**Marie** is a CNRS researcher at the department of computer science at École Polytechnique in Paris, working at the interplay of combinatorics and probability. We meet between lectures, during the thematic trimester “Combinatorics and interactions” she co-organizes at the Institute Henri Poincaré in Paris, to talk about maths and life as a mathematician.

Marie’s diverse research interests have all in common that they involve a combined use of combinatorics and probability. This is the case, for example, of her work in random planar maps, where one considers a discretization (polygonization) of a smooth surface embedded in a sphere. Here, the goal is to study a sequence of these polygonizations (like quadrangulations or triangulations) when the number of polygons increases (or, what is the same, when the size of the polygons shrink). It turns out that although there are many different ways to consider a sequence of polygonizations, many of them converge in the limit to one universal object, called a Brownian map. Much like a random walk converges to a Brownian motion. The mathematical theory behind random maps takes care that these mathematical objects are well defined, can be considered as metric spaces, and that it makes sense to compute with them, that is, that one can define sequences of such objects and take limits in a certain sense. The subject of random maps has gathered a lot of attention in the recent years and is leading to new discoveries in probability theory, because of its interactions with other modern fields, discrete mathematics, geometry and physics.

Marie was always good at maths, and like any good student in France by the end of high-school she was expected to enter a Prépa. Prépa is short for Classe Préparatoire, an elite 2-year program that prepares students to enter the Grandes Écoles, prestigious higher education institutions. “In France, everything is a rank”, Marie explains, and education is no exception, so entering one of the Grandes Écoles is a way to secure a great academic future. But this elite system can come at a cost, and top-ranked Prépas are known for their competitive environment, which can be emotional strenuous for some students. Therefore, when it was Marie’s turn to follow the usual path, she was advised to apply not to a top-ranked Prépa, but to a medium one which was, according to one of her teachers, “better suited for girls”. At this point Marie’s mother, an academic herself who had always supported her daughter, stepped in. Putting all emotional concerns aside, she advised her daughter to take it easy and just apply. Marie recalls that “in that precise moment, she actually made a difference”.

Marie was accepted in a top-ranked Prépa and went on to do her undergraduate studies at the renowned École Normale Supérieure (ENS). If she had never contemplated a career as a mathematician, despite her skills, was mostly due to the rather cold atmosphere she experienced at ENS. Often she would find herself in a classroom with 40 students where only two of them were women. In this isolation, she couldn’t relate herself to the mathematicians working there. Therefore, she passed the national teaching exam (“agrégation”) with the idea of becoming a teacher.

It was then that one of the professors at ENS made her reconsider, as she recalls, “he told me, you should do a PhD. You’re young, you’ve all the time of your life to become a teacher, so start a PhD and see if you like it.” And indeed, she liked it. Marie did a PhD in Combinatorics and Discrete Mathematics at the University Paris 7, in a group where the ambiance was good, students supported each other, and where finally she felt at home.

“At some point I realized that I do maths as some people study ancient Greek. It’s pure knowledge and increasing the amount of human knowledge is just good”.

With the impressive work done in her PhD, Marie succeeded to secure a much envied permanent CNRS position^{[1]}, but despite of this bright start her first year was tough. She had to relocate to Paris, only 6 months into a postdoctoral stay in Montreal, where she had managed to stay close to her partner, solving the two-body problem*. With little experience gained abroad and with once more a two-body problem, soon the thought struck her that she wasn’t ready for it. She explains, “I did my PhD quite fast, but I finished all the questions I had during the PhD so I basically had nothing unresolved anymore. I was missing problems, and I lacked maturity”. Marie’s luck weighted heavily on her, and as a consequence, feelings of isolation and insecurity crept in. She was expected to be an independent researcher and to work on interesting problems, but she didn’t know how to do it. She couldn’t complain about her good fortune either with her colleagues or friends. The situation was so stressful that she considered her options, including accepting the teaching position she had earned after passing the national teaching exam. After all, Marie was in maths because she enjoyed it, and if that joy was overshadowed by insecurity and isolation, then Marie saw now reason to keep doing it.

So things had to change, and Marie took her career in her hands. “It was some small things”, she recalls, and identifies two actions that finally opened her way in academia:

- Reading: “I thought, if I don’t have problems to work on, then I’ll learn new maths. So I started reading things on combinatorics of maps”. This was an active field of research around Paris back then, and being aware of recent progress allowed Marie to establish contact with people working in that field. Simple conversations around maths let her out of her isolation.

- Collaborating: Marie was invited by her colleagues in Montreal to a workshop on “open-problems” in her field. There, she established a collaboration with another female researcher. This provided her with a safe environment where she could show her ideas without having the fear of being judged and where she could regain her self-esteem as a mathematician.

When I ask Marie why does mathematics matter, she laughs, adding “I made progress by stopping asking myself this question”. She did start her career with big questions, though. During her master she did maths applied to biology. However, doing maths for maths sake seems to be enough for her, as she explains “At some point I realized that I do maths as some people study ancient Greek. It’s pure knowledge and increasing the amount of human knowledge is just good”. She also feels the transference of skills is her way to make an impact around her, as when she teaches a class, or supervises a PhD student, or when she explains her latest mathematical results in a talk. Or, when she commits herself to the organization of scientific events, like the current thematic trimester at the Institute Henri Poincaré. Marie is convinced that all these activities are almost as important as having good mathematical results. About the impact of her research, she explains she works on problems she finds important, even if it means having less publications than her colleagues. She states firmly “ I try not to compare myself with other people. That’s never satisfying. To avoid it is tough when you come from a French education background”, and adds “I think that even if I’m not the strongest mathematician, I can contribute at my level to the problems I’m interested in”.

For Marie, professional success is about enjoying and being proud of what you do, and having the appreciation of your colleagues. This comes from a sense of community and the feeling of belonging to a group of people with shared interests that are willing to interact and nurture each other. Listening to Marie’s experience, this is the message I take home: having a community that supports you will be reflected in your work and your own self-appreciation as a scientist.

“I start with small examples. I like the process of listing all the small cases, that is, for n=2,3 or 4, and try to see if something emerges (….) It’s the process I like about it. We really try to infer something from drawings or pictures”.

In very simple words, working on Combinatorics involves describing an object’s complex structure by counting. Marie describes her approach to research in this field as follows “I start with small examples. I like the process of listing all the small cases, that is, for n=2,3 or 4, and try to see if something emerges. Depending on the subject, I also draw pictures. Because I’m doing discrete maths, doing these kind of examples and trying to figure out what can go wrong, or what can be provable, is how I pick my topics. It’s the process I like about it. We really try to infer something from drawings or pictures”. At later stages, Marie also does numerical simulations to corroborate her hypotheses.

On how ideas appear, she jokes “I’ve had some Eureka moments that I can remember in detail, and I’ve tried to reproduce the process but it didn’t work”. In Marie’s case, ideas come after an intense process that involves focusing very hard on something for a long period of time, for example a full day, followed by a break, say, for a couple of days. “Then, when I come back to the problem the idea appears, but I think I need time to process the work”. In Marie’s approach, it is very important not to be shy when trying solutions, “I try not to be inhibited, so even if I’m not sure if some ideas will lead somewhere, I just try them all, even the ones that seem crazy or desperate.”

“the best thing about working with people is that you do maths better, but also that it keeps you motivated to finish your work and write papers”

Another approach is working with other people in front of a blackboard, looking at examples of a problem that is interesting. People make suggestions on what might hold true for that example, and then try together to understand the mechanism behind that truth. In her experience, when working with other people there are often two behaviors : there is the collaborator that throws all the ideas, and the collaborator that is critical and rejects or accepts the ideas. Marie feels she’s able to take both roles, but observes that she tends to propose more ideas when she works with women and has less fear of saying something stupid.

Already finding time to work and focus isn’t easy for Marie. “For maths problems, if you’re only 90% focused, you’re not going to do 90% of the job, you’re just going to do nothing, so the process is much slower if you’re not 100% focused”. Having a child and spending a lot of time commuting makes her days shorter, and having so many distractions between family and work makes it harder for her to dive deep into a problem. However, she finds that inviting or visiting collaborators to have intense working periods works well in this period, and adds “the best thing about working with people is that you do maths better, but also that it keeps you motivated to finish your work and write papers”. The keywords are, therefore, motivation and focus. Marie’s advise is going to the library, for example, and being surrounded by people working, induces motivation.

“I try not to be inhibited, so even if I’m not sure if some ideas will lead somewhere, I just try them all, even the ones that seem crazy or desperate.”

“Some people more or less explicitly told me I was hired at CNRS because I was a woman and it’s hard to get rid of this, because you start believing it”. The people Marie refers to thought she was subject to affirmative action (sometimes called positive discrimination), a measure adopted in many countries in order to quickly rise the number of women in academia. Even if this measure is only applied in particular situations, its effects weight heavily on women in general, as Marie’s experience shows. Still, she is willing to experience this prejudice provided there are more women in science. But its complexity implies there is still debate on the effectiveness of affirmative action in academia. Therefore, one needs to look for better measures. In Marie’s opinion, having more women in hiring committees will help in this direction. “Juries or committees tend to hire people that look like them: white, male, of the same background” and she adds, “if there were more women in the committee, it would be better for female candidates, as they would maybe feel more comfortable” ^{[2]}. However, women participating in hiring committees in France get a bigger workload than their male counterparts, simply because they are a minority, so in order to fulfill the female quota in hiring committees, the few women available need to participate in more committees per year. According to Marie, this is a much needed effort that should be compensated either by a teaching reduction or by offering extra financial support.

Another measure taken by some institutions to help women stay in academia is considering maternity leaves in job or grant applications. This is standard, for example, for European research grants. In Marie’s opinion, these kind of measures should be generalized to grants and prizes, and to other types of leaves, like sickness or other family reasons. She observes with certain frustration how a newly created mathematical prize in France, modeled after the Fields Medal, has completely ignored this trend, and she explains “The Fields medal was created almost 100 years ago, back then they didn’t really care. But to receive this new prize you must be less than 40 and there is no derogation for maternity or paternity leave, and for a new thing, I find it a bit sad.” Indeed, the Fields Medal was created in 1936, when women mathematicians were still a curiosity. Things have changed in science since then, so a prize established in 1936 shouldn’t be followed as an example today. Nowadays science needs not only more female participation, but to figure out how to integrate the family/personal concerns of all its members into the equation.

Notes

1. CNRS is the French National Committee for Scientific Research. CNRS researchers are public employees, with permanent positions, that are chosen after a tough selection prodecure. Back to text..

2. For more about the unconscious bias by hiring committees Marie refers to, see for example this article. The National Science Foundation in EE.UU. has a website with resources on the subject of bias, here. To sensibilize the general public on this issue, the Royal Society produced an animation video explaining what unconscious bias is. Back to text.

*Thanks to Marie Albenque and Gaetan Borot for helpful comments and remarks on the article.*