Serge Lang, 1927–2005 Jay Jorgenson and Steven G. Krantz Editor’s Note: This is the first part of a two-part article. In part two, which will ap- pear in a later issue, the authors discuss the mathematical accomplishments of Serge Lang and the impact of those achievements. n September 12, 2005, the mathemat- informed through the presentation of original doc- ics community lost Serge Lang, who umentation. We have sought to bring out a full passed away in his apartment in Berke- picture of Serge’s life by inviting contributions ley, California. Lang was well known as from a large number of individuals who knew him Oa mathematician, and also as an edu- well. For the editors, it was fascinating to witness cator and political activist. The main force in Serge’s the diversity of these reminiscences; they represent life was his enthusiasm for mathematics. In a world a broad range of interests and achievements. It is of vagaries and irrational passions, he saw math- clear that, with Lang’s passing, we have lost some- ematics as a noble pursuit that represented hon- one unique and irreplaceable. esty and goodness. Within mathematics alone, After Lang’s passing, Yale University president Serge had many facets—a researcher, an expositor, Richard C. Levin wrote about Serge, “While having a popularizer, and a teacher. Generations of math- someone like this in the community is not always ematicians around the world know the name Serge easy, it is salubrious.” It is entirely possible Serge Lang through his numerous books and articles. would have agreed with this assessment, perhaps For those individuals who knew Serge, one strik- even assigning a letter grade for President Levin’s ing feature most everyone noted was the com- summary. partmentalized manner in which he showed him- To repeat, our article is an attempt to follow self to anyone: His mathematical colleagues were Lang’s insistence for an honest and complete rep- told virtually nothing about his personal life, his resentation, allowing readers to draw their own family knew very little abut his mathematical re- conclusions. With this said, we have no doubt that search, his political allies were only slightly in- a common judgment will be drawn by everyone: formed of his mathematical interests, and even With Lang’s death, the mathematical world, and be- his closest friends were unaware of each other’s yond, has lost someone without equal, and in time presence in his life. we will better understand the significance of Lang’s As we prepared this article discussing the many life. aspects of Serge’s life, we chose to follow Serge’s On Serge Lang’s retirement from Yale University method of “file-making”, where the reader is in the spring of 2005, Yale president Richard C. Levin honored him with these words: Jay Jorgenson is professor of mathematics at City College of New York and Graduate Center. His email address is Serge Lang, A.B., California Institute of [email protected]. Technology, Ph.D. Princeton University, Steven G. Krantz is professor of mathematics at Washington faculty member at Yale since 1972: Your University, St. Louis. His email address is sk@math. primary love has always been number wustl.edu. theory and you have written, by one With the assistance of numerous contributors. colleague’s estimate, over 50 books and 536 NOTICES OF THE AMS VOLUME 53, NUMBER 5 monographs, many of them concerned with this topic. Several of your mono- graphs are the only, or nearly the only, book treatments of their important sub- jects. Your famous theorem in Dio- phantine equations earned you the dis- tinguished Cole Prize of the American Mathematical Society. Your textbooks also have garnered accolades. Your cal- culus for undergraduates went through many editions in the seventies and eighties, and your algebra textbook is a standard reference in the field. So prodi- gious are you as a scholar that there are actual jokes in your profession about you. One joke goes: “Someone calls the Yale Mathematics Department, and asks for Serge Lang. The assistant who an- swers says, ‘He can’t talk now, he is writing a book. I will put you on hold.’” In your character, you are uncompro- mising in your insistence on what you perceive as logical consistency and rhetorical honesty, and you have ques- Photograph courtesy of Kenneth Ribet. tioned much received wisdom and many attention to mathematics. That attention never de- authorities in the external world as well viated (except occasionally for his politics) for the as here at Yale. You are an excellent rest of Serge Lang’s life. and deeply caring teacher, and in honor At Princeton Serge Lang fell under the spell of of this several years ago you received the great algebraic number theorist Emil Artin. the Dylon Hixon Prize for teaching in Along with John Tate, a fellow student of Artin, Lang Yale College. Your students keep in developed a passion for algebra and algebraic num- touch with you years after they gradu- ber theory. In later years, Lang and Tate co-edited ate and one has created an endowed the collected works of Artin. Lang earned his Ph.D. fund in your honor. Among your many in 1951. monographs there is one called The Lang’s first academic position was as an in- Beauty of Doing Mathematics, a collec- tructor at Princeton. Lang also had an instructor- tion of three dialogues you gave in Paris ship at the University of Chicago from 1953 to in the ‘80s. Yale is grateful to you for 1955. Lang’s first permanent position was at Co- the passion with which you understand, lumbia University beginning in 1955. In addition practice and profess the mathematical to producing some terrific mathematics and di- arts, and wishes you well as you con- recting five Ph.D. theses, Lang became passion- tinue your lifelong engagement with ately involved with the politics of the time (in their illimitable splendors. protest against the Vietnam war). Serge ultimately resigned his position at Columbia in 1971 (without Serge Lang was born near Paris on May 19, 1927. yet having arranged for another job) in protest His family lived in St. Germain en Laye. Serge’s against Columbia’s treatment of anti-war protest- mother was a concert pianist and his father was a ers. It is also remarkable that, during his tenure at businessman. His sister, with whom Serge main- Columbia, Lang directed two Princeton Ph.D. stu- tained an affectionate relationship all his life, cur- dents: Marvin Greenberg (1959) and Newcomb rently lives in Los Angeles and is a stage and film Greenleaf (1961). actor. Serge’s twin brother was a college basketball After leaving Columbia University, Serge Lang coach. landed a job at Yale University (beginning in 1972), The family decided when Serge was a teenager where he spent the remainder of his career. Lang to move to Los Angeles, California. Serge attended directed nine additional Ph.D. degrees while at Caltech as an undergraduate and finished with a Yale. He was awarded the AMS Frank Nelson Cole B.A. degree in physics in 1946. After spending 1.5 Prize (1959) for his mathematical research and the years in the U.S. Army, Serge entered graduate AMS Leroy P. Steele Prize (1999) for his writing. He school at Princeton University in philosophy. He was elected to the National Academy of Sciences abandoned that study after one year and turned his in 1985. MAY 2006 NOTICES OF THE AMS 537 Although Lang’s first mathematical loves were put it, he “put scholarship in the service of action algebra and number theory, his interests rapidly ex- to stop the nonsense.” panded to cover an astonishing panorama of mod- Serge also was a prolific writer. He wrote more ern mathematics. Areas that he influenced include than 120 research articles and sixty-one books number theory, algebraic geometry, diophantine (and this does not count multiple editions and for- geometry (in which he was a pioneer), diophantine eign translations). In fact he has 198 citations on approximation, differential geometry, analysis, hy- MathSciNet. It is amazing to examine the range of perbolic geometry, Arakelov theory (in which he was mathematical topics covered by Lang’s opus: cal- a pioneer), modular forms, and many other areas culus, real analysis, complex analysis, differential as well. The scope of Lang’s books and papers is geometry, algebra, algebraic geometry, diophan- astonishing not only for its magnitude but for its tine geometry, hyperbolic geometry, math talks breadth. for undergraduates, the heat kernel, and much, Serge Lang resigned from the AMS in 1996 in a much more. Perhaps Lang’s most famous and most dispute concerning an article in the AMS Notices by influential book is Algebra, now in its third edition. Denise Kirschner. He retired from Yale in the spring In it, Lang single-handedly reorganizes and revi- of 2005. talizes this fundamental and central subject. The It gives a sense of Serge Lang to quote from his book has had an enormous impact. formal note of acceptance for the Steele Prize Serge Lang was a man with incredible focus and (which in fact had to be heavily edited because it self-discipline. Mathematics and politics (which he was formulated in such strong language): called “troublemaking”) were his primary inter- ests, and everything else was secondary. As he I thank the Council of the AMS and the grew older, he felt that he had to conserve his en- Selection Committee for the Steele Prize, ergy and he set other interests aside. He made which I accept.