Ingrid Daubechies is the first female full professor of mathematics at Princeton University. She received tenure there in 1993 after working at Bell Labs. She was born and raised in Belgium. For this interview, I actually traveled to Princeton and met with her in her office at Fine Hall. The full transcript of the interview will be revealed in parts.
Ken: Thank you so much for agreeing to sit down with me for this interview! I think that the nature of the mathematics profession remains a bit elusive to our members so the opportunity to speak with one of today’s premier mathematicians is a very fortunate event for us. I’d like to start by asking you about mathematics generally…what is it to you?
Prof. Daubechies: I’ve done work that is pure and work that is much more applied. I did this work on wavelets — it doesn’t really matter what they are for this purpose — but the thing is, it is something that is motivated by concrete applications in signal analysis, in particular, for images and it’s useful for those and it involves some special functions.
Now, when people talk about those they always feel, I feel, everybody feels, they have been constructed. Now, coming from a math background, you probably know that many people feel in mathematics that mathematics is discovered and it is an outside thing and they discover it and they get inside and so on. But about these things [the special functions] people feel that they are constructed. But the feeling, I can tell you, from working on them and figuring it out and so on is exactly the same whether you do pure math or that. So, I try to find out why is that?
I think it’s partly because most of mathematics was motivated by physics. And in physics, you try to describe things that exist while when you do it for technology, it is, obviously, that you try to find ways, patterns, and so on, that help you construct things yourself. But the math part of it feels the same and even people think of it differently. So, in the math, where’s the boundary [between the discovered and the constructed]? Where do you feel that you go over the boundary? And if you start looking, you don’t find it. I believe there is no boundary. I believe that all mathematics is something that we construct. I think that mathematics is something that does not exist “out there”.
I think that mathematics is, in a sense, a very human thing. I mean, it’s our way…it’s the name we give to when we try to really precisely and articulately describe structures that help us in describing nature and studying nature and constructing things and so on. But that whole pattern of precise thinking and making things fit and trying to find patterns, and because we cannot build it all, we have to build smaller building blocks that we then use in building bigger things and that’s why we build all these mathematical concepts and theories. Of course, it is very nice when the thing that you developed here can be used there. To me, that’s mathematics.
So, I think there are lots of mathematical types of reasoning where people don’t write a single formula if they try to really very precisely and unambiguously reason their way through. I consider that a form of mathematics. Instead of saying mathematics is this abstract thing for which you have to be a kind of weird mutant to be good at it, I say, it’s not true. I mean it’s something that we all share. It’s a very human thing. I could conceive of us meeting an alien race that would do its math completely differently and we would have great difficulties in understanding them. I hope we would learn, but I’m not really sure we could, but you hope.
So, I don’t believe in this universal thing. I feel it is a very human thing.
So it’s also something at which some people are more gifted than others…just like you have Olympic athletes and other people. But, I mean, there’s nobody telling all these joggers on the road that they shouldn’t run because they will never be an Olympic gold medalist.
There are now all these Sudoku puzzles that are so popular. I thought once, “oh, it’s fun…it’s not math.” Well, that’s ridiculous. It’s not high level math, but it is definitely math and it is popular because people like doing that kind of figuring out. It’s actually much simpler than everyday life because you have such precise rules. I mean, you only have a few rules and that’s it. Within that, you have to figure it out.
Now, women and math…I think it is great to have venues where you are especially for girls. Actually, I’ve been thinking…I’m originally from Belgium and Belgium is a country that is big about cartoons. Now, everybody is about cartoons because people like manga and so on, but Belgium was big on that way before, and they were very different from American cartoons, although they had started from American cartoons. It started after the Second World War when American cartoons were no longer arriving. So, for all the series that were ongoing, they started writing sequels. So a whole industry started.
There are a couple of heroes in Belgium called Suske and Wiske,1 and Wiske is the girl. But mathematics, for a completely different reason is called wiskunde. So I was thinking of approaching the estate of that cartoonist to do something like wiskunde with this girl as the emblem. Partly because there is, in many countries in Europe now, a shortage of people taking mathematics — and as a result, a shortage of math-trained high school teachers which is disastrous. I mean, I can see what it does in this country. It didn’t happen before in Belgium and in Europe, but it is going to happen. And so, when there is a shortage, all of a sudden, you might not have anymore this thing of, “it is for boys”…if there’s nobody. And maybe you can then, and this has happened before, that in things that were no longer attractive to anybody, it was a good niche for women. This is a sad thing, but…definitely, I see it in every program where you have women that as soon as you have several women its fun together. Because they are so seldom in the surroundings where there are other bright women also interested in math.
Ken: Yes, that’s one thing I love about Girls’ Angle. It’s a very different feel from the co-ed classed I’ve taught. We also believe that when the motivation is there, the learning follows naturally. So we spend a lot of time motivating an interest…getting the girls interested in some math problem. And then, once they’re hooked…just facilitate.
Prof. Daubechies: One thing I notice when I teach, I try to always relate things. I have classes where I teach for non-math majors and where I try to relate to concrete examples. I put in a lot of examples with my kids and with relational situations and so on and personal anecdotes. And I find that I often relate much better with women…I mean that style of teaching relates much better to the women in the class than with the men because the men consider it not serious. But the women feel, oh yeah, this does make sense.
Ken: Have you thought about modes of teaching mathematics that might appeal more to girls?
Prof. Daubechies: [pausing] I don’t know about that. I’ve read about it, but I don’t really know about it. I think different groups have different feelings about it. I haven’t done sufficient experimentation with boys versus girls in the classroom. I could imagine that there might be indeed different modes that might work better. What I do notice is that a certain type of being informal helps me make a bridge to the girls while it sometimes hinders with the boys. Not always, but it sometimes does. With some males I have to do some kind of one-upmanship in order for them to take me seriously, which, with girls, they just clam up. I mean, if people do that with me, I clam up too. I mean, I don’t want to work with collaborators who shout. They can be great mathematicians, but they can go shout somewhere else. Now, it takes all kinds of personalities, so none of these are hard and fast rules, I’m sure, but it’s definitely the case that with there being so few women that if on average, women like a less authoritative touch and a more collaborative touch and if they don’t get it that will discourage them even more…I don’t know if that is something that works…it could well be.
Ken: How did you get interested in mathematics?
Prof. Daubechies: Well, I’ve always been interested in figuring out things. I remember when I was little I was always asking questions…and, actually, resenting it when my father would come with an half hour explanation instead of two sentences, like all kids. But I would want to figure out things. For instance, I remember…I must have been about the age of the girls at Girls’ Angle…I remember once being asleep in a car and waking up and I could see the neon street lights through the green strip Spectral Lines at the top of the windshield. I knew that this green thing discolors everything, but the neon looked just as orange as always. It wasn’t discolored. I mean, I moved my head and looked at it through the clear glass and the green glass, and it looked exactly the same. And I was really puzzling about that. And then later [I realized that], well it’s because it is almost monochromatic. It actually has a double line [see box at right] but it’s almost one monochromatic line. And, of course, it was dimmer but what got through had to be the same color. A green thing doesn’t shift [the frequency of the light]…it may absorb something…but it doesn’t shift. It absorbs some things more than others, so when you use a composite light, you have a different distribution so it may look different. But when you have a monochromatic light, either it doesn’t come through at all or what comes through has to be that color. That really brought home to me very precisely what monochromatic light is. I mean, that’s not mathematics…that was a physics thing, but still…I noticed things and I wondered, how is that possible? How can that be? And so on. And I’ve always had that. But I also had dolls, like many kids and like many girls and I would have a period where I wanted to make clothes for them. And then you ask yourself, how can you, from a flat piece of clothing make something that follows all these curves? And so, that’s when you discover, that you have the shaping and so on and so you discover how to make a non-flat thing out of something flat.
So I always wanted to see how things worked. I always like to put things together too. I still like working with my hands a lot and like seeing things that fit nicely together. So, in that sense, I’ve always been interested in things. But also, I found it really easy because it was so…I mean, you followed rules and you would get there.
My father came from a blue collar family. He was the first person in the family who ever went to college. And his parents came from a coal mining region. So when in high school, the teacher said you should let this boy go to college, it never occurred to his parents that there were many things you could do in college. They knew the coal engineers and they knew doctors and those were the people who went to college. And he couldn’t stand blood so he became a coal mining engineer. It was very, very logical. Later, I think my father would have preferred to be a scientist. He had great regard for science and he was trying to learn more science on his own. So he tried to teach me math and especially physics. That’s probably why I went into physics and not mathematics at first. So, he would teach me the math so I could do the physics. He taught me calculus early on. I thought it was really easy…and it is easy…there are just a couple of rules…if you are willing to take it like that…as a game with rules…then it is really easy. It’s doing things with it that makes it somewhat harder. I mean, when you understand what you are doing, it’s actually not hard. I’m not an advocate of teaching children calculus at that early age, but I thought there were other things in life that were much harder than that.
Ken: How old were you when you did this calculus?
Prof. Daubechies: Twelve. But to me, by and large, it was manipulating symbols. I don’t think I could have solved a serious multivariable problem. That came later. But one variable calculus…there’s not much to one variable calculus really. And the idea of continuity and convergence — it’s a really intuitive idea. If you start doing the epsilon-delta stuff — that’s another thing — that’s to make it precise and articulate, but if you start by saying 3, 3.1, 3.14, and so on, it’s obvious! I mean, that’s another example I use to show that math is constructed…it’s obvious to us now and it’s obvious to kids in elementary school, that you have a number line and that you can pinpoint things like that and the more decimals you have, the more precise you are. It wouldn’t have been obvious to the Greeks or Romans; they didn’t have that notation. The notation already tells you. It has become such a part of what we know that we know it at a very early age. Eudoxus had all these problems with this notion. He had a glimmering of it — in fact, I think he really had a feeling for it. But if you see all the contortions you have to go through in order to define it really precisely — it is quite a bit of construction. But we don’t have that problem anymore because we have notation for it. I mean, continuity…you have to have it…it just says we can make sense of the world…that if we didn’t measure things with absolute precision…if we are almost there…well, then, the result will be mathematician and almost there as well. That happens in most cases…not always…but it happens in most cases. We’re all used to that. So, all these concepts I feel are very natural.
Ken: There are some girls who do get the curiosity about some phenomena they notice and they ask themselves, “why did that happen?” or “how does that work?” but then, another thought interjects itself, and they think, “oh, it’s probably too hard for me to understand” and before they try to make progress, they already decide that it is too difficult. Did this ever happen to you? And if it didn’t, what is it about your attitude that prevents that?
Prof. Daubechies: Well, it is, uh, I tell all my graduate students that you have to be a bit ornery to work in science. You have to…I find it impossible to read a book cover to cover in mathematics. Because you start, and you hit a difficult proof. And you say, “why do they make it so hard? Come on! There has to be an easier way.” And so, you try. And you work, and you work, and you work…and you start understanding why all the different bits are in it. Well, sometimes, you do find an easier proof, which is nice. But this gives you an understanding for why…also you have to understand how math books are written. Math books are not written by saying, look, we would like to get there, but if you want to do this you would do this and this and this but look, there’s this stumbling block, so let’s see how we get around it. We almost find no math books like that. What they do is they figure all that out and then the write it down so that the stumbling block is sort of swept aside. All these logical lines follow through and then at the end you get this polished gem and you say, my, how did they find that? Well, they didn’t! They did all the rest, and then they polished it. So, that’s some beef I have with how math books are written. But that’s another thing. But still, you have to be ornery, you have to ask questions, you have to say, “but, come on, wait a minute!” and when you work together with somebody it’s a little bit like that too. If someone says to you, “I don’t believe it” you should be able to say, “ah, but this” and so on, and that’s how the whole conversation goes. But thinking, “this is too hard for me,” well, we all have that to some extent. I mean, I don’t work on the Riemann hypothesis.2 I’m just not the kind of person who likes to tackle a big thing like that. I do work on things that nobody else has done or that are problems, and there are problems that I haven’t been able to solve and that I set aside and I often work on several projects at the same time. So I think it’s ok to think that something is too hard and you’ll have to set it aside and come back at a later time. It’s not ok to think that everything is too hard. I mean, you have to be prepared to tackle some things. And if it is too hard, say, “how can I make it simpler so that I do understand it?”
Ken: Do you have a confidence that if you keep working, you will find new results?
Prof. Daubechies: No.
Prof. Daubechies: [laughing] No.
You never know!
Well, we don’t really know where ideas come from. It’s a very strange thing. I think they come from trying to remain wide open to many things. You have to really know your stuff You have to really dig into understanding strands of the different things you’re looking at. You should not live in a very narrow crack between boards. And it’s good to go to seminars and it’s good to talk to other people because you have no idea where ideas just fall from.
When my daughter was diagnosed with ADD (Attention Deficit Disorder), and they told me on what basis they diagnosed this, I said, well, I have all those things too. So they asked me some questions and they decided I have ADD too. So I have a mild form of ADD…I didn’t know…and when I learned this, I told my daughter, “well, we can stop worrying” because what it means is that I have tons of things that flip through my head. First of all, it means you see a whole lot of humor in many situations, which is fun. I think any good cartoonist must have ADD of some sort. But, on the other hand, I think it also makes me more creative, to see connections where there might not be any. And most of these connections don’t really exist, but sometimes, it shows something…some patterns. But you don’t know where they come from, so when you start working on something new, since you don’t control it, how will you know that it’s going to happen again?
After some time you start saying, well, it’s happened a couple of times before, so many times before, maybe it will happen again and you say, well, they gave me a job, so they believe it will happen again. But I still, for a long, long time, I felt like a complete fake. I felt if people only knew how inside I was insecure they would never ever…I mean there was a complete gap between the person they thought they had in front of them and the person who I knew inside.
Ken: How did you cope with the insecurity then? How did you manage to keep working and trying?
Prof. Daubechies: Well, first, you want to keep up appearances [laughter]. You don’t want to lose that job! But then, I think that it must be a very rare person who does not feel insecure like that on the inside. After all, you have a very asymmetric way of looking at the world. I mean, you are the only person that you see from the inside. Everybody else you see from the outside. And so from everybody else you don’t see the insecurities unless they have some kind of neurosis and really expose them very badly. I think Orwell said in an essay on Salvador Dali…he said that Dali always struck him as completely insincere in his interviews because he says no person feels on the inside the way Dali pretends he feels. On the inside, you always feel like a whole assembly of failures with the occasional good thing in between. But, first of all, realizing that everybody feels that way helps. And then second, by wanting to do research…that is to say, finding things that nobody else has found before, you’re bound to be on a bad track at times. So when you find something, it’s great! You feel, absolutely…you feel very, very elated. So I tell my students, when you find something new you should enjoy [it] for half an hour and then you check the details because it could be a mistake, but at least you’ve had that half hour of pure joy!
Ken: For half an hour??? Not even an hour?
Prof. Daubechies: Well, ok…but you should always check for mistakes because there could be mistakes. And if there are no mistakes, you feel even better. But it lasts very little. Even if you have no mistakes, it lasts a couple of days. After that, you have understood it even better and you begin to feel very stupid for having looked so long before you found it! And you kind of make it part of the tissue of mathematics that you know and at some point it becomes completely absorbed just like we absorbed decimal notation in the mathematics we teach our children. And at that point, it’s no longer that big joy. It might still be fun to explain it to others who don’t know it, but that pure thing of “Wow!!!”…that’s over. So you choose a profession where you’re frustrated a great deal of the time, you don’t know when you’ll find something, and when you find something, you feel, “woah!!!” and then that high is over a couple of days later. So it’s a frustrating thing…it can be frustrating…but it’s also a lot of fun. And I like teaching also…I like talking about mathematics to people and teaching students. So it’s not just these wows and dips in between.
Ken: I often feel, I don’t know if you agree, that a large part of doing mathematics is psychological, but it doesn’t seem that there are any courses in grad school that try to help students deal with these issues.
Prof. Daubechies: Yeah, well…I tell our incoming students always that they have to really work on building a social group…a social network around themselves…that they will learn half their mathematics from their peers anyway…not from their professors. Just like mathematics, doing mathematics is a very human pursuit and it’s very good to do it with others. I like collaborating with people. I also like having my time to figure it out because sometimes you have to figure out things in the privacy of your own office before explaining it to someone else. So in collaborations, we typically explain things to each other then we work alone then we get together again and so on. I try to foster a lot of getting together of the students. I like to give them reading courses where I explain for each chapter of the book what it is about and then they have to work through the details and they have to assign problems and discuss problems and so on. And then, after they have digested that chapter, explaining it to each other, worked through the problems, done everything, we go to the next chapter. They find that it teaches them a lot. But it’s also the doing it together that teaches them. So that is very important. So, I try to make sure we have nobody falling through the cracks who is too isolated.
If you’re down and you see other people who are not…that helps you. Also, you talk about more things; talking about more things, being exposed to more things, leads to more ways out of a problem.
Ken: We have a girl at Girls’ Angle who I personally think is quite gifted. But she has kind of a disease where whenever she solves a problem she immediately thinks, it must have been trivial because she feels that if she can solve it, it must be something very simple. So, she tends to think of herself as very unintelligent. She’s even said, “I’m so stupid”.
Prof. Daubechies: Yeah, but, uh, well…I don’t know her, so I don’t know whether it is…it could be the result of something at work that is something in the way girls are brought up…girls are not brought up to feel they are stupid, but girls are brought up in a way to try to find common ground among each other, to find ways of sharing. And it might be that by saying, “I am smart” she feels that she is counteracting…that she is not doing the acceptable thing. Or she might even feel that by being smart she is making herself too different from the others…I don’t know. I really don’t know. I know that played a role for me at some point. At the last mentoring program we had for women, we had a discussion about professional interactions between women and men in the math department or, rather, not professional, but how collegial interactions can be different. And one of the senior women said that junior women should be aware of the fact, she said, you know when you meet other women…one way in which women bond is that one of them will say something in a funny way but something about a personal weakness…something disparaging about herself. And the way other women will counter will be by doing the same thing about herself. So you’ve shared a weakness and that creates a bond so you’re both not perfect. Well, this is something that you shouldn’t do with most men in the department. If you do this with a man, most likely, he could start feeling superior or he could start explaining to you how to solve your problem. [laughter] But this is part of a way of interacting…it’s not a ploy…it’s a tactic people use, not consciously, but as a way of making a bridge.
So, I don’t know if it would help, instead of feeling, “I’m so stupid” to think well, “I can do this, but so and so is better at that,” so as to feel she is not singling herself out by being able to do the problem. I don’t know. That’s one thing I can think of, but there are others.
But there’s also the fact that always what you can do yourself doesn’t seem as miraculous as what other people can do because you’ve seen all the mistakes that you did on the way towards it while the others just come out with the answer. How old is she?
Ken: She’s twelve.
Prof. Daubechies: I hope she doesn’t discourage herself from doing mathematics.
Ken: Also, she has an issue with making mistakes. She hates to make mistakes, to the point where I think it is an obstacle. This is a problem we’re having at the club: trying to convince the girls that mathematicians make a lot of mistakes.
Prof. Daubechies: Oh yeah!
Ken: Actually, maybe you could address this?
Prof. Daubechies: Oh…everything I start, when I’ve finished, I joke that I’ve done it ten times, because I started and I find that I made a mistake, so I start over again, and I find another mistake, so I have start over again, and over again! That’s why many of my students, when they write a paper, they write it on the computer, I can’t do that. Because even in the writing, I find, it’s not right the way I say that…it’s not exactly the way I want it and if I do that on a computer, too much of it survives. So I do it in long hand and I erase and so on. I know you can do that on a computer, but it is not the same for me.
But, oh yeah, I make mistakes all the time.
And I have hunches that are wrong. Some hunches are right. But you know, the funny thing is, for one paper that I did, many, many, many years ago, I had kept a notebook with every approach that I did…every attempt…and many of them led nowhere. And, in the end, I solved that problem and it became a paper, and I had the impression that the insight had just come in a kind of flash. I really believe that for many things…and that then, everything had fallen into place. And then, I came upon that notebook some time later, and I realized that it wasn’t like that at all. I could look in the notebook and see in all those places where it hadn’t worked that there were already some of the germs of the things that did work eventually. So it wasn’t true at all that I just found it in a flash, in hindsight. I mean, if I hadn’t made all those mistakes before, I wouldn’t have had all the building blocks to fit the thing together. So all those early things had been necessary, I mean, had been part of it. I was really surprised, because I had this very different perception of how it happened from what this notebook showed me.
Ken: One thing we’re going to try with the Bulletin…there’s a woman who just graduated from Smith College [with a post-baccalaureate degree in math], her name is Anna Boatwright. She’s going to solve a problem keeping an honest record of her attempts to solve it. Then she’s going to write an account of her attempts to solve the problem, errors and all. I think it is very brave of her to do this because I think most mathematicians try to sweep all the errors under the rug before they publish. [Editor’s note: Anna’s problem-solving was documented in a regular column in the Bulletin called “Anna’s Math Journal”. It ran from 2009–2011.]
Prof. Daubechies: Well, because that’s the way you have to publish because publication is expensive. So they try to do it as efficiently as possible. And also because they develop this way of writing with lemma and theorem which made it easier to check whether something is correct or not. In fact what we do when we write a paper is to write it in such a way that somebody who, if all the steps are given, then what they do is give a procedure for checking that the whole thing is correct. It might be ten lemmas and you say, “why would they care whether this obscure fact is true?” Well, because it is a building block later. And of course, they didn’t find that lemma first, but they give you a way in which you can see that the whole thing is correct. But that’s not the way in which it was found.
Ken: In your opinion, should the literature be a repository of truth or a place to explain?
Prof. Daubechies: I think you need both. That’s one thing…I hope you teach the girls this…students who come out of high school and who are good at math…I don’t know if they learn this from a teacher or if it is just the culture, but they believe that you have to figure it out in your head. I mean, you give them a problem, and they stare. My son would do this, and he would say, “I don’t see it”. So I would say, “I can’t help you if all you tell me is ‘I don’t see it’!” They don’t start writing. I mean, when I start a problem, I start immediately writing. I start writing what I know, I start writing what I want to get. I write how can I get from one to the other. I start from the beginning if I know where to start or from the end if I know where I want to go. And I try to connect…I try to knit it all together. I try to see many ways and hope to build a bridge. Of course, there are people who can do all that in their head, but I think at some point, unless they are, they are going to hit a place where they can’t do it all in their heads anymore. And if they are Terry Tao, they don’t need me to teach them anyway [laughter]! And when they hit that place, they have to have in place already the tools to handle a situation like that. And the tool to handle a situation like that is to start writing. Putting down the different pieces so that you can look at them and see how it fits together. I teach a freshman multivariable calculus class which we integrate with physics. When I do that class I tell them that we are going to go way faster than what they are used to, that they will have to study material…usually they don’t study either…they’re used to going so slow that the absorb it by osmosis, and we can’t do that anymore. And that they always have to start writing. They have to write what they know, what they want to get, what they know about the kind of problem, and then start seeing whether they can put the pieces together. If you do that, if you don’t believe that writing a problem is going here to…and then writing linearly to there without a single mistake and this is the answer and I think it is easier also if you see it as a whole process of having here things, and here things, and here’s some knowledge, and now we are kind of embroidering around it until the things start touching, then it might be easier to accept that there are going to be in the end lots of things on the page that have nothing to do with the solution. But that’s ok, you just select out the part that does.
When I teach, I also have a course that is a first-proof course based in applications. I teach styles of proof to the students. I do it in two-columns. I say, how would we build this proof? I say, we want to get here and so on…and after we have the proof, we then write the proof on the right hand side which is a very different thing.
Ken: By the way, I’m just curious, you’ve used a knitting metaphor…do you knit?
Prof. Daubechies: I used to knit. I don’t anymore. I used to crochet even more. I would love to if I have time, I would love to have a loom for weaving. But I make ceramics.
Ken: Do you make your ceramics with any connection to mathematics?
Prof. Daubechies: No…I just like making things by hand. I’ve been thinking maybe after I retire I’d love to make some art works in which you illustrate some mathematics.
Ken: So, I’m going to ask you a completely different question. I’ve been wanting interviewees to address this but many are understandably reluctant to. Do you think there is gender bias in the field of mathematics today?
Prof. Daubechies: [pause] There certainly are still instances that I hear about. If you ask any young woman, she has stories. Among the graduate students I think they’ve encountered it more among their peers than the professors. Some of the professors are not necessarily very friendly towards graduate students…it’s not that they are not friendly, it’s just that they are oblivious in a kind of gender neutral way…but I think it might be resented more by women. But definitely there are people who think yes, who kind of assume that a woman will not be as good and who may even articulate that. Usually, they are more perceived as jerks, but it exists. And then, definitely, if you look at statistics, or, well…the statistics are complicated by many, many issues. Because women also unfortunately drop out more from the field at transition points than men and so we want to do something partly because the numbers are low, I think. So, I think…I haven’t seen many cases of blatant discrimination, but I do think there still is some. I think it’s at the level where it’s just a consequence of the fact that there are much fewer women than men in the profession. I mean, people make implicit assumptions based on what they see.
Ken: There is an explanation put forth by some psychologists that the low representation of women in the upper levels of mathematics is not due to gender bias but is due instead to differences in preferences between what girls like and what boys like. What do you think of that argument? Do you think that it is valid?
Prof. Daubechies: I think that it does not explain why more women than men leave the field. I mean, these women already liked mathematics to begin with and then concluded it is harder for them to stay in and combine a family and career, to make their mark…whatever…so I mean, I think I have no a priori reason to assume that…I don’t believe in it because I’ve seen plenty of women very interested in mathematics. And I’ve seen women talented in mathematics and who did leave the field usually because they don’t like a job where the tenure clock is racing at the same time as raising a family and things like that. Another thing is that many mathematicians seem to believe that, well, there are two things. First of all, many mathematicians who are considered to have left the field, for instance by the AMS, are still doing mathematics in a broader sense…in the sense that they are applying very much their analytical skills and their precise reasoning skills in their new jobs and they find that mathematics trained them very well for that, and they enjoy it. So, we haven’t really “lost them”. The second thing is that so many people in academia seem to feel that it’s almost a failure not to go to academia. For your girls, that’s not an issue, they are still young, but I think that is absolutely so ridiculous. Even people who agree that it is ridiculous still have this implicit assumption. If they have a very good student who then decides to do something else, they say, “oh, such a pity, he could have been!” But what does it mean? It still means you have an implicit value system…I mean, [the thought that] “only the people that couldn’t have been do something else”…which is ridiculous. Mathematics is a skill that is very fundamental that many people have and we need many people who have it in spades, and we need it everywhere, and we should be happy to spread it around.
But, we do lose women more than men. I think it is partly because, well, the track itself is kind of hard for women if they want to raise a family.
Ken: One of the goals of Girls’ Angle is to become a community of support for all women engaged in the study, use or creation of mathematics. One of the issues I think about is this issue of raising a family. I’ve often wondered, you know, every person has two parents…why does it seem that the burden is on the mother to do the child rearing…why is it that when a male mathematician has a child there is no stigma associated with whether he is still going to be able to do the math?
Prof. Daubechies: Well, yeah, well, I don’t know. Well, part of it is that when the baby is really little, the mother is nursing and that is something only the mother can do. But, yeah, I agree. So actually, when graduate students and postdocs ask me how do you combine a family and a career, I tell them that the first thing to do is to choose their husband well. It may seem a bit silly. But it is very important that you discuss ahead of time how you see things going in a family and in some detail so you don’t have vague expectations. Well, I’m happily married now but earlier I had a relation with a man who was a very nice man but I think he expected something different from his fiancé than what he expected from his wife, which can be very frustrating for a young woman to meet a man who really appreciates you because you are intellectual, because you have all these interesting pursuits in life and so on, but then expects that after marriage that you will take care of the house and cooking and…which wouldn’t leave you any time anymore to be the person that they liked before. I had implicitly assumed that since he liked these things, we would work together, that we both would have the time left to be the persons we had been. And it didn’t work that way. But, we hadn’t discussed it. And it took me a while to figure out that was what was wrong. So I tell them, that’s important.
The support of a husband who views it in the same way is absolutely important. But after that, there’s still the rest of the world and people may find it strange that this couple works in a different way from most couples they’ve seen. So, I think having a support group like that would be great.
Ken: Do you have any suggestions for how this can be implemented?
Prof. Daubechies: Ummm, I don’t know…I mean I know that I’ve had support groups with women and we’d hang out, and we’d get together and chat…so, definitely have a corner, I don’t know how big your facility is…but having a corner where people can just chat, or even a separate room, where they can chat and not be overheard by everybody else working on math would be good.
Ken: Someday we hope to expand the age range to include tots and have a daycare center overseen by people who love math. So mothers could…
Prof. Daubechies: Oh, that would be very good.