Sylvie is a French mathematician whose research focuses on problems motivated by physics. When asked why she chose maths, she explains that back in her school days in France, if you were a good student, you were encouraged to study maths, which was considered as a stepping-stone for many career paths. She was a good student, she was attracted to maths, as well as to several other things. Ethnology was one of them, since she was interested, and still is, in culture, people and languages. By the end of high school, she was accepted into a prestigious classe préparatoire[1] in Paris. She knew little beforehand how a “classe prépa” worked and she soon found herself in a male dominated environment, extremely competitive and stressful. And while for some people such tough environment can be an incentive, in Sylvie’s case it was a discouraging experience. She firmly states “I don’t think you should suffer to become a mathematician. On the contrary, mathematics should be a joy, it should be about sharing ideas, communication, creativity”. Luckily, and despite of that painful experience, she pursued maths at university, where she could go on developing her interest for maths, which complemented her interest for languages, “I like to think maths is a language in the process of being built. It’s something I enjoy a lot because I’m very interested in the structure of languages, and like natural languages, mathematics is a language undergoing permanent changes. In speaking and using a language, we contribute to its evolution, whether we want it or not. But in doing mathematics, we are required to actively contribute to its construction. Mathematics is being built as we work with it. It is under permanent construction. And this, this I find fascinating”.

After her undergraduate studies, she became interested in Quantum Field Theory and went to Bochum, in Germany, to do a PhD. Later on, she worked on infinite-dimensional manifolds, and infinities like the divergences of the Riemann-zeta function, which are problems that have a strong connection with physics. In recent years she has been working on renormalization from a mathematical point of view. Back in the 80s, Bochum had a very active mathematical community and an excellent theater scene. Sylvie considers herself lucky to have enjoyed top-quality scientific and cultural activities during her graduate studies and she remembers fondly those training years. From her thesis advisor, Prof. Sergio Albeverio, she learned not to be afraid of the language of physics and to view it as an enrichment to mathematics. She also learnt generosity and open-mindedness, both aspects she tries to implement in her academic life today. Generosity, Sylvie thinks, is fundamental in science, and adds “You need to be generous in life, in general, but in science it’s essential”. About the impact of her thesis on her own research, she says “I’m still working on ideas which have been triggered by this thesis, even though the topics might seem completely different. I’ve changed methodology and my approach, but the ideas are still how to make sense of infinite dimensional measures, traces,…”.

“Mathematics is being built as we work with it. It is under permanent construction. And this, this I find fascinating.”


Searching for ideas

When asked how to get ideas, Sylvie answers, “I think everybody has a different way of thinking, of working. I often have a problem at the back of my mind which, even if I’m not working at it actively, remains in my brain as I go running, swimming, whatever. Thinking of it passively during such an activity can sometimes trigger some idea. So I often have a concrete question in mind, trying to make progress in one direction”. She adds that the main ingredient is curiosity, “I like listening to other people, discussing and attending talks, even those outside my area of research. I like interdisciplinarity and I like to be open to other points of view.” All these processes involve a lot of questioning, which is central in Sylvie’s creative process “ I think that [questioning] belongs to maths. The main thing is to constantly question. Whatever you’ve stated or you have thought as definite needs to be questioned”. And she insists that this should be a pleasure, not be painful. She also admits that it can be tiring because it implies that one never stops thinking about some question or the other. So there is no rest for mathematicians and Sylvie describes well the mathematician’s general state-of-mind: whatever happens, “ideas and questions lie at the back of your mind”.

Another aspect that is fundamental, in Sylvie’s opinion, is creativity. She believes that this feature can be nurtured by having other interests besides mathematics. In Sylvie’s case, these are languages, art, sports, music, literature, theater and politics, among others. Her other interests also makes her academic life richer. For example, she speaks Spanish fluently, which has helped her to establish close relations with colleagues from Latin-America, with whom she is responsible for long-standing research schools in Colombia. Sylvie’s interest in art and the creative process behind the mathematician’s work, led her to co-author the book “Rencontres entre artistes et mathématiciennes” (Editions L’Harmattan, 2001), which is a collection of exchanges between (female) mathematicians and artists.

How work is done

“I like working with other people a lot. This is, I find, the best part of mathematics: to create and share with other people”. For Sylvie, writing an article can take years, and this implies a constant communication with her co-authors. This involves a constant exchange of updated files, e-mail discussions and video-meetings. To students, she advises to always have a manuscript on which to base discussions. She considers the written support to be essential and the reason she gives is simple: “there is often a difference between what you think you have understood, and what actually you can write”. And Sylvie couldn’t be more right.

“This is, I find, the best part of mathematics: to create and share with other people.”

The perils of academic life

illus2_color_v3_cutWhen a mathematician complains of having too much work it should be understood as “too much paperwork”. Currently, scientific research is funded via grants, either from public or private sources. In order to obtain funding, scientists need to prepare proposals, apply and go through a lengthy and time-consuming selection procedure, often with low success rates[2].  Sylvie regrets, “The tendency is for the worst. We’re asked, specially in Germany, to do more and more paperwork, apply for grants, and this is not helping research. It’s going against fundamental research” and she continues “If it’s [about] how many articles one wants to produce, then indeed these short-term projects that you apply for can be useful. However, in terms of fundamental research, which one can’t plan in advance to the extent that is required to fill in the form for the application, short-term funding has a negative impact on research and we feel it. I feel it as a researcher, and I’m not the only one. On a daily basis it has become very difficult to just think, have time to think.” Combining teaching, administrative work and research is not easy and she confesses “I actually have to hide away to think”. After meetings, teaching, seminars and mentoring students, she takes the time, often in the evenings, to think about research. Does one need to be organized to be efficient in this ocean of activities? Certainly. “One has to push oneself to follow up the various activities beyond what you would naturally be inclined to do. You would think, oh dear, I’m not ready for this appointment coming up today, but this very appointment pushes you to think about that specific project that day. Organizing is making sure there is a regularity in the projects you’ve committed yourself with”.

The excellence model

Sylvie’s view is that the current model for funding research promotes a competitiveness that is not always constructive, by which researchers are forced into a race against each other. With the new funding policies based on efficiency, the researcher’s role has changed : “We’re now managers rather than researchers, we’re asked to think in an efficient organizational way at the cost of a deeper research thinking, which is what we were trained for”. To that, one should add the pressure to obtain funding, which is conditioned to performance at the highest level. “We’re asked to be in the best group, in the best university, in the best country. This idea of excellence, which focuses on very few people, very few groups, seems to me counterproductive, specially in maths, where you don’t need much money”. In maths, one does not need supercomputers or much expenditure, unlike in other domains like experimental science. In maths, money is usually spent in research stays, hosting and visiting collaborators, books and organization of conferences.

“We’re now managers rather than researchers, we’re asked to think in an efficient organizational way at the cost of a deeper research thinking, which is what we were trained for.”

When asked about the future of models based on the concentration of funding on “centers of excellence”, Sylvie’s answer is categorical: “I think it’s a huge mistake”. To illustrate her pessimism, she gives the example of France: “The French system had its drawbacks in its past form, but you can see how many Fields medals it has produced and that has a lot to do with the fact that money was sprinkled around France and not concentrated in very few parts. Ideas could emerge in small universities because there was just enough money for people to go to a congress, exchange ideas and not be overloaded with teaching, as will now be the case for those who are not a part of these privileged groups”. Sylvie explains that in this new world view, the researchers who will be left out of the massive grants will need to justify their existence by teaching or doing administration, all of it at the cost of doing research. However, in mathematics one can only see the effects of this policies in the long-term. In Sylvie’s opinion “These models based on the concentration of funding on centers of excellence are conceived on a short-term basis. They’re thought of on the scale of a political mandate term, not on the scale of mathematical research, which is quite different”. She adds “The problem with maths is that we will realize the effect on research in maths of these short-term policies very late, too late to correct the mistakes made, because mathematics is an investment over centuries”. Sylvie’s concerns make me realize a sad fact: Leo Szilard’s story on how to slow down scientific progress[3] has been an inspiration to the people managing research funding.

“Mathematics is an investment over centuries.”


Women in maths

In this frenzy of short-term budgets, permanent positions are decreasing in number, giving way to fixed-term contracts at all levels, post-docs and professorships alike. In Sylvie’s opinion, these are difficult times for holders of a PhD degree in their late 20s, early 30s, when they have to go from one place to the next searching for the next short-term contract. This is hard on everybody, specially on women.

Sylvie believes women are less determined than men when it comes to apply persistently for positions, and they tend to give up the race for personal reasons. But is this because women are more insecure than men? Sylvie disagrees, and imagines the following picture “[Women] have to compete with many people, the waiting lists are very long. It’s like when you see a long queue in front of an administration office, either you think “ok, I’ll just stand in the queue until I get there” or else you think “well, I’ve got so many other things to do right now, I think I’d rather give up”. According to Sylvie, it’s not insecurity, but self-censorship, “Women censor themselves more easily than men. You need deep self-confidence to wait five years for a permanent position”. And this does not apply only to jobs, but also to grant applications. Sylvie explains that in an academic life you have to be ready to be constantly compared to your peers. Her advice is “You have to build some kind of shield to protect yourself from feeling deeply questioned by small non-success. I wouldn’t say “failure” because it’s not failure, I would say non-success”. And she speaks from her own experience: during her first position at the University of Strasbourg, Sylvie had two children and did her habilitation (qualification that allows to supervise PhD students), which meant she was ready to apply for a professorship. Despite having a good research record, she had doubts. To do her habilitation she had to force herself to stop listening to that little voice that would tell her that she wasn’t good enough, that she wasn’t ready. She sought the advice of Prof. Daniel Bennequin, a senior professor, who positively assessed her CV and Sylvie took his positive answer as the last push she needed to go and apply for a professorship, which she got not in the first try, but in the second one.

The moral in Sylvie’s personal story is the following: “So, what I’m saying is, when you feel discouraged you should try to think, ok, well, let’s turn things around and take this discouragement as an impulse to go on, to make a step further”. Her message is to use these “non-success” experiences, as she calls them, to find value in what we do, and to find a way to push our performance to become more visible and more confident.

Sylvie has ever since then kept an excellent research record, becoming a leading researcher in the field of Mathematical-Physics.  To date, in one way or another, Sylvie’s work continues to deal with infinities. Details on her work, a description of research interests and a list of publications can be found in her website. In parallel to her research activities, Sylvie has been engaged in several initiatives to promote the participation of women in mathematics, in the European Mathematical Society (EMS), the European Women in Mathematics (EWM) and other local initiatives both in France and Germany.  In 2013 she conducted interviews with women mathematicians around the world, which you can find here. This project developed into an exhibition called “Women Mathematicians around Europe. A gallery of portraits”, curated by Sylvie in collaboration with Sara Azzali (U. Potsdam), Magdalena Georgescu (U. Potsdam), Alexandra Antoniuk (Kiev Academy of Science) and photographer Noel Matoff. The exhibition will be presented in several places around Europe starting in Berlin during the 7th European Congress of Mathematics, in July 18-22, 2016.



1. Classe préparatoire is a 2 year training after high-school whose goal is to prepare students to pass the entrance tests for grandes écoles, an excellence educational system that runs in parallel to university. Back to text.

2. For example, initiatives funded by the European Research Council (ERC) for established researchers have a success rate of approximately 10%. Concerning  young researchers, individual fellowships funded by the European Commission via the FP7-People program (2007-2013),  had a success rate that dropped to 14% by 2013 and was 20% in average in the whole funding period. For a full report on FP7 see here. Back to text.

3. Renowned physicist Leo Szilard, in his short story “The Marc Gable Foundation” (from the book “The Voice of Dolphins”, 1961), gave a recipe to slow down scientific progress: “You could set up a foundation, with an annual endowment of thirty million dollars. Research workers in need of funds could apply for grants, if they could mail out a convincing case. Have ten committees, each committee, each composed of twelve scientists, appointed to pass on these applications. Take the most active scientists out of the laboratory and make them members of these committees. And the very best men in the field should be appointed as chairman at salaries of fifty thousand dollars each. Also have about twenty prizes of one hundred thousand dollars each for the best scientific papers of the year. (…) First of all, the best scientists would be removed from their laboratories and kept busy on committees passing on applications for funds. Secondly, the scientific workers in need of funds would concentrate on problems which were considered promising and were pretty certain to lead to publishable results. For a few years there might be a great increase in scientific output; but by going after the obvious, pretty soon science would dry out. Science would become something like a parlor game. Some things would be considered interesting, others not. There would be fashions. Those who followed the fashion would get grants. Those who wouldn’t would not, and pretty soon they would learn to follow the fashion, too.” Thanks to Denis Guthleben (CNRS), from whom I first learned this quote and who provided me with its French translation. Back to text.

Last but not least, a big “thank you” to Sylvie Paycha for helpful comments on the text.

Second and third illustrations contain pictures taken from the following women magazines from the 50s and 60s, “Münchner Illustrierte”, “Stern” (Germany), and “Rosita” (Chile).

One thought on “Sylvie Paycha (U. of Potsdam & U. Blaise Pascal)

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