# Jean-Pierre Serre

# Jean-Pierre Serre

**1926-**

**French Mathematician**

As do many mathematicians working at the frontiers of the discipline, Jean-Pierre Serre specializes in topology, the study of geometric figures whose properties are unaffected by physical manipulation. Despite the fact that he has grappled with subjects far beyond the understanding of all but a few highly trained specialists, Serre has proven his ability to write about mathematics in a lucid, easily understood style. He received the Fields Medal in 1954.

Serre was born in Bages, France, on September 15, 1926, to Jean and Adèle Diet Serre. Both parents were pharmacists and they brought their son up with a fascination for chemistry. From an early age, however, Serre took an interest in calculus and began poring over his mother's books in advanced mathematics. When he was just 15, he taught himself the fundamentals of derivatives, integers, series, and other aspects of calculus that most people only absorb—if indeed they ever do—under the guidance of an instructor. As a boarding student at the Lycée de Nîmes in high school, he kept himself from being bullied by the older students by helping them with their math homework-even though they were taking more advanced classes than he.

In 1944, the 19-year-old Serre won the Concours Général, a national mathematics competition, and in the following year he entered the highly prestigious Ecole Normale Supérieure in Paris. Up to this point he had planned to become a high school mathematics teacher, but, as he later recalled, his acceptance to the school, which had required him to pass extremely competitive examinations, gave him the confidence to believe that he could make a living as a research mathematician. In 1948 he married Josiane Heulot, a chemist, with whom he later had a daughter.

In the late 1940s and early 1950s Serre did some of his most important work in topology, the subject in which he earned his doctorate from the Sorbonne in 1951 with a dissertation on homotopy groups. He spent two years on the faculty of the University of Nancy before becoming chairman of the department of algebra and geometry at the Collège de France.

During this time, Serre investigated spectral sequences, an algebraic construction formulated by the French mathematician Jean Leray. He used them to study the relations of homology groups—that is, groups of geometric components such as points, lines, or triangles. This work suggested numerous connections between homology groups and homotopy groups (classes of functions that are equivalent under a continuous deformation), and gave him insights concerning the homotopy groups of spheres.

His work on spectral sequences as applied to sheaves (a group of planes passing through a common point) earned Serre the Fields Medal, which is awarded every four years to an outstanding mathematician under the age of 40, when he was 28 years old. Serre had already stimulated thinking among mathematicians concerning the loop space method in algebraic topology, and as early as 1952, in a lecture at Princeton University, he was discussing the extension of homotopy groups in a field he termed C-theory.

After receiving the Fields Medal, Serre went on to investigate new mathematical territories, including complex variables, cohomology, algebraic geometry, and number fields. Beginning in the early 1950s, he published a major work every few years and earned widespread recognition as a mathematician and writer. The Royal Society of London made him an honorary fellow, and he became a member of the French, Dutch, Swedish, and American academies of science. He was awarded the Medaille d'Or of the Centre Nationale de la Recherche Scientifique and received the Balzan Prize.

Serre retired from the Collège de France in 1994, assuming the position of honorary professor. In 1995 he received the Leroy P. Steele Prize for Mathematical Exposition from the American Mathematical Society. This award came in recognition for his writing, specifically the book *A Course in Arithmetic,* first published in 1970. Nevertheless, the award's citation read, "Any one of Serre's numerous other books might have served as the basis of this award. Each of his books is beautifully written, with a great deal of original material by the author, and everything smoothly polished."

**JUDSON KNIGHT**

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