1966 Fields Medal (2)
Reason for Award
Used technique called "forcing" to prove the independence inset theoryof theaxiom of choiceand of thegeneralized continuum hypothesis. The latter problem was the first ofHilbert's problemsof the 1900 Congress.
Laureates
Paul Joseph Cohen,
United States of America
Other works in the same year
- Did joint work withHirzebruchinK-theory; proved jointly withSingertheindex theoremof elliptic operators oncomplex manifolds; worked in collaboration withBottto prove afixed point theoremrelated to the "Lefschetz formula".
- Built on work ofWeilandZariskiand effected fundamental advances inalgebraic geometry. He introduced the idea ofK-theory(theGrothendieck groupsand rings). Revolutionizedhomological algebrain his celebrated "Tohokupaper"
- Worked indifferential topologywhere he proved the generalizedPoincaré conjecturein dimension n≥5: Every closed, n-dimensional manifoldhomotopy-equivalentto then-dimensional sphereishomeomorphicto it. Introduced the method ofhandle-bodiesto solve this and related problems.