Friedrich Hirzebruch, the leading German mathematician of the second half of the twentieth century, died May 27 at the age of 84. His early work in the 1950s on the signature theorem and on the high-dimensional Riemann-Roch problem made important use of the abstract tools introduced into topology and complex analysis by the French school and was one of the first triumphs of the conceptual mathematics that would flourish in subsequent decades. (Image: Max Planck Institute for Mathematics.) This work paved the way for many of the most important developments in mathematics in the 1960s, such as the Atiyah-Singer index theory and the work of Grothendieck in algebraic geometry. Hirzebruch also contributed to these developments, both on the side of topology, for example through his work, jointly with Michael Atiyah, on topological K-theory, and on the side of algebraic geometry, through his studies of surfaces and three-folds and of the arithmetic of Hilbert modular varieties.

Hirzebruch was the most influential scholar in the rebuilding of German mathematics after the devastations of the Nazi period and of World War II. Through his many international contacts and collaborations, through the creation of the emblematic “Arbeitstagung,” and through the establishment of the Sonderforschungsbereich Theoretische Mathematik, and, later, of the Max-Planck-Institute for Mathematics, he made Bonn into an outstanding mathematical center.

Hirzebruch’s achievements in mathematics, and in supporting and nurturing mathematics, have been widely recognized and he has been the recipient of many honors, such as the 1988 Wolf Prize, the 1989 Lobachevsky Prize, and the 2004 Cantor Medal of the German Mathematical Society. He was elected to several academies and societies including the U.S. National Academy of Sciences, the American Academy of Arts and Sciences, and the Royal Society of London. In addition, Hirzebruch served as president of the German Mathematical Society from 1961 to 1962 and again in 1990, and was founding president of the European Mathematical Society from 1990 to 1994. He was a member of the AMS since 1953. Read an interview with Hirzebruch, and see his biography on the MacTutor History of Mathematics website.