# Mathematician:William Paul Thurston

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## Mathematician

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.*

## Nationality

American

## History

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

## Theorems and Definitions

- Thurston's Geometrization Conjecture (solved in $2003$ by Grigori Perelman)
- Milnor-Thurston Kneading Theory (with John Willard Milnor)
- Misiurewicz-Thurston Points (with Michał Misiurewicz)
- Thurston's Double Limit Theorem
- Nielsen-Thurston Classification (with Jakob Nielsen)
- Earthquake Theorem
- Koebe-Andreev-Thurston Theorem (with Paul Koebe and E.M. Andreev) (also known as the Circle Packing Theorem)

Results named for **William Paul Thurston** can be found here.

## Publications

- 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**, $1990$

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## Sources

- John J. O'Connor and Edmund F. Robertson: "William Paul Thurston": MacTutor History of Mathematics archive

- 2008: David Joyner:
*Adventures in Group Theory*(2nd ed.) ... (previous) ... (next): Chapter $2$: 'And you do addition?': $\S 2.2$: Functions on vectors: $\S 2.2.5$: Determinants