THE 1981 WOLF FOUNDATION PRIZE IN MATHEMATICS

The Wolf Prize Committee for Mathematics has unanimously decided that the award for 1981 should be equally divided among:

**Oscar Zariski Harvard University Cambridge, Massachusetts, USA**

Creator of the modern approach to Algebraic geometry, by its fusion , with Commutative algebra.

Lars V. Ahlfors

Harvard University

Cambridge, Massachusetts, USA

for seminal discoveries and the creation of powerful new methods in geometric function theory.

For over half a century the theory of functions of a complex variable was guided by the thought and work of Professor (Emeritus) Lars Ahlfors. His achievements include the proof of the Denjoy conjecture, the geometric derivation of the Nevanlinna theory, an important generalization of the Schwarz lemma, the development (with Beurling) of the method of extremal length, and numerous decisive results in the theories of Riemann surfaces, quasi-conformal mappings and Teichmuller spaces. Ahlfors celebrated finiteness theorem for Kleinian groups, and his work on the limit set, revitalized an important area of research. He is now doing pioneering work on quasiconformal deformations in higher dimensions.

Ahlfors influence was pervasive and beneficial. His methods combine deep geometric insight with subtle analytic skill; he presents them with utter clarity and simplicity. Time and again he attacked and solved the central problem in a discipline. Time and again other mathematicians were inspired by work he did many years earlier. Every complex analyst working today is, in some sense, his pupil.

Professor (Emeritus) Oscar Zariski harnessed the power of modern algebra to serve the needs of algebraic geometry. This made possible to do algebraic geometry over arbitrary fields and to apply it to deep problems in number theory. Zariski put algebraic geometry on a secure foundation, retaining the intuitive language and insight of the Italian school, in whose tradition, he was trained. He showed that purely algebraic notions, like local rings, valuations, normality, etc., are intimately connected with basic properties of algebraic ,varieties. His wonderful algebraic intuition led him to a number of fundamental theorems and concepts, including the resolution of singularities in two and three dimensions in characteristic zero, minimal models and criterion of rationality in dimension two, the 'Zariski topology', holomorphic functions in abstract algebraic geometry, the connectedness theorem and the famous 'Zari ski main theorem'.

Zariski’s papers and teachings had a tremendous impact. Algebraic geometry is one of the most active fields in modern mathematics, and perhaps half of its leading practitioners are his former students. At the age of 82 he is still the leader in studying equi-singularity, a concept he created.