MM: In my experience it was more in academia but I don’t know really the reason of that actually. There were more women where I used to be in academia than where I am in industry but since I really don’t know if it’s a rule or a fact or if it’s just a coincidence.

MP: Sure, absolutely. And would you say there is anything that you would maybe want to see change in either of the two systems in order to make things more welcoming for female mathematicians that would perhaps be more encouraging for them to actually choose mathematics as a profession?

MM: Yeah maybe.

MP: If so, what can be changed?

MM: Actually, I think in the professional world it’s all right, it’s kind of pretty welcoming for women in mathematics. Things should change earlier like in school or something because when you’re in high school or even in the university sometimes, yeah as a woman in mathematics you hear some things like it’s for men, shouldn’t you do something else. But I think it’s really more earlier, not in the professional careers. There as a woman in general, I think it has already changed, you know?

MP: I see. So basically you would say we would need to start encouraging young women in perhaps school?

MM: Absolutely! If they like mathematics then to go on with that passion for mathematics. It’s worth it.

MP: And so speaking of this passion for mathematics that you just mentioned, how did it happen for you? How did you come realize that you really like mathematics, that you really enjoy doing it and that you really want to make a career out of it? What would your sources of inspiration be?

MM: Actually when I was really a kid my father taught me mathematics and he really loved mathematics and so I think he gave me his own passion for that and so it has always been something that I liked – mathematics. But I thought I could never do my job of it and so I was thinking of what I could do after and the day I was sixteen I learned that I could really learn mathematics in the university and maybe make a job of it and then it was obvious because it was like a dream to have the possibility of doing this for a living.

MP: Absolutely I think that’s a great privilege that we have actually to be doing something that we really enjoy and that we really like and at the same time be paid for it.

MM: Yeah yeah yeah, that’s kind of extraordinary, in my opinion. We are really lucky. Absolutely I guess I don’t appreciate that enough but that is certainly very true.

MP: And then tell me a little bit about any role models you might have had in terms of your passion for mathematics. Have there been any people other than your father who has also kind of inspired you or became one of the people you wanted to sort of, emulate?

MM: Yes, sure. Well I had a teacher during last grade of high school. He was very passionate himself in mathematics and the way he was telling us anything about mathematics like it was some kind of a game but also something really fun for himself and that encouraged me very much. And also he encouraged me to study mathematics afterwards if I wanted to and I’m really thankful for him. And after in the university I met one of the two professors that were my advisors for the thesis, Philippe Toint – he was really fun and just completely passionate about what he was saying. And I think that’s really the reason after I have loved to teach. It’s this passion I received from them; it’s so nice, so encouraging, you know. They never give up.

MP: Absolutely yeah, I think it’s really really important to have inspiring teachers and we really need more inspiring teachers to make sure we have people continuing to go into mathematics. And one of the things that I wanted to also ask you, the people I have interviewed so far, one was based in Canada and one was based in Japan and you’re in Belgium. So we kind of get a lot of geographic variety, which is great. So how do people in Europe usually react when they find out you’re a mathematician? Are there any stereotypes that people associate with mathematicians and you know how do people’s reactions usually go?

MM: Well the first reaction I generally have is oh, that’s great you’re a mathematician but I am sorry I don’t really like that. Or yes that’s great but that’s really too complicated for me so don’t really try to explain that but that’s OK. I mean they generally like the fact that I am a mathematician but it’s like a strange object like a strange thing they don’t really know and they kind of like or don’t like but they just don’t know what really can be done as a mathematician’s job in everyday life. And that’s one of the reasons you are doing your blog and I think it’s really important.

MP: Well thanks, I hope that you know we’ll start slowly not just focusing on doing really good math but also gradually start doing a better job of communicating the importance and the joy of what it is that we do to people who are not mathematicians or to people who might not even like math that much. So what would you think are some good ways of communicating to the general public or to the people who are not mathematicians the fact that we are doing something cool and interesting and useful?

MM: Well I think we first have to forget about the complexity of mathematics that we generally like and then as an applied mathematician, I found that talking about what it’s used for and the end use of mathematics is generally useful for explaining to people the importance of mathematics and for the joy I generally say it’s a game and you should never forget it’s a game to do mathematics. If you find it it’s a game, then you will enjoy it. I think we generally forget that part.

MP: That’s right. I really like that comparison. I think especially very early on there is this game-like aspect to doing mathematics that is really addictive in a way.

MM: Yeah yeah, exactly. I totally agree.

MP: And kind of like maybe like a Russian doll a little bit—you start out with something on the surface and then you open it up and there is something else inside. You know it keeps going and going. You can go really in depth with that. Yeah, that’s a really great analogy. I’m really glad that you brought that up. And speaking of the end uses of mathematics you mentioned so I know that you work on models that are used in two very different fields, one of which is aeronautics and another one is hydrology. So first if you don’t mind very quickly just give us a quick definition of what it is; what aeronautics is and what hydrology is because I realize I am not even sure what hydrology is exactly.

MM: OK so well for aeronautics I just worked on optimization for models of planes, the purpose was just to define a design of a plane in order to let’s say consume less fuel in the plane to make it more efficient to fly. Yeah, to make it more energy-efficient. That was for the aeronautics part and for the hydrology the goal was to try to predict the behavior of some main rivers. I worked on a model that wanted to evaluate the height of the Amazon River everywhere at every time. That was the main goal of that. Well of course it’s difficult as you know but that was really the goal.

MP: I see OK. And what was the application? For energy efficient planes, that seems very clear. For measuring the height of the Amazon was the idea just to sort of understand how it evolved over time?

MM: No actually it was first to prevent floods, like when the water comes out of the river bed and so on and also to, you know, you have sometimes electric plants based on hydrology, you know, and so they need to know the river behavior very well to adapt the way the plants work actually.

MP: Sure. Those were the two aspects. I see. Fantastic. So what would you say would be sort of the cause and what was the consequence? Was it that you were interested in these applications and then you wanted to develop the tools or were you more interested in the tools or maybe you already had some idea of the tools and those were the applications for them?

MM: For the aeronautics actually I worked on optimization during my PhD and the aeronautic industry was actually interested in the kind of algorithms my team has developed and even if they were in the basic steps of doing optimization it was really first the mathematics and then the application in that case. And for the hydrology I had the opportunity to meet the people working in that field and they generally don’t work with mathematicians really. We just thought it could be a good opportunity to work together and actually my boss on that project was an engineer in hydrology and she thought that maybe having a mathematician to help in that field would be interesting, well would give something different. And then it was true because we thought about developing optimization part for the model and so on, we had ideas coming from that collaboration that were really interesting.

MP: OK so that’s excellent. That sounds fantastic! So I guess this is one of those situations where you can have either the mathematics first and then the application or the application first and then the mathematics and you have done both so that’s really great. I think if there is too much of, I am not necessarily advocating one or the other but I do know that a lot of the times what happens is you know somebody develops a really nice theoretical tool or approach or algorithm or whatever and then spends a lot of time just trying to find something that it would be helpful for or useful for. And I think that can be very frustrating for some people.

MM: I think that’s true. That’s the main problem of academia.

MP: Right I guess it is definitely a significant problem. Well great so then since we’re coming back to this question that we started from, the choice between academia and industry, I was hoping to get your thoughts about how one should be making that choice if that’s the choice that needs to be made and maybe more specifically let’s imagine that we have a young mathematician who maybe, you know, just finished their Master’s or their PhD and is deciding whether to go into academic research or industrial work so what would you suggest? What kind of advice would you give to somebody like that?

MM: Well I think it’s a difficult choice because the goal and as we said the freedom is kind of very different so I think it first depends on the person and what the person really wants to do for a living but if there is really a consideration of both sides well I would stress to at least try both because for example if you have a PhD you have an idea of what academic research could be and it might be interesting to at least do a part of a year in industry to test to learn how things go in practice and also to have more of an idea of the final customers, what they want , what they need, and then to direct what you do in research if you end up in research more with that idea of that final customer. So it would be maybe easier to find a final customer even if you’re in the academic world. But really try both if you can and if you have the opportunity.

MP: Yeah, I think that’s really great advice and I think it’s really hard to know because everybody likes different things and I think a lot of academically-minded people feel that, you know, industry is very different and that it might not necessarily be just based on their impressions or experiences of other people, whereas trying it out for themselves might actually give them a better idea of what it’s really like. Fantastic. Well I am really glad that we got a chance to talk about all this. I think that there were really interesting topics and I certainly learned a lot from talking to you so I am really grateful for that. Thanks and I hope that things continue to go well for you at your new position.

MM: Thank you and I hope your blog will be really read by many people, mathematicians as well as non-mathematicians. I think it’s a very useful tool to give that idea that mathematics is really cool.

MP: Absolutely, well thanks so much, once again.

MM: You’re welcome.

MP: I am going to put this up on the blog very soon.

MM: OK great. Well, thanks very much and have a great evening.

Black holes, cryptography, and quantum computers – an interview with Patrick Hayden

Dear readers,

It’s my pleasure to present to you my recent conversation with Patrick Hayden. Patrick was my Quantum Information professor at McGill University. His class was so fascinating that I changed my plans of taking a summer off before starting graduate school and instead did a summer project with him.

The field of quantum information remained one of my primary interests through the first year of graduate school, and I have since then been a passive observer of its development. Thus, it was a really great opportunity for me to learn about its current challenges. I hope you enjoy our conversation, recorded here.

For more information about Patrick’s work please visit his homepage.

Mathematics helps address global HIV: an interview with Brooke Nichols

Dear readers,

I’ve been traveling in Europe for the past few weeks and hence haven’t had the chance to put up any new posts. However, towards the end of my trip I had the pleasure of interviewing a friend and colleague, Brooke Nichols, who like me works on modeling infectious diseases. Brooke’s specific area of expertise is HIV/AIDS in Southern Africa. She is currently a graduate student at Erasmus University located in Rotterdam, Netherlands.

In addition to her graduate studies in mathematical modeling, Brooke also has many other interests, including an awesome blog on vegetarian cooking. Our conversation took place at her house and was divided into two parts. The first part is here, the second one here.

Hope you enjoyed our interview, and I look forward to hearing any comments you have!

Mathematics: Exposing Lies, Solving Crimes

Dear readers,


What do you think about when you look at a picture like this one? Chances are you try to find the ways in which the child resembles its parents. Sometimes it resembles one parent much more than the other, and this can also change as it grows older. Most often, however, the child will have traits that are a complicated mixture of its parents’ traits (for instance, if you look at the color of this particular baby’s eyes, you will notice that it differs from the color of both of its parents’ eyes). Not surprisingly, the way this mixture works can be explained by mathematics.

Many traits, such as eye color, nose shape, and height, depend on our genetic code, which, as I discussed in my interview with Mathieu Blanchette, can simply be thought of as a very long string of As, Cs, Gs and Ts. But when a child is conceived, it will get a part of its genetic code from the mother and a part from the father. The choice of which part comes from which parent is largely random, although some contiguous regions, called linkage disequilibrium blocks, will usually come entirely from one parent. The majority of traits, however, are influenced by multiple parts of multiple genes, and this is where the complexity comes from.

For instance, if height were entirely determined by a single gene (and nutritional and other environmental factors did not play a role), the child’s height would either be equal to its mother’s or its father’s height. However, if 100 different genes were to influence a child’s height, and each one had an equal probability of coming from the mother and from the father, and contributed equally to the child’s height, what would the height distribution look like? The answer is the same as the answer to this question: if you flip a fair coin 100 times, what is the distribution of the number of heads you will get? This is the binomial distribution, which looks like this:


Notice how closely the histogram matches the red line – a bell curve, or a normal distribution. This is a consequence of the central limit theorem, an important result in mathematics, which says that if you draw a lot of samples from the same probability distribution, the average is going to look like a normal distribution. By the way, height is actually influenced by about 200 genes, but new ones are still being discovered in large GWAS (genome-wide association studies), which I briefly discussed in an earlier post.

This example suggests that whenever a large number of random events (such as which gene comes from which parent) are involved, mathematics can provide useful insights and precise statements about the chances of a particular outcome observed in real life. This gets us to how mathematics can expose lies, or at least infidelity.

Suppose that the father in the picture has doubts that the child is really his. There is a simple procedure that can allow him to test whether his doubts are justified. He can swab the child’s cheek, as well as his own, and send the two swabs to an agency. For a small fee, the agency will then extract the genetic code of each and compare a small number of genetic loci (spots in the genome). If the child and the father are indeed genetically related, then we would expect them to have about half of these genetic loci. On the other hand, if they are not, then we would expect the match to be very low, in fact very close to 0.

There is one exception to this, however – if the child is not his, but his identical twin’s, there is essentially no way to determine that. (By the way, I’m not endorsing infidelity with one’s partner’s close relatives by any means, but mathematically, the closer the relative the less likely the resulting child can be distinguished from your partner’s; however, even the child of a partner’s non-identical twin would be easily distinguishable provided that enough genetic loci are tested).

However, it is not only human genetics that provides fodder for mathematicians. In a famous case from the mid-nineties, a doctor was convicted of infecting his former lover with HIV. The conviction was done on the basis of the virus’s genetic code. The human immunodeficiency virus (HIV) mutates fairly quickly, which results in different people being infected with different strains of it. The particular strain of HIV found in the doctor’s lover, however, matched very closely the strain found in a sample taken from one of the doctors’ patients.

To rule out a simple coincidence, the strains of a number of other HIV-infected people living in the state were collected and compared to it as well. No other strain matched it as closely. With just a little bit more mathematics than I described here, it was possible to estimate the probability of the original match occurring at random, and since it was incredibly small the doctor was convicted of attempted murder and is now serving a 50-year prison term.

Of course, the potential uses of mathematics in solving crimes are far from limited to genetics. A mathematical observation known as Benford’s law is frequently used to detect fraud (both fiscal and electoral) – but that will be the subject of a future post, so stay tuned!

Picture credit: www.namingforsuccess.com and http://zoonek2.free.fr/UNIX/48_R/07.html

Transcript of my Pi Day interview with Mathieu Blanchette

Dear readers,

Some of you have asked me to post transcripts of my interviews so that you could go through them by reading rather than listening to them. Today, I’m putting up my first transcript, of the interview I did with Mathieu Blanchette. I would like to thank my assistant for preparing the initial transcript. I will be posting the transcripts of the other interviews I did over the next few weeks, and I also got a couple of new exciting interviewees lined up, so stay tuned!

Transcript: Interview with Mathieu Blanchette

MP: Hi Mathieu! Thanks so much for finding the time to speak with me today.

MB: Hi Leonid! It’s a great pleasure to join you on this.

MP: Fantastic. I’m really glad we’re getting a chance to discuss things and I got this start question that I would want to ask you about your responsibilities as a professor of Computer Science at McGill University. Of course there are different aspects to what you do; there is teaching and there is research and there is administrative work so I’m wondering which of those you feel is the most important aspects of your work?

MB: Yeah, it’s a good question. It’s always a balance between the three and they are all interrelated as well. I would say that for me personally the aspect that I think has the most impact is the supervision of students, whether they are undergraduate students working on projects or graduate students, so that’s kind of at the intersection between teaching and research -because it’s the supervision of research projects. I feel that this is how in the long term I have the most impact because training a person to become an independent researcher means that once they are trained and then they get to do research that I’m doing, so it’s really kind of multiplicating the effect of our work. So the more qualified students I train the more research gets done, and so it’s not just the research that I’m doing with my students now but the research that they’ll be able to do in the future. That, I think, is the main impact and that’s what excites me most about the work. That is not to say that teaching like classroom teaching is not important but I think the most impact is through these closer relationships with students on specific research projects.

MP: Fantastic, so you mentioned you supervised undergraduate students, Masters students, I guess PhD students, probably post-docs as well. Out of these different groups, which would you say you enjoy working with the most?

MB: Well, it’s a good question. I must say that I think what I enjoy the most is to work with people who are very excited and dedicated to what they are doing, and often the group of students with whom I find the most of that is undergraduate students.  So I think at McGill and I think at many universities undergraduate students have the opportunity to get involved in research projects, and in particular during the summer. And I find that although these students might not have all the knowledge that more senior students might have, they have the excitement. The first time they do research projects they are really involved in it and they are really excited about it and they invest themselves completely into it and they’re bright students for the vast majority. I think in the area like where I’m working – bioinformatics – it is not the case that students need to have a very very deep knowledge of mathematics or computer science to be able to make an interesting contribution, so students can really become researchers and have an impact early on in their career, and this is where I find the most satisfaction. Often these students will go on to a Masters or a PhD and they’ll do great things and it will continue to be fun to supervise them, but the most kick I get is out of supervision of undergrads.

MP: Fantastic. Well I was just thinking back to my own experiences as an undergraduate researcher under your supervision –actually that was also my first time doing any kind of research.

MB: That’s right, I think you were among the first undergraduates or any students I supervised when I came to McGill if I remember correctly, and you really are among the people who got this trend started, but it has continued after you moved on and it continues to be the the newer, satisfying part of my work.

MP: Fantastic. Yeah and I guess this kind of brings up another question in my mind. So of course you know in the area of bioinformatics and computational biology it’s not so knowledge based and you don’t need to have necessarily a ton of background, I guess more important is the excitement and interest you have and the willingness to work hard to make a contribution. So thinking then of the more advanced students, let’s say PhDs and especially post-docs, do you feel that sometimes they get as, and I’m also thinking of myself, as a current post-doc, do you think that sometimes people at more advanced levels tend to get sort of set in their ways of doing things and tend to you know stick with things that have worked in the past rather than taking risks and really sort of trying out new things, new ideas, and so how do you feel about that?

MB: There is certainly a risk of that and it’s more comfortable to keep doing what you’re good at when you’ve become good at it whereas these younger undergraduate students are not formed yet. They don’t know what they’re good at and so they’re perhaps more open to trying very weird new ideas. On the other hand, I think that in a field like computational biology where first the technologies generating the data that are being analyzed, these technologies move very quickly, and so the problems change very quickly as well. What was an interesting problem five years ago may not be not so much of an interesting problem anymore, and so we really have to keep on our toes to be able to react, and that means using or taking new approaches to problems. And not just the technological advances, but the kind of questions that people are asking about biological systems are evolving very quickly as well, and so I can give you an example if you want.

MP: Sure, that would be great.

MB: During my career, I’ve been thinking of DNA sequences as a computer scientist would as a chain of characters, As, Cs, Gs and Ts that fit very nicely on any computer file and then can be analyzed in all kinds of ways.

MP: Sure.

MB: But more recently people, biologists have known all along that in fact a DNA sequence is not a chain of characters. It’s a molecule. And that molecule is basically a long string of smaller molecules that are the As, Cs, Gs and Ts and that molecule has a 3D shape and it’s folded inside the nucleus of cells, and that shape really has a major impact on how the information that’s inside that sequence, how the cell interprets that information. And so what we used to think of as a very linear set of As, Cs, Gs and Ts now becomes a very geometric object in 3D and the geometry matters a lot, and so we have to adapt to this. I was not used to thinking in terms of geometry but now I have to and so that’s one example where really the paradigm shift forces you to adapt your types of questions and the approaches you have taken.

MP: Absolutely. Yeah that’s a fantastic example. I think that as we know more of the technology progresses we are kind of forced to think in new ways about even such fundamental things as DNA molecules for instance.

MB: Right.

MP: Right. That’s a really good example. So I also have a question about sort of the way that you manage the projects and the collaborations that you’re involved with because you’re involved in a lot of projects and a lot of collaborations. So I guess specifically I am interested in, you know, is it ever the case that you feel there is too much going on, and what are your criteria for you know making decisions and making choices as far as the projects that you keep working on versus the projects that you leave behind perhaps or terminate.

MB: Well this is a very tricky question and I don’t think I have a very good approach to this. I am overwhelmed with all the things that are going on and I’m getting involved in, so I have the opportunity of getting involved in all kinds of projects that are all interesting but that all or many of them require very different approaches, require being familiar with areas of research that are completely different, and that’s really hard because each of these areas is moving very quickly. There are hundreds of papers published every month in each of these areas. And it’s impossible for one person to keep track with all these things. So on the one hand I rely very much on my students who are working in each of these areas to keep up with the literature and tell me about what they read, so that helps keeping me up to date. On the other hand I have to say no to some very interesting projects or people coming to me with ideas. At some point it would be doing them a disservice, to them or to my students, to commit to too many things because then I would not be able to well-attend any one of them. But it’s very hard, it’s so hard to say no to interesting projects and I don’t think I’ve become good enough at doing that yet. I am involved in more things than I can handle. There are some things that are, that get delayed a little bit, but with a good group of students and post docs and people like this we get through. And I think it’s important to push yourself in terms of getting involved in projects that might not be directly in line with your main line of research in your lab so that you get exposed to these ideas, the example I was giving you earlier about the 3D conformation of DNA itself was not something I would have thought about but when my collaborator Josée Dostie came to me with these questions I felt that this was something important to get involved in and that is taking time and it’s a lot of efforts but that’s how you really move things forward; otherwise you keep making small incremental steps to what you’ve already done.

MP: That’s right.

MB: I don’t have a very clear strategy here. I go by the guts. I guess it’s especially because it’s an area that is really growing quite quickly and there is a lot of new data, but also a lot of new subfields that are opening up on a regular basis as the technology progresses.

MP: That’s right.

MB: So I think you have to keep an eye open on your main line of research, but you have to be open to these kinds of things that are not exactly in line with this but that can inform or that can help towards that main direction that you have.

MP: And how would you describe the main direction that you’re pursuing and has that changed over the years?

MB: So the main direction that I am pursuing is to understand what is the function of different portions of the human genome. So the human genome it is a sequence of DNA of about three billion As, Cs, Gs and Ts. We kind of know the function of maybe one percent of this, which is the genes, but we don’t really know very well, we don’t have very much information about the pieces of sequences that are there to activate or repress genes when they need to be activated or repressed. Those are called regulatory regions. And much of the work that we’re doing is to develop computational approaches to better understand where these regions are located and how they work. And you might ask or people might ask how can computer scientists say anything about what’s going on inside a cell? Well, one approach that we’re taking is to study the evolution of DNA sequences, so we know today the DNA sequence of a human, but we also know the DNA sequence of several other species like a mouse or a dog or a cat. And by comparing these sequences we can learn pretty accurately what is the function, or we can predict what is the function of different portions of the genome and that requires the development of pretty sophisticated mathematical and computational approaches and that’s what we are after.

MP: OK I guess then following up on that I know you mentioned that one percent of the genome is genes, how much would you estimate to comprise of the regulatory region? All the rest of it, or is it also a small fraction?

MB: Well, there’s still debate about that. There’s pretty clear evidence that there’s at least two or three times more DNA that is there for the regulation than there are genes. So if there’s one percent genes then there would be two or three percent of the DNA that might be regulatory. And then if that’s the case then the next question is well what about this ninety five/ninety six percent of the DNA that would not be genes and would not be regulatory regions, well why is that? And it might be there because it fulfills an important role that we don’t really know already and as research progresses we discover a role for more and more of these regions. And it’s also very likely that much of it is there not because it contributes anything to the function of the human cell but for other reasons. Because there’s all kinds of mechanisms that add basically random pieces of DNA to the genome; as long as they don’t hurt too much then they will just stay adhered to the genome and it looks like a large portion of your genome or anybody’s genome is made of this DNA that probably isn’t doing very much or anything at all to help. But it’s really, really hard to just look at the piece of DNA and say, oh yes that’s clearly the regulatory region whereas this one is just clearly not doing anything; to a human or to a computer it’s all just As, Cs, Gs and Ts, and so that’s the challenge – to recognize what is the function of each of these portions and which portions might not have any function.

MP: Sure. And if we were to, you know, go back to what you were saying earlier about the conformation and the importance of the three-dimensional structure, do you feel that that’s like understanding or if let’s say we do a thought experiment ok where we know exactly how you know the DNA sequence folds in a particular situation. Would that sort of give us, which of it are actually sort of doing stuff and which are not?

MB: Yes, it would, definitely. It would be extremely informative because right now there’s, if we just look at the DNA sequence as a chain of characters, there’s a lot of regions that look like they have all these signatures of a region that should be functional but when people test them in real settings they don’t do anything. And so what is one possible explanation for this is that in the three-dimensional confirmation of DNA inside the nucleus somehow these regions are prevented from doing the job that they could do and so they are kind of blocked inside or something like that.

MP: That’s right. That’s exactly right.

MB: And so knowing the three-dimensional structure it would be very important. That structure, by the way, is not fixed. It changes with time and with different, I mean your skin cells and your brain cells have essentially the same DNA but that DNA is not arranged in the same way in the nucleus and that’s in large part why they behave differently, and so this is really I think a very exciting area of biology that raises very challenging mathematical and computational questions. So I think it’s really a direction that has a lot of future, a bright future.

MP: Fantastic. Well I think that was a very interesting sort of thought experiment to do and also a very interesting set of question to explore. I definitely am starting to understand better now just from talking about this with you right now. But I was also wondering about this last thing that you mentioned when you talked about the mathematical models and the computational problems, so would you say, you know, how would you sort of describe the balance between those two, so is it, you know, more of the case that we need to build good mathematical models, or is it more important that we be able to sort of compute something even if it’s not quite necessarily the best description or the perfect description of the system that we work with, but we just need to get a computational answer, so how would you describe that tension between those two things?

MB: Well, there’s definitely a big tension between the two. I think one of the main challenges in my work is to translate biological questions into a more formal mathematical or computational question. And much of the success or the failure of a project lies in this translation of a biological question into a mathematical one. Now, there’s the tradeoff between the sophistication of the mathematical model versus the computational side; it happens every day. And it happens at several levels. One is that it’s typically easier. So first, I am dealing with large data sets of DNA sequences or three-dimensional conformations, and so we cannot think separately about the mathematical aspects and the computational aspects. If we want to go somewhere both of these things have to fit together. And that means; sometimes that means simplifying the mathematical aspects so that we can do some computation on it and get some answers on the large data sets that we’re talking about. And so typically the way I like to approach a problem is that we’ll try to translate the biological question into a mathematical question and come up with a mathematical model that we think is the most appropriate, irrespective of computational questions. Then try to develop the computational aspects that would allow us to study that model, and most of the time it’s not possible because there’s just, it’s too complicated and/or the data set is too large.

MP: Sure.

MB: But then, you can make principled choices about what aspects of your sophisticated mathematical model do you want to give up on or what kind of approximations you want to do so that you know what you’re giving up on.

MP: And I think there’s a lot of pressure in our field to get results out quickly.

MB: That’s true, absolutely true. When there’s a big study on autism that identifies certain genes that might be involved in something, I’m just taking this as a random example.

MP: Sure.

MB: There’s lots of people involved, there’s millions of dollars that have been invested, and there might be competing groups who might be getting their results out before ours, so that there’s a pressure to do relatively quick analysis so we can get a paper out quickly, so the leaders of these projects might not want a mathematician or a computational biologist to take two years to come up with a solution which is what it might take if we wanted a really satisfying, mathematically solid solution, so there’s this pressure that is happening all the time.

MP: Sure, yeah.

MB: And I think it’s important to resist that pressure to some extent and to say: well, I need to be able to come up with a reasonably good mathematical model and the computational aspects that go with it, maybe not perfect but that’s a fight that’s going on every day in my work, or not a fight, but a tension that’s quite difficult to resolve.

MP: Absolutely, and do you feel that the increase in computing power tends to alleviate that tension, or is it actually the case that, you know, with the increase of computing power we also get an increase in the amount of data that’s coming in and so the problems also become harder, perhaps they become harder faster than our resources actually increase?

MB: Right. I think having a lot of computing power is good, and sometimes it’s good enough, meaning you don’t have to be too clever about how you solve a particular problem because you can just throw a lot of computers at it and you’ll get your results. And that’s fine, and that’s useful to be able to move on to more interesting questions, so if you don’t have to spend months optimizing a particular program so that it runs close enough, that’s a good thing.

MP: Right.

MB: I think though that what you were saying towards the end of your question, it reflects the reality that if you think in terms of DNA sequencing power, like a machine that I could have on my desk can generate a billion pieces of DNA, and if you look ten years back the cost of having done that would have been probably ten million dollars, whereas now it’s a thousand dollars.

MP: Right, yeah.

MB: And so this aspect of computational biology has changed very quickly. The amount of data that can be generated very quickly now is probably a million fold more than it was ten years or ten thousand or a hundred thousand fold more than it was ten years ago, and the computing power has not scaled to that extent. So data generation increases a lot faster than computing power and that’s one big concern, and the other one is the sophistication of the questions that we want to ask, which require more and more advanced algorithms and mathematical approaches, which means more need for computation. And so we’re not about, so the computing power is not about to get rid of the need for sophisticated math and computer sciences.

MP: Right, OK. Fantastic. I think that really describes the tension quite well, and it’s definitely something that I’ve also experienced a few times when, you know, things really do become a little bit stressful because there’s a pressure to, you know, analyze things quickly, but at the same time you know analyzing things well sometimes requires a lot more time than we actually have, and so definitely, you know, some of that tension is present. So I wanted to ask you about another aspect of your work, which is the teaching. So you got the very prestigious Leo Yaffe teaching award in 2008, and you were awarded that by the Faculty of Science at McGill. And so I guess my question there is this: what are some of your secrets in the way you approach teaching, and, you know, how did you do that and how did you get that award?

MB: Right, well there’s no secret, I think. Teaching is something I love doing, and I think that helps doing a good job at it for sure. To me, the most important part about teaching is not really conveying advanced concepts in computer science or mathematics, but it’s conveying the excitement for, or the interest for why these concepts are useful. So once somebody understands, somebody gets excited about a particular question then they’ll want to know how to solve that question and they’ll be willing to listen to you explaining some more advanced computational or mathematical concepts, and so on, whereas if I just go in front of a class and I say, well this is what a binary search tree is and here are the properties, it’s not so exciting. Because why do I care? And so I try, and it’s not always easy, but I try to spend as much time explaining or motivating why a concept is needed as explaining itself. I think, especially now, with all the information being available on the internet about all these things, what students need the most is motivation and more than somebody who will just read the textbook in front of them, basically. And so this is what I’m trying to do and it’s not always easy. There are some basic concepts in computer science and math that are hard to motivate, especially in the context of the knowledge that students have at that point, but this is what I’m trying to do.

MP: Yeah, you know, I can definitely tell from the fact that, you know, the first computer science class that I took that you taught, you definitely succeeded in making it really interesting and exciting, and I was actually not completely sold at the time on computer science as an idea because I was actually still playing with the idea of doing math and physics, and then shortly after that I of course decided to switch to mathematics and computer science. Not sure if I mentioned that to you before, but that was, sort of, definitely one of the motivating factors, because I realized how interesting that could be.

MB: I am glad; I hope you don’t regret it.

MP: No, it was definitely the right decision for me, although I still think that physics is really fascinating.

MB: Oh yeah, the most fascinating thing is the intersection of all these areas.

MP: Perhaps, yeah. So I guess another question I wanted to ask you is about language, and this is perhaps somewhat controversial, although perhaps not really so. It’s always been an interest of mine to sort of explore this idea of, you know, how can we have a community in the sciences and the mathematical sciences, especially in the life sciences that is inclusive of native speakers of different languages, and in particular, for yourself as a native speaker of French, I was wondering how easy is it for you to, you know, have to basically do most of your research, you know, writing and publishing in English, and what are your thoughts on, you know, well, first of all, is there a need to make things more inclusive, and if so, how would you start bringing that about, or how could we start to think about making that happen.

MB: Yeah, that’s a hard question. It’s not a question I would ask myself very often because most of my career, although I am a native French speaker as you’re saying, all my work has been done in English and then most of my studies have been done, well most of my graduate studies have been done in English, and at this point, actually, it’s easier for me, actually, to communicate science in English than in French but, that being said, I think it would be a very useful to be as inclusive as possible in terms of languages, and of course the tension is between accessibility of information, say if I write something in French, only people who can read French can understand what I’m writing, and that might just be 10% of the scientific community. Nonetheless, the ability to write in English is probably a challenge for many people in countries outside of Canada and the US and that probably is slowing down the advancement of research. So I don’t know if there is a way around this. I think, and my hope is, that automated translation tools are getting better and better. They are far from perfect, but they are getting better, and you can hope that they’ll get pretty good, pretty soon, and at that point it might become possible to publish something in French and have it translated automatically to something that will be actually readable and understandable by somebody in another language.

MP: I guess another sort of relevant fact to the discussion that I just wanted to bring up, and I am not exactly sure on the statistics for this anymore, but it’s actually the case that in the last few decades, the relative proportion of all research in science that has been communicated in English versus other languages has increased quite dramatically, because even as late as let’s say the middle of the 20th century, there was a wide variety of French and Russian of course, Spanish, and German and perhaps even Chinese and Japanese research journals that were mostly published in those languages. And all that has very quickly sort of become absorbed into English language journals. I guess one of the things I was thinking about was that’s sort of a necessary consequence of everything becoming more global.

MB: Yes, I think, well, I don’t really see a way around it. As unpleasant as it is, the accessibility of information now has become so easy and so important. If it took me two months to order a journal written in Japanese and have it translated so that I can understand what it is talking about, things would go a lot slower. And honestly, I would probably not do it. I would be too lazy or in too much in a hurry, and so, that paper would not be read by me.

MP: Sure, that’s fair. Yeah, well there is definitely hope and I know there is a lot of work being done on automated translation tools as you mentioned, so perhaps one day we will get to a point where we can actually translate things back in a high quality in all these different languages.

MB: And eventually that might even be better than somebody who is not a great English writer try to write their paper in English. It might be better to write it in their native language and then have a really good translation, so that might get there.

MP: And then I have another couple of questions that are related to human genetics and human genomics, which you’re an expert on. So, the first question that I wanted to ask around that is, what do you feel is the payoff like with work in regard to human genetics and human genomics, and, you know, how sort of realistic are the expectations that a lot of people are currently placing on this line of work?

MB: Right. So, I think the impact is several fold. There’s a lot of work that’s being done on identifying genes or mutations that would be associated to particular diseases, so I could have my genome sequenced now for a few thousand dollars, and I could know potentially that I have certain mutations in certain genes that maybe at this point would not really cause me any trouble, but might mean that I would be more subjected to heart disease later on, which might mean that, but if I exercise well or I eat well, then I can reduce my risk also. So this aspect of personal genomics where we can measure the real risks of having certain diseases, I think we’re not quite there yet, we’re getting there. And I think that’s going to be an important aspect. The choice of treatment for certain diseases should also depend on the genetic makeup of the person who is being treated. People realize more and more that certain people will have very severe side effects with a particular drug, whereas the drug works perfectly well for others, and if we could tell ahead of time and test the person who would be a candidate for that drug, and tell whether that person will have the bad side effects or not, that would be a great way to allow better treatments. So those are two of the things that I think in the long run my work, and the work of many researchers in the field could contribute to it, and it’s just two examples, but they are interesting.

MP: What would you say the timelines are for this, because certainly, when the human genome project was first completed, there was very widespread optimism about our ability to solve all diseases within the next decade or two, and now it’s been over a decade and we still haven’t solved any of them, well maybe that is not completely fair, but we have only solved a handful of fairly straightforward diseases so far.

MB: That’s very true. I think that the real need to get there is on the mathematical and computational scientists. So, one of the big challenges toward taking the understanding of genomics and bringing it to have real biomedical implications was the ability to read people’s DNA, just to tell what mutation they might have. Now that is done. You can sequence your DNA very easily and cheaply, but the challenge that we’re facing is interpreting this set of mutations that everybody bears, to tell which ones might be associated with what kind of consequences, and that’s a statistical/mathematical question.  And this is where things have moved very quickly in the past few years, and I don’t think it’s going to be solved in the next three or four years, but I think that in the next ten or fifteen years you will be able to get a pretty decent picture of the risks that you might be exposed to in terms of your genetic makeup.

MP: OK well that sounds very promising so I guess we’ll hopefully re-visit this conversation in ten years or so.

MB: Right; I may be in trouble!

MP: But I would certainly not hold you to this. Well another sort of speculative question, even more speculative than the previous one, that I wanted to ask you about, is this idea of being able to recreate ancestral species, like relatives of humans, or perhaps ancestors to humans, from their DNA sequence. In particular, as I am sure you know, there was a proposal from George Church who has basically managed to extract DNA sequence from Neanderthal fossil and is looking for a person who is willing to give birth to a Neanderthal baby, and so what are your thoughts about that, given that genomic reconstruction, ancestral genomic reconstruction, is a particular expertise of yours.

MB: Right, so I think having the ability to look at DNA sequences from Neanderthals, or from mammoths, or the ability like we are working on to infer what the ancestral DNA sequences were, I think this is very interesting and very informative about questions like, what is the function of the different regions of our own genome. And so, the question of using this information to learn more about how our genome works, I think that is extremely valuable. Now I don’t really see the point of trying to grow a living Neanderthal human or a living mammoth. I would not support this idea, mostly first for ethical reasons, but also for more very practical questions like why, what good could that do?

MP: I was going to say that the argument could be that potentially, we might be able to, not just understand their biology but also something about the way that they actually lived and the way that they actually did things, and we could perhaps conduct some experimental studies that would help us learn even more about, not just the biological functions, but also, you know, more physiological things and so on.

MB: Yeah I understand that. I certainly think the same ethical standards that are being applied to humans today should at least be applied to these new revived species, that I don’t know the gains are worth the risk or the obstacle.

MP: OK, so I think I definitely agree with that, in the sense that the ethics are slightly murky there as soon as you start to get into these ancient species, but I think we do need to hold ourselves to at least the same level of ethical standards as we do when we do research on our own species.  So then, with that being said, I guess I would just like to conclude with the following question, which is: suppose that you are talking to somebody, a young person who is interested in a career in the mathematical sciences, and potentially having some interest in biological applications, what kind of advice would you give to that person, and in particular, would they do best to focus on learning mathematics, or would they do best to focus on learning biology, or a bit of both. What advice would you give to somebody like that?

MB: Right, well, I think that although the area of computational biology or mathematical biology has both terms in it, biology and math, it’s important that people are really good at one of the two aspects and good enough in the other.

MP: I see.

MB: I would say becoming excellent in math and then learning the biology is certainly a good way to go, or becoming excellent in biology and learning enough math is alright too. Being too thin on both sides I think is a problem. I think, particularly if you want to become a cutting-edge researcher, I think you need to be excellent at one of the two.

MP: I see, so basically maybe just focus on the one that they are most interested in as their sort of main area of expertise, and then just develop enough of an understanding of the other one, would that be a fair assessment?

MB: That would be my advice. It’s tempting to want to learn about everything and physics could be on your list too, right, and statistics and chemistry, because all these things are important, and it’s important to have at least a minimal understanding of these things, but I think if you want to really push science, you have to be aware of these things and be excellent at one of them.

MP: OK well on that note I would like to thank you again for taking the time to speak with me and I think this has been a fantastic conversation. I have certainly learned a lot from it and gotten a lot of interesting ideas from discussing these with you. I am looking forward to checking back hopefully, not in ten years but definitely will be checking back to see where things are.

MB: Well it was a great pleasure to talk to you and it will be a great pleasure to talk again in ten years or tomorrow if you want.

MP: Absolutely, well thank you so much.

MB: It’s a great pleasure.