ANNIVERSARY 100th100th BirBirthdaythday ofof HenriHenri CarCartantan

On July 8, 2004, the outstanding French mathematician Henri Cartan turned one hundred years old. The French Mathematical Society held a seminar in honour of Henri Cartan on June 28. Its programme, some of the contributions, a biography, several photos and documents can be found on the web site http://smf.emath.fr/VieSociete/Rencontres/JourneeCartan. The 100th issue of Gazette des Mathématiciens, the news publication of Société Mathématique de France, carried some tributes to Cartan, two of which are reproduced in this issue of the Newsletter along with a resolution from the International Mathematical Union (IMU). At the closing ceremony of the 4th European congress of mathe- maticians, EMS-president Sir John Kingman sent his cordial congratulations to Prof. Cartan in the name of all the participants.

Three-quarters of a century with Henri one more child. Then as research advisor, Cartan who did not propose a thesis topic, but who, Jean Cerf (CNRS, Université Paris- one day, pointed out to me the article of Sud, Orsay, France) Feldbau concerning homeomorphisms of spheres, which became the starting point of This article appeared (in French) in Gazette my thesis. des Mathématiciens 100, April 2004, p. 7-8. Even before this last period, I was suffi- The Newsletter’s thanks go to the author and ciently close to him to occasionally glean to the editor of Gazette for the permission to confidential remarks such as the following reproduce it and to Larry Siebenmann (Univ. that I remember concerning René Thom, Paris-Sud) for the translation into English. whom he ‘discovered’ before anyone else in spite of their quite different ways of thinking: In a special section in Le Monde of 3 March “Thom is a boy brimming with ideas, but 2004 entitled “Matière grise: la bataille mon- how hard it is to make him write them diale” (Grey Matter: the worldwide contest), down!” Then, over a long period: his battles, one of the first observations by the biologist mostly victorious, to, as he formulated it, E.E. Baulieu reads: “French mathematicians “raise the level of the Sorbonne in are among the very best in the world”. Above Mathematics”; his vain efforts to have a chair and beyond reservations concerning certain created at the Collège de France for André excesses perpetrated under the Bourbaki concern! I saw him again in 1939 in Weil. His precocious commitment in favour banner, it is my conviction (hopefully, one Clermont-Ferrand, where the University of of Franco-German reconciliation – in a peri- widely shared) that this high reputation is in Strasbourg had been moved following the od when that demanded lofty vision, a utopi- large measure the heritage of that group of outbreak of war, and later in La Bourboule, an vision whose realization is today one of young men who, in the thirties of the last after the defeat of June 1940, of which he had our grounds for hope in the face of seeming- century, conceived the Bourbaki project to been one of the few to voice premonitions. ly insoluble conflicts. His militance in the write a treatise that would develop mathe- Then again in Strasbourg in 1945 after the defence of Human Rights everywhere in the matics from the ground up. In this group, I abyss of war from which my own family was world, and for the construction of Europe as see, in the front rank, Henri Cartan flanked rising safe and sound, but not his. Next in a federal state, an aim to which he attaches by his friends André Weil and Jean Paris at the École Normale (rue d’Ulm), such high value. Dieudonné. when he was the professor and I a student: Jean-Pierre Serre has written: “I believe I have had the privilege to frequently cross the course for second year students, in which that the Cartan style is the finest to be found the path of Henri Cartan. The first occasion he taught us what a differentiable manifold in mathematics”. (by his own account) was in Strasbourg in was, and where, from the back of the lecture I would add that the Cartan style is the 1930; admittedly, I have forgotten this room, an unknown person (it was Alexander finest to be found in life in general. Thank encounter – I was just two years old – but I Grothendieck) ventured to dialog with him you, Monsieur Cartan, for showing, by your have retained clear memories from succeed- as an equal; the first Cartan Seminar on example, that it is possible to become with ing years. Cartan was a colleague of my Topology (1948), for which, under his guid- age ever more humane. father’s and a friend of the family, a friend ance, I presented “exposé no. 3” (thereafter who was admired, but somewhat feared for entirely written up by him alone); and fre- Jean Cerf has been Professeur and Directeur his caustic turn of mind and tongue; at the quently in his family gathering, Boulevard de Recherche (CNRS) at Université Paris- same time, his fragile health was a cause for Jourdan, on Sunday, where I was a little like Sud (Orsay), France.

20 EMS September 2004 ANNIVERSARY Personal souvenirs of Henri Cartan made us share his enthusiasm for recent Pierre Samuel (Université de Paris- discoveries or trends, e.g. the notion of a Sud, Orsay, France) functor and various topics from S. Eilenberg and his book “Homological This article appeared (in French) in algebra”. Gazette des Mathématiciens 100, April In spite of the fact that our domains of 2004, p. 13-14. The Newsletter thanks the research were quite distinct, our friendship editor of gazette for the permission to and our common concerns intensified. reproduce it and the author for providing Gradually, and especially when I became the translation into English. an environmental activist, he made me share his enthusiasm for the unification of My first meeting with Henri Cartan took Europe. place in August 1940. I was a candidate at I also admired his ceaseless actions for the Ecole Normale Supérieure and he was persecuted mathematicians. During the one of the examiners. Classmates, who May 1968 movement, we were both open had already taken the examination, told to some demands of the students, e.g. the me that he was a “nice” examiner as inclusion of personal studies in the cur- opposed to some examiners at the Ecole riculum. In 1970, we both successfully Polytechnique who tried to destabilize the requested to be transferred to the new candidates. In fact, Henri Cartan wanted to of a topic which has been the subject of Université de Paris-Sud (Orsay). There he make the candidates reveal as much as recent research, but in a field distinct from worked very hard to embody statutes pro- possible in order to find out which ones the field of the thesis itself). Cartan chose viding a good balance between teaching were the most promising. I noticed the the relations between homology and and research. same quality when, much later, we sat homotopy and spent a lot of time pointing Other mathematicians, more competent together in doctorates juries. The good out the articles to be read and making sure than me, will surely describe his results on questions he put to the candidates enabled that I was mastering this topic that was functions of several complex variables, him to predict from their answers which new to me. sheaves, algebraic topology, homological candidates would become first-rate mathe- In the meantime, I became full-fledged algebra, etc. I just know that they are fun- maticians. He was never wrong. member of Bourbaki. During the damental and that the “Séminaires I met Henri Cartan again in 1944-1945 Congresses, I admired the acuteness of Cartan”, the topics of which were chosen at the Ecole Normale Supérieure, when I Cartan’s comments and his mastery of by him each year with a remarkable intu- was preparing for the Agrégation de most branches of Mathematics. If one of ition of what would be important, awak- Mathématiques. At that time, the oral part his proposals was not accepted immediate- ened the vocations of many first-rate of this competitive examination consisted ly, he tried hard to convince other mem- mathematicians. in preparing (without documents) and giv- bers during the recesses; either they were ing lectures on classical subjects (like or the proposals got improved. When trav- Pierre Samuel is Professeur émérité at Euclidian Geometry, Analytic Geometry, elling by train to the Congresses, he also Université Paris-Sud (Orsay), France. Calculus) in front of the jury – just like in front of a high school class. We practiced lecturing in front of Henri Cartan. His crit- On the Occasion of the 100th Birthday of icisms were incisive and to the point and Henri Cartan his suggestions were very valuable. Even It is a great honour for the International Mathematical Union to associate itself with at this elementary level, we learned a lot of the hundredth birthday of Henri Cartan, on July 8, 2004. deep Mathematics from him. The son of the great mathematician Elie Cartan, his contributions to mathematics I had written to Bourbaki, pointing out have been fundamental, from several complex variables to algebraic topology and mistakes in the exercises of the published homological algebra. A member of the Bourbaki group, his participation in the reju- volumes, so he took an interest in me and venation of the French mathematical school was essential, in particular through his invited René Thom and myself as “guinea seminar held at the École Normale Supérieure. His roles as teacher and mentor were pigs” to a Bourbaki congress, which took also exceptional, and were felt well beyond national boundaries. place in July 1945 at the Ecole Normale During the critical years after the second world war, Cartan's enduring friendship Supérieure. This was one of the great with the German mathematician Heinrich Benhke, and his own personal generosity, experiences in my life. contributed greatly to the rebirth of German mathematics. He was made an honorary From 1945 to 1947, I got a research fel- member of the German Mathematical Society (DMV) in 1994. lowship at Princeton University and I His natural preoccupation with international cooperation led to his active involve- returned with a research project on inter- ment with the International Mathematical Union, of which he was President from section multiplicities in Algebraic 1967 to 1970. As such he chaired the Fields Medal Committee for the Nice Geometry, mostly inspired by Claude International Congress of Mathematicians in 1970. Chevalley. When this work was completed He has been actively involved in the defense of mathematicians who were jailed or in 1949, I presented it as a thesis to the discriminated against in their countries, and is an ardent defender of European unity. Université de Paris. I asked Henri Cartan Mathematicians worldwide unite with respect and admiration in warmly congratu- to be in the jury by giving me the subject lating Henri Cartan, great mathematician and great man, on this happy occasion. of the so-called “seconde thèse” (in which the candidate studies and gives an outline International Mathematical Union EMS September 2004 21