William Thurston facts for kids

Quick facts for kids William Thurston
Thurston in 1991
Born	William Paul Thurston (1946-10-30)October 30, 1946 Washington, D.C., United States
Died	August 21, 2012(2012-08-21) (aged 65) Rochester, New York, United States
Nationality	American
Alma mater	New College of Florida University of California, Berkeley
Known for	Thurston's geometrization conjecture Thurston's theory of surfaces Milnor–Thurston kneading theory Orbifold
Awards	Fields Medal (1982) Oswald Veblen Prize in Geometry (1976) Alan T. Waterman Award (1979) National Academy of Sciences (1983) Doob Prize (2005) Leroy P. Steele Prize (2012).
Scientific career
Fields	Mathematics
Institutions	Cornell University University of California, Davis Mathematical Sciences Research Institute University of California, Berkeley Princeton University Massachusetts Institute of Technology Institute for Advanced Study
Thesis	Foliations of three-manifolds which are circle bundles (1972)
Doctoral advisor	Morris Hirsch
Doctoral students	Richard Canary Benson Farb David Gabai William Goldman Richard Kenyon Steven Kerckhoff Yair Minsky Igor Rivin Oded Schramm Richard Schwartz Danny Calegari

William Paul Thurston (October 30, 1946 – August 21, 2012) was an American mathematician. He was a leader in the study of low-dimensional topology, which looks at shapes in 2 or 3 dimensions. He won the Fields Medal in 1982 for his important work on 3-manifolds, which are like 3D spaces.

Thurston taught mathematics at several universities. These included Princeton University, University of California, Davis, and Cornell University. He also led the Mathematical Sciences Research Institute.

Early Life and Education

William Thurston was born in Washington, D.C.. His mother, Margaret, was a seamstress, and his father, Paul, was an engineer who designed airplanes. When William was a child, he had a vision problem that made it hard for him to see depth. His mother helped him learn to understand 3D shapes from 2D pictures.

He went to New College and was part of its first class, graduating in 1967. For his college project, he explored new ideas about topology, which is a branch of mathematics. Later, he earned his doctorate in mathematics from the University of California, Berkeley in 1972. His main teacher was Morris Hirsch.

A Career in Mathematics

After finishing his Ph.D., Thurston spent a year at the Institute for Advanced Study. Then, he was an assistant professor at the Massachusetts Institute of Technology.

In 1974, Thurston became a full professor at Princeton University. He later returned to Berkeley in 1991. He was a professor there and also directed the Mathematical Sciences Research Institute (MSRI) from 1992 to 1997. He taught at UC Davis from 1996 to 2003. After that, he moved to Cornell University.

Thurston was one of the first mathematicians to use computers in his research. He encouraged another mathematician, Jeffrey Weeks, to create a computer program called SnapPea. This program helps study complex shapes.

While leading MSRI, Thurston started new educational programs. These programs are now common at many research centers. He also guided many students who went on to become important mathematicians.

Exploring 3D Shapes

Thurston's early work in the 1970s focused on something called foliation theory. This is about dividing a space into layers, like the pages of a book. He solved many big problems in this area very quickly.

The Geometrization Idea

Later, in the mid-1970s, Thurston discovered that hyperbolic geometry was very important for understanding 3-manifolds. These are like different kinds of 3D spaces. Before him, only a few examples of these spaces were known.

Thurston showed that a specific shape, the figure-eight knot, could be understood using hyperbolic geometry. He found that this knot's space could be made from two special 3D shapes called tetrahedra. These shapes fit together perfectly to create the knot's space.

He also proved that if you change a hyperbolic 3-manifold in a certain way (called Dehn filling), you usually get another hyperbolic 3-manifold. This is known as his hyperbolic Dehn surgery theorem.

Thurston then proposed his famous geometrization conjecture. This idea suggested that all 3-manifolds could be broken down into simpler pieces. Each piece would have one of eight special types of geometry. Hyperbolic geometry was the most common and complex of these. Another mathematician, Grigori Perelman, proved this conjecture true in the early 2000s.

Orbifold Theorem

Thurston also worked on orbifolds, which are like spaces with special "corners" or "edges." In 1981, he announced the orbifold theorem. This was an extension of his geometrization idea to these special spaces. Other mathematicians later completed the full proof based on Thurston's lectures.

Awards and Honors

William Thurston received many awards for his amazing work in mathematics.

• In 1976, he shared the Oswald Veblen Prize in Geometry.
• He won the Fields Medal in 1982. This is one of the highest honors in mathematics. He was recognized for changing how we study 2D and 3D shapes.
• In 2005, he won the first American Mathematical Society Book Prize. This was for his book Three-dimensional Geometry and Topology.
• In 2012, he received the Leroy P. Steele Prize for his important research.

Personal Life

William Thurston had three children, Dylan, Nathaniel, and Emily, with his first wife, Rachel Findley. His son, Dylan, also became a mathematician. With his second wife, Julian Muriel Thurston, he had two more children, Hannah Jade and Liam.

William Thurston passed away on August 21, 2012, in Rochester, New York. He had been diagnosed with a type of cancer in 2011.

Selected Publications

• William Thurston, The geometry and topology of three-manifolds, Princeton lecture notes (1978–1981).
• William Thurston, Three-dimensional geometry and topology. Vol. 1. Edited by Silvio Levy. Princeton Mathematical Series, 35. Princeton University Press, Princeton, New Jersey, 1997. x+311 pp. ISBN: 0-691-08304-5
• William Thurston, Hyperbolic structures on 3-manifolds. I. Deformation of acylindrical manifolds. Ann. of Math. (2) 124 (1986), no. 2, 203–246.
• William Thurston, Three-dimensional manifolds, Kleinian groups and hyperbolic geometry, Bull. Amer. Math. Soc. (N.S.) 6 (1982), 357–381.
• William Thurston, On the geometry and dynamics of diffeomorphisms of surfaces. Bull. Amer. Math. Soc. (N.S.) 19 (1988), no. 2, 417–431
• Epstein, David B. A.; Cannon, James W.; Holt, Derek F.; Levy, Silvio V. F.; Paterson, Michael S.; Thurston, William P. Word Processing in Groups. Jones and Bartlett Publishers, Boston, Massachusetts, 1992. xii+330 pp. ISBN: 0-86720-244-0
• Eliashberg, Yakov M.; Thurston, William P. Confoliations. University Lecture Series, 13. American Mathematical Society, Providence, Rhode Island and Providence Plantations, 1998. x+66 pp. ISBN: 0-8218-0776-5
• William Thurston, On proof and progress in mathematics. Bull. Amer. Math. Soc. (N.S.) 30 (1994) 161–177
• William P. Thurston, "Mathematical education". Notices of the AMS 37:7 (September 1990) pp 844–850

See Also