Medalla Fields 1966: Ganadores

Destinatarios

1. Michael Atiyah

   Matemáticas

   Did joint work with Hirzebruch in K-theory; proved jointly with Singer the index theorem of elliptic operators on complex manifolds; worked in collaboration with Bott to prove a fixed point theorem related to the 'Lefschetz formula'.

2. Paul Joseph Cohen

   Matemáticas

   Used technique called "forcing" to prove the independence in set theory of the axiom of choice and of the generalized continuum hypothesis. The latter problem was the first of Hilbert's problems of the 1900 Congress.

3. Alexander Grothendieck

   Matemáticas

   Built on work of Weil and Zariski and effected fundamental advances in algebraic geometry. He introduced the idea of K-theory (the Grothendieck groups and rings). Revolutionized homological algebra in his celebrated ‘''Tôhoku'' paper’.

4. Stephen Smale

   Matemáticas

   Worked in differential topology where he proved the generalized Poincaré conjecture in dimension n \geq 5: Every closed, n-dimensional manifold homotopy-equivalent to the n-dimensional sphere is homeomorphic to it. Introduced the method of handle-bodies to solve this and related problems.