Jean-Pierre Serre

Jean-Pierre Serre (born 15 September 1926 in Bages, Pyrénées-Orientales) is a French mathematician whose work spans algebraic topology, algebraic geometry, and algebraic number theory. He received the Fields Medal in 1954 and, in 2003, became the first person ever awarded the Abel Prize. His parents were pharmacists. Serre attended the Lycée de Nîmes, then studied at the École Normale Supérieure in Paris from 1945 to 1948, and earned his doctorate from the Sorbonne in 1951. From 1948 to 1954 he worked at the Centre National de la Recherche Scientifique in Paris. In 1956 he was made a professor at the Collège de France, where he stayed until retiring in 1994.

His wife, Josiane Heulot-Serre, was a chemist and directed the École Normale Supérieure de Jeunes Filles. Their daughter, Claudine Monteil, worked as a French diplomat, historian, and writer. The mathematician Denis Serre is his nephew. Outside mathematics, Serre enjoys skiing, table tennis, and rock climbing in Fontainebleau.

Serre emerged early as a key figure in Henri Cartan’s school, working on algebraic topology, several complex variables, commutative algebra, and algebraic geometry. He introduced sheaf theory and homological algebra techniques. His doctoral thesis dealt with the Leray–Serre spectral sequence tied to a fibration. With Cartan, he developed methods using Eilenberg–MacLane spaces to compute homotopy groups of spheres, then a major topological problem. When awarding him the Fields Medal in 1954, Hermann Weyl praised Serre highly and noted that the prize was going to a non-analyst for the first time. Serre later shifted his research focus.

During the 1950s and 1960s, Serre collaborated with Alexander Grothendieck, who was two years younger, on foundational work largely driven by the Weil conjectures. Two major papers from Serre are *Faisceaux algébriques cohérents* (FAC, 1955), on coherent cohomology, and *Géométrie algébrique et géométrie analytique* (GAGA, 1956). Early on, Serre saw the need for more general cohomology theories to address the Weil conjectures, since coherent sheaf cohomology over finite fields could not capture as much topology as singular cohomology with integer coefficients. Around 1954–55, he explored candidate theories using Witt vector coefficients. Around 1958, Serre suggested that isotrivial principal bundles on algebraic varieties—those that become trivial after pullback by a finite étale map—were important. This idea helped inspire Grothendieck to develop étale topology and étale cohomology, tools later completed in Séminaire de géométrie algébrique (SGA) 4 and SGA 5, which ultimately enabled Pierre Deligne to prove the Weil conjectures.

From 1959 onward, Serre turned increasingly to group theory and number theory, especially Galois representations and modular forms. Among his most original contributions are: his still-open “Conjecture II” on Galois cohomology; the use of group actions on trees with Hyman Bass; the Borel–Serre compactification; results on the number of points on curves over finite fields; Galois representations in ℓ-adic cohomology and proofs that these representations often have “large” image; the concept of p-adic modular forms; and the Serre conjecture (now a theorem) on mod-p representations, which connected Fermat’s Last Theorem to mainstream arithmetic geometry. In FAC, Serre asked whether every finitely generated projective module over a polynomial ring is free. This question spurred much work in commutative algebra and was answered affirmatively by Daniel Quillen and Andrei Suslin independently in 1976, a result now called the Quillen–Suslin theorem.

Serre won the Fields Medal in 1954 at age 27, making him the youngest recipient ever. He later received the Balzan Prize in 1985, the Steele Prize in 1995, the Wolf Prize in Mathematics in 2000, and the first Abel Prize in 2003. He also earned the Gold Medal of the French National Scientific Research Centre (CNRS). He is a foreign member of many scientific academies, including those of the United States, Norway, Sweden, Russia, the Royal Society, the Royal Netherlands Academy of Arts and Sciences (1978), the American Academy of Arts and Sciences, the National Academy of Sciences, and the American Philosophical Society. He holds honorary degrees from Cambridge, Oxford, Harvard, Oslo, and other universities. In 2012 he became a fellow of the American Mathematical Society. France has awarded him its highest honors: Grand Cross of the Legion of Honour and Grand Cross of the Ordre National du Mérite.