The magic of permutations

Mathilde Bouvel, winner of the MHV Prize

The mathematician Mathilde Bouvel wins the Marie Heim-Vögtlin Prize 2017. We meet a researcher who is rather surprised at the amount of interest she has generated.

Beautiful. This adjective keeps on cropping up whenever Mathilde Bouvel talks about mathematics. Listening to her, you might think it was an objective criterion. "If something comes together without needing many words or arguments... that's beautiful." It's as simple as that. It sounds as if this quest for beauty might be an end in itself. "If a result is beautiful and self-explanatory, then it holds a promise." A bit like gymnasts who attain full mastery over their discipline and make it look like child's play. Except that the scientist strings together numbers instead of doing pirouettes.

Her field is combinatorics, a branch of mathematics linked to probability theory and statistics, or "the art of counting" as she calls it. Her special field, permutations, addresses the question "in how many ways can a set of whole numbers from 1 to n be arranged", for instance the 52 cards in a deck or the 22,000 genes that make up the human genome. Bouvel, who works at the University of Zurich, has distinguished herself particularly through her studies on pattern avoidance in permutations, which focuses on ways of arranging numbers that do not have any given order or pattern, such as a sequence of three numbers in ascending order.

The knowledge creator

Abstract? "Precisely," says the French researcher, her eyes sparkling, "it's a way of thinking that comes naturally to me. To do maths, you only need a piece of paper and a pencil ... it's like magic in a way". Not being able to directly apply her research in a practical field does not worry her. "I create knowledge and I transmit it," she explains. "It gets people thinking, and maybe one day they will find an application for it." This could happen in fields such as genomics, information technology or statistical physics. But Bouvel, who has an informatics PhD from the University of Paris VII, doesn’t seem to be in any particular hurry. "If someone had told the mathematician Joseph Fourier that his work in the early 19th century would lead to the audio compression algorithm behind the MP3 and revolutionise the music industry almost 200 years later, he would have found it hard to believe."

Not everyone shares her passion for pure mathematical research, however. Mathilde Bouvel, who has a three-year-old son and a five-month-old daughter, says no one was more astonished than she was on receiving the Marie Heim-Vögtlin Prize 2017. She won the award in recognition of her outstanding work and career progress, which she achieved in spite of interrupting or reducing her research in order to care for her family. "I'm always surprised when people outside my special field take an interest in my work," she confesses. But it also makes her very happy. "This distinction gives me so much pleasure, I am going to give it pride of place in my CV," she says laughingly. She also hopes it will give her the necessary self-confidence to fight the fear of positive discrimination that regularly grips her. "Every time my work is evaluated I ask myself if they haven't been a bit nicer to me because I'm a woman... I'm not sure I'll ever overcome this fear."

Besides inviting her colleagues to a good restaurant, she intends to use the prize money of 25,000 francs to pay for her daughter's first year of day care. "This will fit seamlessly into the concept of the MHV Prize, which is intended to help women who start a family continue their scientific careers."

Information technology and synchronised swimming

As far back as she can remember, the 34-year-old researcher always loved maths. "As a child, I was spellbound by the mathematical puzzles in my dad's science journal, even if I wasn't able to solve them yet," says Bouvel, who is the daughter of a psychiatrist and an anaesthetic nurse. The little redhead, shy and often the best pupil in her class, didn't feel particularly comfortable at school. "Children are sometimes cruel if you don't do as they do." But she found friends while pursuing her other passion, synchronised swimming, to which she devoted up to 15 hours a week. "I enjoyed this demanding sport. It requires strength, but also agility and technique." Given her keen mathematical mind, she seemed almost predestined to play the role of choreographer. "It gave me great pleasure to visualise movements that would make the transitions from square to diamond-shaped to circular formations more fluent.”

The young woman from Lorraine found her place outside the pool when she started studying science. After high school, she studied information technology in Paris and later found a job as researcher at the LaBRI (Laboratoire Bordelais de Recherche en Informatique) in Bordeaux. Here she met her future husband, also an expert in combinatorics. In 2012, he was offered an assistant professorship at the University of Zurich. "He told them he was interested, but actually he needed two professorships," she says with a laugh. Mathilde then asked for - and received - a Marie Heim-Vögtlin grant to work as a postdoc at the same institution. She will be able to keep her post as researcher after finishing the grant.

Reimagining maths

Mathilde Bouvel, who is fluent in English and Italian and can converse in German, is currently researching different topics linked to permutations and giving a weekly course on fundamental mathematical principles. She is also eager to make her subject more accessible. "I would like to change the clichéd thinking that maths is only for "geeks". With this in mind, she has taken part in summer camps for disadvantaged kids which combine maths with outdoor activities in the hope of kindling a desire for mathematical or scientific study. "The camp was first held six years ago, and we have seen some promising careers launched since then. That's great!"

Two years from now, Mathilde Bouvel and her husband are supposed to return to France, where research positions await both of them. But nothing is final yet. "We really enjoy being in Zurich and we'll stay if we get the chance." One thing is certain: wherever she is, given access to a paper and pencil, Mathilde Bouvel will continue her quest for mathematical beauty.

Between information technology and mathematics

Mathilde Bouvel, born in Nancy in 1983, is a researcher at the Institute of Mathematics of the University of Zurich. A specialist in combinatorics, she did her PhD in information technology at the University of Paris VII in 2009, with co-supervision by the department of information systems of the University of Florence. Since 2010, she has worked as a researcher at the French National Center for Scientific Research (CNRS). She is married and has two children.