# Oscar Zariski

Wolf Prize Laureate in Mathematics 1981

**Oscar Zariski**

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

**Harvard University, USA**

#### Award citation:

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

#### Prize share:

**Oscar Zariski **

**Lars V. Ahlfors**

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 “Zariski 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. He is a leader in studying equi-singularity, a concept he created.