Friedrich E.P. Hirzebruch (born 17 October 1927) is a German mathematician, working in the fields of topology, complex manifolds and algebraic geometry, and a leading figure in his generation.

He was born in Hamm, Westphalia. He studied at the University of Münster from 1945-1950, with one year at ETH Zürich. He then had a position at Erlangen, followed by the years 1952-54 at IAS in Princeton. 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.

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. 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 collaborate with Armand Borel on the theory of characteristic classes. In his later work he provided a detailed theory of Hilbert modular surfaces , working with Don Zagier.

He was awarded a Wolf Prize in Mathematics in 1988 and the Cantor medal in 2004 amongst many other honours.

See also: Atiyah-Hirzebruch spectral sequence .