by Don Zagier
Friedrich Hirzebruch, who passed away on May 27, 2012, at the age of 84, was the outstanding German mathematician of the second half of the twentieth century, not only because of his beautiful and influential discoveries within mathematics itself, but also, and perhaps even more importantly, for his role in reshaping German mathematics and restoring the country’s image after the devastations of the Nazi years. The field of his scientific work can best be summed up as “Topological methods in algebraic geometry,” this being both the title of his now classic book and the aptest description of an activity that ranged from the signature and Hirzebruch–Riemann–Roch theorems to the creation of the modern theory of Hilbert modular varieties. Highlights of his activity as a leader and shaper of mathematics inside and outside Germany include his creation of the Arbeitstagung, his presidency of the Deutsche Mathematiker-Vereinigung during two especially critical periods and his later services to the European Mathematical Society and the International Mathematical Union, the founding of the Max Planck Institute for Mathematics in Bonn, and his role in preserving mathematical contacts between the Federal Republic of Germany and the German Democratic Republic and Soviet Union during the Soviet period and later in establishing close mathematical links between Germany and many other countries, notably Japan, Poland and Israel. He was a superb lecturer, teacher, and expositor of mathematics and above all a man whose human qualities were an inspiration and a model for those around him.
Accounts of several periods of Hirzebruch’s life and activities, told in his inimitable style, can be found in a number of his own articles, while more systematic accounts are given in the article by Joel Segel, the long video interview with Matthias Kreck for the archives of the Simons Foundation, and the AMS memorial article edited by Michael Atiyah and myself, which also contains portraits of him by several of his friends and associates. The exact references for all of these are given in the short bibliography at the end of this article. A book-length biography by Winfried Scharlau is also in preparation. The emphasis here is different: I would like to both recount the main stages of Hirzebruch’s career and to give a somewhat more in-depth look at some of his mathematics and at the many ways in which he helped shape the development of mathematics during his time. The article will be organized roughly chronologically, but alternating between the events and activities of his life and a description of his mathematics.
This article owes much to Michael Atiyah and Matthias Kreck, with whom I had many helpful discussions. Above all I would like to thank my wife, Silke Wimmer-Zagier, who participated in every step of the writing. Our friendship with Fritz Hirzebruch transformed both of our lives.
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