Friedrich Hirzebruch (1927–2012) Michael Atiyah and Don Zagier, Coordinating Editors riedrich Hirzebruch (universally known achievements. More detailed accounts will then as Fritz) died on May 27, 2012, at the age follow in the individual articles by the two coordi- of eighty-four. He was the outstanding nating editors, with the one by Atiyah concentrating German mathematician of the postwar on the work in topology and the years before 1970, years who helped to restore mathematics and the one by Zagier on the work in number F theory and the years after 1970. The subsequent in his country after the devastation of the Nazi era. Appointed at a very early age to a full professorship articles by the invited contributors describe further at the University of Bonn, he remained there for aspects of his personality, his scientific work, and the rest of his very active life and moved the the role that he played in the mathematical lives center of gravity of German mathematics from of many individuals, organizations, and countries. the traditional centers of Göttingen and Berlin *** to Bonn. The famous “Arbeitstagungs” (more properly Arbeitstagungen), which he established in Bonn in 1957, have been running annually or biannually ever since and are a focal point of mathematics worldwide. They carried his personal imprint in their content, attendance, and style, being always broad, topical, and informal and doing much to educate succeeding generations and to foster cross-fertilization. Many new ideas and collaborations grew out of these encounters. Another lasting contribution to mathematical research in Germany and in the world is the Max Planck Institute for Mathematics, which he founded, operating on the same lines and creating bonds between mathematicians from many countries, including those that were otherwise cut off from the international scene. Although Fritz, given his multiple roles, retired several times, he remained active till the very end and was preparing to attend a conference in his honor in Poland when he was struck down. In this introduction we will give an overview of Fritz’s life and of some of his most important Friedrich Hirzebruch in 2006 at the Max Planck Michael Atiyah is honorary mathematics professor at the Institute. University of Edinburgh. His email address is m.atiyah@ed. ac.uk. Friedrich Ernst Peter Hirzebruch was born Don Zagier is a scientific member at the Max Planck Insti- on October 17, 1927, in Hamm, Germany, to tute for Mathematics in Bonn and a professor at the Collège Dr. Fritz Hirzebruch and Martha Hirzebruch (née de France in Paris. His email address is don.zagier@ Holtschmit). His father, who was the headmaster of mpim-bonn.mpg.de. a secondary school and himself an inspiring teacher DOI: http://dx.doi.org/10.1090/noti1145 of mathematics, gave him his first introduction to 706 Notices of the AMS Volume 61, Number 7 the subject—including,p when he was nine years discussed in detail in the contribution by Michael old, the proof that 2 is irrational—and the love Atiyah. of it that was to last throughout his life. This period also in- Still a teenager, Fritz was drafted into the cluded three major German army during the final year of World War II, events in Fritz’s personal but his military career was mercifully short and life: his marriage to Inge he was never sent into combat, being assigned Spitzley in August 1952 instead to an antiaircraft battery with the task of just before taking the computing artillery trajectories. He was even able boat to Princeton, and to attend some scientific courses, though when the birth of his first two his commanding officer asked him on one such children, Ulrike (1953) occasion to confirm that winter and summer are and Barbara (1956). His caused by the earth’s varying distance to the sun third child, Michael, was and Fritz dared to contradict him, pointing out that born a little later, in 1958. then the seasons in Germany and Australia would Inge, known to and loved coincide, he was punished for insubordination. In by countless mathemati- the final months of the war the Americans put him cians, was a big part of Friedrich Hirzebruch into a prisoner of war camp, and even there he everything he built up during his life. Both of ca. 1985 in Bonn. managed to do mathematics (partly on toilet paper, his daughters later studied mathematics and still preserved today). He was released in July 1945 eventually worked in related areas (Ulrike in mathe- and entered Münster University that winter. matical publishing and Barbara as a schoolteacher), The city and the university lay in ruins and while Michael was to become a doctor. Ulrike’s conditions were very difficult, with lectures being contribution to this article gives us a vivid picture held only at long intervals, but he had very good of Fritz as a father. teachers, especially Heinrich Behnke, from whom When Fritz returned to Germany in 1956 to he learned the function theory of several complex take up his duties at his new chair in Bonn, he variables, and Behnke’s assistant, Karl Stein, a had a clear ambition and a mission: to establish a former pupil of his father’s. His third teacher was center that would attract mathematicians from all Heinz Hopf, a German who had gone to Switzerland over the world. After the First World War, German before the Nazi takeover and who invited the young mathematics had been ostracized by the interna- Fritz, first to be his house guest and then for one tional community, led by France. This lasted for and a half years to be a research student at the many years and embittered relations. Fortunately, ETH in Zürich. Fritz returned to Münster with the 1945 generation of French mathematicians, the essentials of a beautiful doctoral thesis about led by Henri Cartan, was more enlightened, and the resolution of certain singularities in complex prewar mathematical friendships were rapidly surfaces. Already this earliest work showed the renewed. The Münster school members under characteristics of all of his mathematics: elegance Heinrich Behnke were welcomed back into the field and brevity of thought and exposition, an effortless by Cartan, while Fritz, part of the Behnke team, synthesis of sophisticated theoretical ideas with insights inspired by nontrivial concrete examples, and the fusion of ideas from analysis, topology, and number theory. In 1952 came the development that was not only to be a turning point in Fritz’s mathematical career but, as it transpired, to have a major influence on the later development of mathematics in Germany and in Europe: he was invited to the IAS in Princeton, where he remained for two years. At the IAS, he came into contact with many of the most brilliant mathematicians and most exciting new ideas of the period and where he made the two discoveries with which his name is most strongly associated: the Signature Theorem and the Hirzebruch-Riemann-Roch Theorem. Those years and also the early years in Bonn, when Karl Stein, Reinhold Remmert, Friedrich the core of Fritz’s research was still in topology Hirzebruch, and Henri Cartan in the 1950s. and its applications to algebraic geometry, will be August 2014 Notices of the AMS 707 direction. With his Sonderforschungsbereich, he started the envisaged visitor program on a limited basis. This turned out to be so successful that when the support ended and Fritz applied for a takeover from the Max Planck Society, his project no longer met with the former reservations, and a permanent Max Planck Institute for Mathematics was founded in Bonn in 1981 and has been flourishing ever since. Through the Arbeitstagung, the Sonderforschungsbereich, and finally the Max Planck Institute, Fritz created an extensive visitor program that he guided with his many outstanding qualities: his personal tastes in mathematics were Friedrich Hirzebruch with Gerd Faltings in the broad and generous—he was no narrow specialist; MPIM Library ca. 2000. his international contacts were extensive; his efficiency became legendary; and above all, he encouraged an informal and friendly atmosphere, played a full role in this rapprochement. So with his far removed from the traditional rigidity of German Princeton contacts, including Kodaira from Japan academia. and the new talent emerging from Paris (Serre, After about 1970 the main thrust of Fritz’s Borel, Grothendieck, …), Fritz was well placed to mathematical work slowly moved from pure topol- reintegrate German mathematics into the world ogy and algebraic geometry to the connections community. Contacts with Britain came initially of these domains with number theory. They will via the Cambridge geometry school of Hodge and be discussed in more detail in the contribution Todd and later the younger generation (Atiyah, by Don Zagier. During these years he also be- Adams, Wall, …). The division of Germany and, came more and more active and influential in more generally, the cold war partition of Europe the development of mathematics, both nationally were particularly challenging, but Fritz spent many and internationally. These activities, which will years of his life forging links between East and be described in more detail later, included most West, including notably the German Democratic notably his unflagging efforts to build up relations Republic and the Soviet Union. with the countries of the Eastern Bloc, his many He achieved his goals remarkably quickly. At contributions to rehabilitating Germany’s image Bonn University he built up the mathematics after the years of the Third Reich and to creating department to a high level, doubling the number new scientific and human bonds with Israel, his two of full professors and attracting people such presidencies of the German Mathematical Union, as Klingenberg, Tits, Brieskorn, and Harder.