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,

parents-baby-reading

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:

BinomialNormal

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.

Mathematics: attitudes matter!

Dear readers,

It’s been a long time since my last post, over 3 months in fact! I’ve been dealing with a lot of personal challenges during that time, but I’m happy to report that they are now behind me and I’m getting back on my weekly posting schedule again!

Today, I’d like to share with you part of an excellent piece I found in a newsletter from Annie Murphy Paul, who has a blog about education that I recently subscribed to (and highly recommend), www.anniemurphypaul.com. It reviews the latest research revealing links between parents’ and teachers’ attitudes towards mathematics and the students’ success in learning them. I especially liked this piece because it sheds some new light on possible reasons for the underrepresentation of women in mathematical professions.

Elizabeth Gunderson, a researcher at the University of Chicago, and her colleagues recently published an article in the journal Sex Roles that examined the “adult-to-child transmission” of attitudes about learning—in particular, how mothers’ unease with mathematics may be passed down to their daughters. Parents’ “own personal feelings about math are likely to influence the messages they convey about math to their children,” Gunderson notes—and kids will readily recognize if these feelings are negative. Becoming aware of our anxiety is the first step toward stopping such transmission in its tracks.

Previous studies have looked at how parents’ stereotypes (“boys are better at math, and girls are better at reading”) and expectations (for example, holding sons’ academic performance to a higher standard than daughters’) affect their children’s orientation toward learning. Gunderson takes a different tack, suggesting that parents may influence their offspring’s attitudes in two more subtle ways: through their own anxiety, and through their own belief that abilities are fixed and can’t be improved (expressed in commonly-heard comments like “I’ve never been good at science,” and “I can’t do math to save my life”).

Research shows that school-aged children are especially apt to emulate the attitudes and behaviors of the same-sex parent—a source of concern if we want to improve girls’ still-lagging performance in traditionally male-dominated fields like science and mathematics. If mom hates math, a young girl may reason, it’s O.K. for me to dislike it too.

Teachers aren’t immune to negative feelings about learning, either. In fact, studies show that undergraduates who study elementary education have the highest math anxiety of any college major. Instructors who are uncomfortable with mathematics feel less capable teaching the subject, research indicates, and are less motivated to try new and innovative teaching strategies. A study by cognitive psychologist Sian Beilock, published in the Proceedings of the National Academies of Science in 2010, demonstrates how teachers’ unease with math can influence the students in their classrooms.

Beilock and her coauthors evaluated 52 boys and 65 girls enrolled in first and second grade and taught by 17 different teachers. At the beginning of the school year, there was no connection between the students’ math ability and their teachers’ math anxiety. By the end of the year, however, a dismaying relationship had emerged: the more anxious teachers were about math, the more likely the girls in their classes were to endorse negative stereotypes about females’ math ability, and the more poorly these girls did on a test of math achievement.

Adults who want to avoid passing on pessimistic attitudes about learning can do more than simply watch their language (no more “I’m hopeless at math” when the dinner check arrives at the table). They can jump into the subject they once feared with both feet, using their children’s education as an opportunity to brush up on their own basic skills. Learn along with your kids, and you may find that math and science, or writing and spelling, are not so scary. And let kids know that it’s always possible to change and improve our abilities—you being a prime example.

A crowd-sourcing experiment

Dear readers,

The summer has been a lot busier than I expected, which is why there haven’t been any posts here for over a month now. But today, there is an exciting project I’d like to tell you about, and also get some ideas from you about it.

A few days ago I talked to someone who works in education, and was asked if I could do an hour-long show for primary-school students (Grades 4 through 6) about mathematics. The goal of the show would be to get them more interested in mathematics in a fun and informal way. I need to put together a proposal by the end of next week, and I already have some ideas, but would love to hear yours as well.

Here are some of the things I’ve thought about so far:

- card tricks with explanation (in particular, the 4 piles of 4 cards trick my dad taught me)

- a guitar piece involving harmonics, with an explanation of how these harmonics work

- some mental calculation tricks, like fifth-root extraction and guessing by binary search

But it would be nice to do something even more spectacular as part of this show. This is where you all come in. Please let me know any suggestions you might have in the comments to this post. To motivate you, I’m going to give a nice prize to the best idea that I end up using in the show!

What it feels like to do mathematics

Dear readers,

I recently had a very interesting conversation with someone who had a background in computer science and information systems, to see what their perception of math (and mathematicians) was like. It is frequently the case that computer scientists (as well as physicists, biologists, social scientists, and so on) use the mathematical tools relevant to their needs without necessarily having a deep appreciation for the underlying framework that they fit into. This is certainly both reasonable and cost-effective in many cases. After all, unlike mathematicians, these scientists also have to know everything about their own fields, leading some to suggest putting even less emphasis on mathematics, a position I argued against previously. However, I often get questions like the one recently popular on Quora: What is it like to understand advanced mathematics? I often get the related question: What is it like to use it?

When I try to answer this question, I usually break the answer down into three stages. The first one is exploration, which involves a lot of trial and error. The second one is analysis, which comes from systematically thinking about your experiences. The third one is confirmation, which allows you to make sure that what you are doing is right. Let me try to briefly explain each one of these on an example that comes from my doctoral work on regulatory networks – it is simple enough to follow without much background, yet complex enough to enter unknown territory.

In graphs (collection of edges, which you can think of as roads, connecting vertices, which you can think of intersections), one common problem is to rewire the edges in a way that preserves the degrees (the number of edges found at every node). For example, one would like to get from the graph on the left to the graph on the right.

Graph LeftGraph Right

 

If the edges (roads) don’t have directions, it is known that switching a pair of edges (that is, going from the configuration on the left to the configuration on the right) is enough to get from any graph to any other graph that preserves the degrees.

Switch RightSwitch Left

However, if the edges have a direction (that is, a beginning and an end), and we need to preserve the number of incoming and outgoing edges at each vertex, then the switches are not enough, and so-called triangle flips are needed, as shown below.

Triangle RightTriangle Left

The problem I was facing was one where each edge not only had a direction, but also one of two types, say “solid” or “dashed”. What were the moves that I had to allow in order to get from a given graph to any other graph with the same number of incoming edges of each type and the same number of outgoing edges of each type at every vertex?

The exploration stage started with some simple examples, like the ones below (with the goal of obtaining the same configuration, but with edge types reversed), where a simple sequence of edge switches or triangle flips would not be enough.

Hard Configs The discovery stage involved trying to see how those “obstacles” could be fixed. Pretty soon I discovered a procedure that actually allowed me to do this, provided I had some extra edges that were available elsewhere in the graph. For instance, the picture below shows how to deal with the configuration on the right (which we call a strong triangle) in 4 steps, using three extra edges. First, switch each triangle edge with an extra edge. Second, flip the problematic triangle. Third, switch the edges to restore the parallel triangle. Fourth, switch once again to restore the auxiliary edges.

Solve TriangleThe confirmation stage was to see whether it was enough to be able to fix these bad configurations, or if there were others that could not be fixed with this approach. Unfortunately, as the computer simulations written by my co-author showed, there were other configurations that could arise that did not yield to our techniques (even though we never encountered any in practice). For this reason we left this problem open for whoever was going to be interested in pursuing it further (it is still open).

This process is more or less what happens whenever I try to solve a mathematical problem. If we compare it to hiking, then the exploration stage is like getting your bearings; the discovery stage is like observing the terrain and making notes; the confirmation stage is like making a map that others can follow to retrace your steps. But what exactly makes the discovery happen? This will be the subject of a future post!

P.S. I’d like to thank Amy Rossman, Wikipedia and Google Image search for the images used.

Exciting prime breakthroughs!

Dear readers,

These last few weeks have seen two very exciting developments in number theory, my “first love” in mathematics. In particular, two important conjectures about prime numbers have been proven for the first time.

The first one states that there are infinitely many pairs of prime numbers that differ by at most 70 million. One would ultimately like to establish that there are infinitely many pairs that differ by 2, but showing that the smallest gaps between prime numbers are bounded is a huge step in the right direction. An interesting twist on the story is that it was proven by a relatively unknown mathematician, Yitang Zhang, using a modification of well-known techniques, which, surprisingly, most experts in the field believed would not be sufficient. This is reminiscent of the AKS primality testing algorithm I discussed in an earlier post.

The second one states that every odd number can be expressed as the sum of 3 primes, and was proven by my friend Harald Helfgott (I actually met Harald not through our work on mathematics, but through our common interest in the constructed language Esperanto; that, however, is a story for another time). This is the so-called “odd Goldbach conjecture”.  The harder statement, known as the “even Goldbach conjecture”, states that every even number can be expressed as the sum of 2 primes. It’s unlikely we’ll see a proof of that one anytime soon, but then again, we’ve had many unexpected surprises in this area recently.

However, in today’s post I’d like to highlight the recent work of another friend, Yufei Zhao, whom I met during my math competition days. Yufei investigated a topic more broadly related to making use of random patterns in prime numbers (and not just them). I highly encourage you to check out his blog, and especially this post. It discusses the context of the recent results, Yufei’s own work, and a possible way forward to make progress on these tantalizing, long-standing results. For my part, let me just add that one of the attractions of number theory is that it is extremely easy to make statements which are probably true, but immeasurably difficult to prove (Fermat’s infamous last theorem being just one example). What makes it worthwhile to explore such questions, however, is that even if one doesn’t find the Eldorado (prove the difficult result), there are a lot of pretty gems to be found along the way.