Jean-Pierre Serre Biography

Jean-Pierre Serre received a Fields Medal for his work in topology, the study of geometric figures whose properties are unaffected by physical manipulation. He has received international acclaim for both his theoretical contributions to mathematics and the clarity of his writings. Serre has authored a dozen books and numerous technical articles in the areas of topology, analytic geometry, algebraic geometry, group theory, and number theory.

Serre was born in Bages, France, on September 15, 1926, to Jean and Adèle (Diet) Serre. Both pharmacists, his parents instilled in him an early interest in chemistry. That interest eventually gave way to mathematics, however, when Serre began reading his mother's calculus books. By the age of 15, he was teaching himself the fundamentals of such topics as derivatives, integrals, and series. During high school at the Lycée de Nîmes, Serre found a practical use for his mathematical talents. He told C. T. Chong and Y. K. Leong (for an article published in The Mathematical Intelligencer) that some of the older students at the boarding house where he lived had a tendency to bully him. Even though they were taking more advanced classes than he was, he pacified them by doing their math homework for them. "It was as good a training as any," he recalled. In 1944, Serre won first prize in the Concours Général, a national mathematics competition.

In 1945, having passed the competitive entrance examination, Serre entered the prestigious École Normale Supérieure in Paris. Soon after enrolling at the institution, he decided to abandon his plans to become a high-school mathematics teacher and to concentrate instead on research. It was not until then, he later told Chong and Leong, that he realized he could earn a living as a research mathematician. Serre married Josiane Heulot, a chemist, in 1948, and they have one daughter. Between 1948 and 1954, he held various positions at the Centre National de la Recherche Scientifique in Paris. His earliest research was in the field of topology; he was awarded his doctorate from the Sorbonne in this subject in 1951 after writing a dissertation on homotopy groups. After two years on the faculty of the University of Nancy, he became professor and chair of the department of algebra and geometry at the Collège de France, which remained his home throughout his career. Serre retired in 1994, assuming the position of honorary professor.

Produces Award-Winning Research

The Fields Medal, given once every four years by the International Congress of Mathematics, is intended to recognize outstanding contributions to mathematics by a researcher under age 40. It was awarded to Serre in 1954, when he was 28 years old. The citation read that Serre "achieved major results on the homotopy groups of spheres, especially in his use of the method of spectral sequences. Reformulated and extended some of the main results of complex variable theory in terms of sheaves" (a sheaf is a group of planes that pass through a common point). In fact, Serre's work on homotopy groups (classes of functions that are equivalent under a continuous deformation) was the origin of the loop space method in algebraic topology, which led quickly to numerous results. In 1952, he lectured on homotopy groups at Princeton University, discussing the topic's extension, called C-theory.

Since receiving the Fields Medal, Serre has explored other topics in mathematics, including complex variables, cohomology, algebraic geometry, and number fields. He explained to Chong and Leong that he finds it easy and natural to move gradually from one topic to another as he perceives their relationships to each other. Serre hesitates to categorize some of his work as being in one field or another, saying "such questions are not group theory, nor topology, nor number theory: they are just mathematics."

Serre is a member of the French, Dutch, Swedish, and U. S. academies of science and has been made an honorary fellow of the Royal Society of London and the London Mathematical Society. In addition to the Fields Medal, he has been awarded the Balzan Prize in 1985 and the Medaille d'Or of the Centre National de la Recherche Scientifique.

Wins Praise for Exposition

In 1995, Serre was awarded the Leroy P. Steele Prize for Mathematical Exposition by the American Mathematical Society. Specifically, the prize was given for his book A Course in Arithmetic, which was originally published in 1970. However, the citation noted: "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." It went on to mention that many of Serre's books have become standard references in their respective topic areas. In general, the citation continued, "they are alive with the breath of real mathematics, and are an example to all of how to write for effect, clarity, and impact." A Course in Arithmetic was praised for both its presentation of basic topics in algebra and its explanation of the link between function theory and the combinatorial aspects of elementary number theory, which formed a basis for modern developments in number theory and the geometry of numbers.

In his acceptance of the Steele Prize, Serre explained that the book had been a compilation of notes for various lectures he had given during the early 1960s. "Strangely enough," he said, "the different pieces fitted well together; I was especially pleased with the way algebraic and analytic arguments complemented each other." With characteristic humor, he recalled some problems, typographical as well as technical, that had plagued both the original French and English versions of A Course in Arithmetic,leading him to refer to the earlier editions as "A Curse in Arithmetic."

Another of Serre's books, Abelian L-Adic Representations and Elliptic Curves, was reissued in 1989 (it was originally published in 1968). In reviewing the book for the Bulletin of the American Mathematical Society, Kenneth Ribet noted that, although numerous advances had arisen in the field since it was first published, the original text was certainly not outmoded. "For one thing, . . . it's the only book on the subject. More importantly, it can be viewed as a toolbox which contains clear and concise explanations of fundamental facts about a series of related topics . . . . The tools introduced in this book have been, and will continue to be, extremely useful in other contexts."

In a more recent book, published in 1992, Serre presents a historically based explanation of the inverse Galois problem and explores its applications in algebraic number theory, arithmetic geometry, and coding theory. According to Michael Fried, who reviewed Topics in Galois Theory for the Bulletin of the American Mathematical Society, Serre was heard to remark at a friend's birthday celebration in 1990, "The inverse Galois problem gives us excuses for learning a lot of new mathematics."

Not only have Serre's books proven to be popular. Serre is often invited to lecture at universities around the world, including Bonn, Göttingen, Mexico, Moscow, and Singapore. He has made numerous visits to Harvard and the Institute for Advanced Study at Princeton.

When Chong and Leong asked Serre about the style of writing he prefers, he replied, "precision combined with informality!" Although noting that such writing is rare, he mentioned Michael Atiyah and John Milnor as examples of mathematicians whose work is accessible to nonmathematicians. Elaborating on his views about good exposition, he suggested that mathematical papers should contain more side remarks and open questions, which are often more interesting than the theorems themselves. "Alas," he said, "most people are afraid to admit that they don't know the answer to some question, and as a consequence they refrain from mentioning the question, even if it is a very natural one. What a pity! As for myself, I enjoy saying 'I do not know.'" Indeed, it is that admission that leads to investigation and discovery.