Hirzebruch then held a position at
Erlangen, followed by the years 1952–54 at the
Institute for Advanced Study in
Princeton, New Jersey. After one year at
Princeton University 1955–56, he was made a professor at the
University of Bonn, where he remained, becoming director of the
Max-Planck-Institut für Mathematik in 1981. More than 300 people gathered in celebration of his 80th birthday in Bonn in 2007. The
Hirzebruch–Riemann–Roch theorem (1954) for
complex manifolds was a major advance and quickly became part of the mainstream developments around the classical
Riemann–Roch theorem; it was also a precursor of the
Atiyah–Singer index theorem and
Grothendieck's powerful generalisation. Hirzebruch's book
Neue topologische Methoden in der algebraischen Geometrie (1956) was a basic text for the 'new methods' of
sheaf theory, in
complex algebraic geometry. He went on to write the foundational papers on
topological K-theory with
Michael Atiyah, and collaborated with
Armand Borel on the theory of
characteristic classes. In his later work, he provided a detailed theory of
Hilbert modular surfaces, with
Don Zagier. He even found connections between the
Dedekind sum in
number theory and
differential topology, one of the many discoveries found between these different fields. His work influenced a generation of prominent mathematicians like
Kunihiko Kodaira,
John Milnor, Borel, Atiyah,
Raoul Bott and
Jean-Pierre Serre. Hirzebruch is famous for organizing the
Mathematische Arbeitstagung ("working meetings" in German) in
Bonn University, beginning in 1957, and the first speakers include Atiyah,
Jacques Tits,
Alexander Grothendieck,
Hans Grauert,
Nicolaas Kuiper, and Hirzebruch himself. It allowed international cooperation in the mathematical world for the last 60 years and was a major source of developments in
topology,
geometry,
group theory,
number theory as well as
mathematical physics in a few decades' time. He also established the
Max Planck Institute for Mathematics at Bonn in 1980. The institute became the place for the Arbeitstagung and Hirzebruch was its director until 1995. The second Arbeitstagung began in 1993 and continues to this day. From 1970 to 1971 he was the
Donegall Lecturer in Mathematics at
Trinity College Dublin. According to the
Mathematics Genealogy Project, Hirzebruch has supervised the doctoral studies of 52 mathematicians. Some of them include
Egbert Brieskorn,
Matthias Kreck,
Don Zagier,
Detlef Gromoll, Klaus Jänich,
Lothar Göttsche, Dietmar Arlt,
Winfried Scharlau, Walter Neumann, Wolfgang Meyer, Kang Zuo, Hans Scheerer, Erich Ossa, Klaus Lamotke, Eduardo Mendoza, Dimitrios Dais and
Friedhelm Waldhausen. Hirzebruch died at the age of 84 on 27 May 2012. ==Honours and awards==