# Friedrich Hirzebruch

Wolf Prize Laureate in Mathematics 1988

**Friedrich Hirzebruch**

#### Affiliation at the time of the award:

**Max-Planck-Institut fuer Mathematik, Germany **

**University of Bonn****, Germany**

#### Award citation:

**“for outstanding work combining topology, algebraic and differential geometry, and algebraic number theory; and for his stimulation of mathematical cooperation and research”.**

#### Prize share:

**Friedrich Hirzebruch **

**Lars Hörmander**

The name of Professor Friedrich Hirzebruch has been connected with famous results in the areas of topology, algebraic geometry, and global differential geometry, results which all mark the beginning of important theories and which have had an enormous influence on the development of modern mathematics.

Hirzebruchws achievements include :

(1) the discovery of the signature theorem for differentiable manifolds and the formulation and proof of the Riemann-Roch theorem for algebraic varieties.

(2) the integrality theorem for characteristic classes of differentiable manifolds

(3) the proportionality theorem for complex homogeneous manifolds and (with A. Borel) the general theory of characteristic classes of homogeneous spaces of compact Lie groups.

(4) complex K-theory and its spectral sequence and various geometrical applications (with M.F. Atiyah).

(5) the “topological” proof of the Dedekind reciprocity theorem through 4-manifold theory and other fascinating relations between differential topology and algebraic number theory.

(6) the systematic study of Hilbert modular-forms and-surfaces and their relation to class numbers.

Many mathematicians have expanded and generalized Hirzebruch’s ideas. He himself has always been interested in the beautiful particular case and concrete problem, which he solves by creating new methods that combine unusual geometric, algebraic, and arithmetic intuition. Moreover, through his brilliant lecturing and writing, through the “Arbeitstagung Bonn” (yearly international meetings at the highest level), and through his dedicated work in scientific organizations he has greatly stimulated world-wide cooperation in research.