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.