Paul Erdos, mathématicien itinérant

Undoubtedly an exceptional mathematician, Erdős had a life that one can certainly describe as "original", entirely devoted to mathematical problems. In permanent transit, from city to city, from conference to seminar, with a suitcase in hand and a theorem in each house, he thus established very many collaborations. His atypical behavior gave rise to many anecdotes, not always authentic. Gérald Tenenbaum, who was one of his co-authors, testifies to an experience sometimes disconcerting but always pleasant and enriching.

Paul Erdős solved many problems in all fields, but his primary passion is certainly number theory. He thus devoted many works to prime numbers. While most of his results, quite advanced, are difficult to popularize, some remain nevertheless accessible, at least in their formulation. This is the case, for example, in geometry, of problems of distances defined by a set of points, of the dissection of a square into squares of different sizes, or of the number of lines passing through given points.

In the field of combinatorics, Paul Erdős's contributions have been fundamental. They enabled this discipline to reach its full scope. Much current research is based on his work to study graphs in all areas in order to, for example, model number divisors, Internet infrastructure, or epidemics. One of his innovations was to rely on probability to prove results about large sets. He was also interested in random graphs in which edges are added randomly until a certain property appears.