1970 Fields Medal (2)
Reason for Award
Generalized work ofZariskiwho had proved for dimension ≤3 the theorem concerning the resolution of singularities on analgebraic variety. Hironaka proved the results in any dimension.
Laureates
Heisuke Hironaka, 1931年 - ）
Japan
Other works in the same year
- Generalized theGelfond-Schneider theorem(the solution to Hilbert's seventh problem). From this work he generatedtranscendental numbersnot previously identified.
- Made important advances in topology, the most well-known being his proof of the topological invariance of thePontrjagin classesof thedifferentiable manifold. His work included a study of the cohomology and homotopy of Thom spaces.
- Proved jointly with W. Feit that all non-cyclic finitesimple groupshave even order. The extension of this work by Thompson determined the minimal simple finite groups, that is, the simple finite groups whose proper subgroups aresolvable.