Twenty-Five Years with Nicolas Bourbaki, 1949-1973

Abstract

T he choice of dates is dictated by personal circumstances: they roughly bound the period in which I had inside knowledge of the work of Bourbaki, first through informal contacts with several members, then as a member for twenty years, until the mandatory retirement at fifty. Being based largely on personal recollections, my account is frankly subjective. Of course, I checked my memories against the available documentation, but the latter is limited in some ways: not much of the discussions about orientation and general goals has been recorded.1 Another member might present a different picture. To set the stage, I shall briefly touch upon the first fifteen years of Bourbaki. They are fairly well documented2, and I can be brief. In the early thirties the situation of mathematics in France at the university and research levels, the only ones of concern here, was highly unsatisfactory. World War I had essentially wiped out one generation. The upcoming young mathematicians had to rely for guidance on the previous one, including the main and illustrious protagonists of the so-called 1900 school, with strong emphasis on analysis. Little information was available about current developments abroad, in particular about the flourishing German school (Gottingen, Hamburg, Berlin), as some young French mathematicians (J. Herbrand, C. Chevalley, A. Weil, J. Leray) were discovering during visits to those centers.3 In 1934 A. Weil and H. Cartan were Maitres de Conferences (the equivalent of assistant professors) at the University of Strasbourg. One main duty was, of course, the teaching of differential and integral calculus. The standard text was the Traite d’Analyse of E. Goursat, which they found wanting in many ways. Cartan was frequently bugging Weil with questions on how to present this material, so that at some point, to get it over with once and for all, Weil suggested they write themselves Armand Borel is professor emeritus at the School of Mathematics, Institute for Advanced Study, Princeton, NJ.