Mathematician:William Paul Thurston

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American mathematician who specialised in low-dimensional topology.

Won the Fields Medal in 1982 for his work on $3$-manifolds.

Fields Medal

William Paul Thurston was awarded a Fields Medal in $\text {1982}$ at the International Congress of Mathematicians in Warsaw, Poland:

Revolutionized study of topology in $2$ and $3$ dimensions, showing interplay between analysis, topology, and geometry. Contributed the idea that a very large class of closed $3$-manifolds carry a hyperbolic structure.




  • Born: 30 October 1946 in Washington, D.C., USA
  • Died: 21 August 2012 in Rochester, New York, USA

Theorems and Definitions

Results named for William Paul Thurston can be found here.


  • 1978 -- 81: The geometry and topology of three-manifolds
  • 1982: Three-dimensional manifolds, Kleinian groups and hyperbolic geometry (Bull. Amer. Math. Soc. Vol. 6: pp. 357 – 381)
  • 1986: Hyperbolic structures on 3-manifolds. I. Deformation of acylindrical manifolds (Ann. Math. Vol. 124, no. 2: pp. 203 – 246)
  • 1988: On the geometry and dynamics of diffeomorphisms of surfaces (Bull. Amer. Math. Soc. Vol. 19, no. 2: pp. 417 – 431)
  • September 1990: Mathematical education (Notices of the AMS Vol. 37:7: pp. 844 – 850)
  • 1990: More mathematical people
  • 1994: On proof and progress in mathematics (Bull. Amer. Math. Soc. Vol. 30: pp. 161 – 177)

Notable Quotes

I think mathematics is a vast territory. The outskirts of mathematics are the outskirts of mathematical civilization. There are certain subjects that people learn about and gather together. Then there is a sort of inevitable development in those fields. You get to a point where a certain theorem is bound to be proved, independent of any particular individual, because it is just in the path of development.
-- More mathematical people, $1990$