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Samuel Eilenberg 1913--1998

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Samuel Eilenberg 1913--1998 mem-eilenberg.qxp 9/9/98 4:10 PM Page 1344 Samuel Eilenberg (1913–1998) Hyman Bass, Henri Cartan, Peter Freyd, Alex Heller, and Saunders Mac Lane Samuel Eilenberg died in New York, January 30, Sammy traveled and collaborated widely. For fif- 1998, after a two-year illness brought on by a teen years he was a member of Bourbaki. His col- stroke. He left no surviving family, except for his laboration with Steenrod produced the book Foun- wide family of friends, students, and colleagues, dations of Algebraic Topology, that with Henri and the rich legacy of his life’s work, in both math- Cartan the book Homological Algebra, both of ematics and as an art collector. them epoch-making works. The Eilenberg-Mac Lane “Sammy”, as he has long been called by all who collaboration gave birth to category theory, a field had the good fortune to know him, was one of the that both men nurtured and followed throughout great architects of twentieth-century mathematics their ensuing careers. Sammy later brought these and definitively reshaped the ways we think about ideas to bear in a multivolume work on automata topology. The ideas that accomplished this were theory. A joint work on topology with Eldon Dyer so fundamental and supple that they took on a life may see posthumous publication soon. of their own, giving birth first to homological al- Among his many honors Sammy won the Wolf gebra and in turn to category theory, structures that Prize (shared in 1986 with Atle Selberg), was now permeate much of contemporary mathemat- awarded several honorary degrees (including one ics. from the University of Pennsylvania), and was Born in Warsaw, Poland, Sammy studied in the elected to membership in the National Academy Polish school of topology. At his father’s urging, of Sciences of the USA. On the occasion of the he fled Europe in 1939. On his arrival in Princeton, honorary degree at the University of Pennsylvania Oswald Veblen and Solomon Lefschetz helped him in 1985, he was cited as “our greatest mathemat- (as they had helped other refugees) find a position ical stylist”. at the University of Michigan, where Ray Wilder was The aesthetic principles that guided Sammy’s building up a group in topology. Wilder made mathematical work also found expression in his Michigan a center of topology, bringing in such fig- passion for art collecting. Over the years Sammy ures as Norman Steenrod, Raoul Bott, Hans Samel- gathered one of the world’s most important col- son, and others. Saunders Mac Lane’s invited lec- lections of Southeast Asian art. His fame among ture there on group extensions precipitated the certain art collectors overshadows his mathemat- long and fruitful Eilenberg-Mac Lane collabora- ical reputation. In a gesture characteristically tion. marked by its generosity and elegance, Sammy in In 1947 Sammy came to the Columbia Univer- 1987 donated much of his collection to the Met- sity mathematics department, which he twice ropolitan Museum of Art in New York, which in turn chaired and where he remained till his retire- was thus motivated to contribute substantially to ment. In 1982 he was named a University Pro- the endowment of the Eilenberg Visiting Profes- fessor, the highest faculty distinction that the sorship in Mathematics at Columbia University. university confers. —Hyman Bass 1344 NOTICES OF THE AMS VOLUME 45, NUMBER 10 mem-eilenberg.qxp 9/9/98 4:10 PM Page 1345 the sense of Cheval- Henri Cartan ley and Eilenberg, Samuel Eilenberg died in New York on January cohomology of as- 30, 1998, after spending two years in a state of pre- sociative algebras). carious health. I would like to write here of the Then came the con- mathematician and especially of the friend that I cept of hyperho- gradually discovered in the course of a close col- mology. laboration that lasted at least five years and that Of course, this taught me many things. work together took I met Sammy for the first time at the end of De- several years. cember 1947: he had come to greet me at La- Sammy made sev- Guardia Airport in New York, a city buried under eral trips to my snow, where airplanes had been unable either to country houses (in take off or to land for two days. This was my first Die and in visit to the United States; it was to last five months. Dolomieu). Outside Of course, Eilenberg was not unknown to me, be- of our work hours cause since the end of the war I had begun to be he participated in interested in algebraic topology. Notably I had our family life. studied the article in the 1944 Annals of Math- Sammy knew ematics in which Eilenberg set forth his theory of how to put his singular homology (one of those theories which im- friends to work. I mediately takes on a definitive shape). I had, for think I remember my part, reflected on the “Künneth formula”, which that he persuaded gives the Betti numbers and the torsion coeffi- Steenrod to con- Photograph courtesy of Columbia University. tribute the preface cients of the product of two simplicial complexes. Samuel Eilenberg In fact, that formula amounts to a calculation of of our book, where the homology groups of the tensor product of two the evolution of the graded differential groups as a function of the ho- ideas is explained perfectly. He arranged also for mology groups of each of them. The solution in- other colleagues to collaborate in the writing of the volves not only the tensor product of the homol- chapter devoted to finite groups. Our initial pro- ogy groups of the factors but also a new functor ject of a mere article for a journal was transformed; of these groups, the functor Tor. At the time of it became a book that we would propose to a pub- my first meeting with Sammy, I was quite happy lisher and for which it would be necessary to find with telling that to him. a title that captured its content. We finally agreed This was the point of departure for our collab- on the term Homological Algebra. The text was oration, by means of postal mail at first. Then given to Princeton University Press in 1953. I do Sammy came to spend the year 1950–51 in Paris. not know why the book appeared only in 1956. He took part in my seminar at the École Normale, For fifteen years Sammy was also an active devoted that year to cohomology of groups, spec- member of the Bourbaki group. It was, I think, in tral sequences, and sheaf theory. Sammy gave two 1949 that André Weil, who was living in the United lectures on spectral sequences. Armand Borel and States, made contact with him in order to have him Jean-Pierre Serre took an active part in this semi- collaborate on a draft for use by Bourbaki, entitled nar also. “SEAW Report on Homotopy Groups and Fiber Independently of the seminar, Sammy and I had Spaces”. It is therefore very natural that Eilenberg work sessions with the aim of writing an article that was invited to the Congress that Bourbaki held in would develop some of the new ideas born out of October 1950. He was immediately appreciated the Künneth formula. We went from discovery to and became a member of the group under the discovery, Sammy having an extraordinary gift for name “Sammy”. It is necessary to say that he mas- formulating at each moment the conclusions that tered the French language perfectly, which he had would emerge from the discussion. And it was al- learned when he was living in his native Poland. ways he who wrote everything up as we went along The collaboration of Sammy with Bourbaki in precise and concise English. After the notion of lasted until 1966. He took part in the summer satellites of a functor came that of derived functors, meetings, which lasted two weeks. He knew ad- with their axiomatic characterization. Gradually the mirably how to present his point of view, and he theory included several existing theories (coho- often made us agree to it. mology of groups, cohomology of Lie algebras, in The above gives only a faint idea of Samuel Henri Cartan is professor emeritus of mathematics at Eilenberg’s mathematical activity. The list made in Université de Paris XI. This segment is translated and 1974 of his publications comprises, besides 4 adapted from the Gazette des Mathématiciens by per- books, 111 articles; the first 37 articles are before mission. his emigration from Poland to the United States in NOVEMBER 1998 NOTICES OF THE AMS 1345 mem-eilenberg.qxp 9/9/98 4:10 PM Page 1346 1939, and almost all are written in French. He was position for him was found at the University of not yet twenty years old when he began to publish. Michigan. There Ray Wilder had an active group of The celebrated articles written with S. Mac Lane ex- topologists, including Norman Steenrod, then a tended from 1942 to 1954. The list of his other col- recent Princeton Ph.D. Sammy immediately fitted laborators is long: N. E. Steenrod, J. A. Zilber, in, did collaborative research (for example, with T. Nakayama, T. Ganea, J. C. Moore, G. M. Kelly, to Wilder, O. G. Harrold, and Deane Montgomery). cite only the main ones. Starting in 1966, Sammy His 1940 paper in the Annals of Mathematics for- became actively interested in the theory of au- mulated and codified the ideas of the “obstruc- tomata, which led him to write a book entitled Au- tions” recently introduced by Hassler Whitney.
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