Jean-Pierre Serre - Biography

Jean-Pierre Albert Achille Serre Quick Info Born 15 September 1926 Bages, Pyrénées Orientales, France Summary Jean-Pierre Serre is a French mathematician who has made important contributions to algebraic topology, algebraic geometry, and algebraic number theory. He was a member of Bourbaki. Biography Jean-Pierre Serre's parents, Jean Serre and Adèle Diet, were both pharmacists. His mother Adèle had been a pharmacy student at the University of Montpellier and she took a calculus course (just for fun, she said, since she liked mathematics). In 1932 Jean-Pierre began his primary school education at the École de Vauvert. It was at the age of seven or eight that he began to enjoy doing mathematics. In 1937 he moved from the École de Vauvert to study at the Lycée Alphonse-Daudet in Nîmes. His mother had kept the calculus books that she had bought when she took the mathematics course at the University of Montpellier and Jean-Pierre began to learn mathematics from these books [9]:- When I was 14 or 15, I used to look at these books, and study them. This is how I learned about derivatives, integrals, series and such (I did that in a purely formal manner - Euler's style so to speak: I did not like, and did not understand, epsilons and deltas.) At this time mathematics wasn't the only subject he enjoyed. Although he never took much interest in physics, he enjoyed chemistry which was a topic that his parents, being pharmacists, knew a lot about. In particular his father had a lot of chemistry books which Jean-Pierre read when he was fifteen or sixteen years old. In fact he enjoyed one of these books so much that he kept a copy of it - this was the book "Les colloïdes", Gauthier-Villars, 1922 by Jacques Duclaux (1877-1978). However, as he went deeper into chemistry he became less enthusiastic about the subject and became more convinced that mathematics was the topic for him. He spoke about his time at the Lycée Alphonse-Daudet in Nîmes in [9]:- In high school I used to do problems for more advanced classes. I was then in a boarding house in Nimes, staying with children older than I was, and they used to bully me. So to pacify them, I used to do their mathematics homework. It was as good a training as any. At the Lycée in Nîmes in the year 1943-44 he had a good mathematics teacher who was nicknamed "Le Barbu" since he had a beard. He was [9]:- ... very clear, and strict; he demanded that every formula and proof be written neatly. He coached Serre for the Concours General in mathematics which he sat in 1944 and was placed first. Also in 1944 he sat the Concours General in physics but since he spent the whole six-hour examination using an incorrect formula, he scored poorly. Serre was awarded his Bachelier ès sciences et ès lettres in 1944 but remained at the Lycée until 1945 preparing to take the entrance examination to enter the École Normale Supérieure in Paris. While at the Lycée [9]:- I had no idea one could make a living by being a mathematician. It was only later I discovered one could get paid for doing mathematics! What I thought at first was that I would become a high school teacher: this looked natural to me. Then, when I was 19, I took the competition to enter the École Normale Superieure, and I succeeded. Once I was at "l'École", it became clear that it was not a high school teacher I wanted to be, but a research mathematician. From 1945 to 1948 Serre studied at the École Normale Supérieure and was awarded his Agrégé des sciences mathematique in 1948. At this time he became the youngest member of the Bourbaki group of mathematicians. This group included those who had been involved since the mid 1930s such as Henri Cartan, Claude Chevalley, Jean Delsarte, Jean Dieudonné and André Weil. Around the time that Serre joined the Bourbaki group, others such as Roger Godement, Pierre Samuel and Jacques Dixmier also joined. Serre married Josiane Heulot (1922-2004) on 10 August 1948; they had one child, a daughter Claudine born on 29 November 1949. Josiane was an organic chemist working at the École Normale Supérieure de jeunes filles at Sèvres. From 1948 to 1954 Serre held positions at the Centre National de la Recherche Scientifique in Paris, first as attaché and then as chargé de recherches. In 1948-49 he attended Henri Cartan's seminar which was on algebraic topology and sheaf theory. Also attending Henri Cartan's seminar in that year were Claude Chevalley, Jean Delsarte, Jean Dieudonné, Roger Godement, Laurent Schwartz, and André Weil. One of Serre's fellow students was Alexander Grothendieck and he also attended the seminar. Grothendieck and Serre became friends at this time. Serre was advised by Henri Cartan but [18]:- ... Cartan did not suggest research topics to his students: they had to find one themselves; after that he would help them. This is what happened to me. I found that Leray's theory (about fibre spaces and their spectral sequence) could be applied to many more situations than was thought possible and that such an extension could be used to compute homotopy groups. He was awarded his doctorate from the Sorbonne in 1951 for his thesis Homologie singulière des espaces fibrés. Applications Ⓣ. In 1952 he went to Princeton where he lectured on the results in his thesis and also on CC-theory which was the continuation of this work. While in Princeton he attended the Artin-Tate seminar on class field theory. Returning to Paris, he again attended the Henri Cartan seminar which, in that year, was discussing functions of several complex variables and Stein manifolds. The ideas he met in this seminar motivated the direction of his research. In 1953-54 he was maître de recherches at the Centre National de la Recherche Scientifique. In 1954 Serre went to the University of Nancy where he worked until 1956. From 1956 he held the chair of Algebra and Geometry in the Collège de France until he retired in 1994 when he became an honorary professor. He describes in [16] his inaugural lecture at the Collège de France:- I was a young man, about 30, when I arrived at the Collège. The inaugural lecture was almost like an oral examination in front of professors, family, mathematician colleagues, journalists etc. I tried to prepare it, but after a month I only managed to write half a page. When the day of the lecture came, it was quite a tense moment. I started by reading the half page I had prepared and then I improvised. A few months later he was informed that inaugural lectures were published and he was asked to supply a transcript. As the lecture had been improvised he had no transcript but tried to recreate it by giving an impromptu lecture into a tape recorder and then giving the tape to a secretary to type up. However, the secretary said that the recording was inaudible. Serre then gave up and his inaugural lecture was never published. This makes it unique as every other inaugural lecture at the Collège de France that has been published. He has also spoken about his teaching career at the Collège de France (see for example [16]):- Teaching at the Collège is both a marvellous and a challenging privilege. Marvellous because of the freedom of choice of subjects and the high level of the audience: Centre National de la Recherche Scientifique researchers, visiting foreign academics, colleagues from Paris and Orsay - many regulars who have been coming for 5, 10 or even 20 years. It is challenging too: new lectures have to be given each year, either on one's own research (which I prefer), or on the research of others. Since a series of lectures for a year's course is about 20 hours, that's quite a lot. His permanent position in the Collège de France allowed Serre to spend quite a lot of time making research visits. In particular he spent time at the Institute for Advanced Study at Princeton (in 1955, 1957, 1959, 1961, 1963, 1967, 1970, 1972, 1978, 1983, 1999) and at Harvard University (in 1957, 1964, 1974, 1976, 1979, 1981, 1985, 1988, 1990, 1992, 1994, 1995, 1996). Here is a list of the universities where Serre delivered courses (in alphabetical order): Algiers (1965, 1966), Bonn (1976), CalTech (1997), Eugene (1998), Geneva (1999), Göttingen (1970), McGill (1967), Mexico (1956), Moscow (1961, 1984), Princeton (1952, 1999), Singapore (1985), U.C.L.A. (2001), Utrect (1974). Serre's early work was on spectral sequences. A spectral sequence is an algebraic construction like an exact sequence, but more difficult to describe. Serre did not invent spectral sequences, these were invented by the French mathematician Jean Leray. However, in 1951, Serre applied spectral sequences to the study of the relations between the homology groups of fibre, total space and base space in a fibration. This enabled him to discover fundamental connections between the homology groups and homotopy groups of a space and to prove important results on the homotopy groups of spheres. Serre's work led to topologists realising the importance of spectral sequences. The Serre spectral sequence provided a tool to work effectively with the homology of fiberings. For this work on spectral sequences and his work developing complex variable theory in terms of sheaves, Serre was awarded a Fields Medal at the International Congress of Mathematicians in 1954. Serre's theorem led to rapid progress not only in homotopy theory but in algebraic topology and homological algebra in general. As an example of Serre's approach to attacking a problem, we quote from the interview [9]. Here Serre was answering a question about the importance of inspiration:-