Mathematics is often perceived by the general public as a solitary pursuit, an exercise in pure logic carried out in the isolation of the researcher in front of his blackboard. However, the day-to-day work of mathematicians bears witness to an ongoing dialogue between disciplines, researchers and ideas, culminating in original solutions.
Meet Pegah Pournajafi*, mathematician at the Collège de France.
A specialist in Combinatorics, Pegah Pournajafi's early work explored the many ramifications of graph theory. Graphs are abstract models of network designs connecting objects. " You can model many things with graphs ," she explains. Behind the simplicity of a seemingly playful problem-" I want to hand out colorful T-shirts to a group of friends, but no friend should wear the same color " - lies a complex mathematical structure, with applications far beyond play. Graph theory is used in a variety of fields, from urban transport planning to connections between users of social networks. And yet, the game did indeed shape the researcher's passion for mathematics. " The mathematical problems my father used to set me as a child created this desire for theoretical discussion through exchanges that were as amusing as they were stimulating ", she explains.
Today, the researcher is working on a number of problems exploring the interactions of Combinatorics, a branch of mathematics that determines the number of possible combinations of objects into sets and subsets, with other branches of mathematics, such as algebra and geometry. " Since I knew graph theory, I was able to ask new questions that had not yet been explored. " This ability to navigate from one field to another perfectly illustrates his vision of mathematics as a fluid space, where every advance is based on a constant dialogue between intuition and rigor. " Isolved one of my thesis problems thanks to a discussion with a mathematician friend in a completely different field from mine ", she recalls. For the researcher, the creative side of mathematics is also embodied in these conversations that encourage the imagination: " Mathematicians create worlds that don't exist. "
Opening up mathematics
Mathematics should not be reduced to a rigid sequence of theorems confined to watertight domains. On the contrary, it's a field where concepts circulate freely, where a problem in algebra can find an elegant solution in Combinatorics, where an intuition from geometry suddenly illuminates a question in analysis. " When you attend a seminar in a field you know nothing about, you listen, suddenly an idea pops up, and you realize you can use it in your work ! " This decompartmentalization, which she considers essential, encourages unexpected advances and feeds more fruitful research.
Far from the image of the mathematician alone at her blackboard, Pegah Pournajafi insists on the deeply collaborative dimension of research. " We walk into a room together, we write on the blackboard, we brainstorm. My reasoning may be wrong, but my colleague will correct it and propose a proof. " Exchanges are not confined to university offices. They take place on a train, at a conference, in an informal exchange in the corridor. " Even if you work alone, your work has meaning because it connects with that of others ", she stresses. For while each mathematician charts his or her own path, it's the bridges between these paths that enable great advances.
Being a mathematics researcher
Originally from Iran, Pegah Pournajafi has found France a fertile breeding ground for her research. But she doesn't shy away from the specific challenges of being a woman in a field that is still largely male-dominated. " When you attend a conference, if there are sixty participants, there are sometimes only three women. " If mathematics is to thrive on dialogue, all voices must be heard. Aware of the obstacles, she remains optimistic. " The mathematical community in France is benevolent and open ", she asserts. This is undoubtedly one of the paradoxes of the discipline. As it becomes more complex, it opens up, and it is in this openness that it finds its true impetus and resolves its questions. A question that supports the need for the collective spirit of mathematics. By decompartmentalizing fields and strengthening exchanges between its various players, Pegah Pournajafi is paving the way for a richer, more inclusive mathematical future.
*Pegah Pournajafi is a researcher on the Prof. Timothy Gowers Combinatorics Chairand winner of The Hugot Foundation of Collège de France Award 2024.
