The Fields Medal awarded in 1982 to William Thurston recognized a singular transformation in the study of three-dimensional manifolds. Born in Washington, D.C. in 1946, Thurston shifted the trajectory of topology by proving that hyperbolic geometry occupied a central position in the structure of 3-manifolds, establishing a rigorous framework that governed the field for decades thereafter.
Academic Formation and Early Work
Thurston earned his bachelor's degree from the New College of Florida in 1967. He subsequently completed his doctorate at the University of California, Berkeley in 1972, writing a thesis on the foliations of three-manifolds. Following a year at the Institute for Advanced Study and another at the Massachusetts Institute of Technology, he secured a professorship at Princeton University in 1974. During the early 1970s, he achieved breakthroughs in foliation theory, specifically disproving the prevailing belief that Godbillon–Vey invariants were restricted to integer values.
Twenty questions, eight minutes on the clock, and a percentile measured against everyone who has taken it. No sign-up.
Take the IQ test →The Geometrization Conjecture
Starting in the mid-1970s, Thurston pioneered the application of hyperbolic geometry to 3-manifolds. His work on the figure-eight knot complement, which he decomposed into ideal hyperbolic tetrahedra, provided the foundation for his hyperbolization theorem for Haken manifolds. Often termed the Monster Theorem due to its intricate proof, this work demonstrated that closed hyperbolic 3-manifolds exist in abundance. These insights culminated in the geometrization conjecture, which posits that all 3-manifolds can be partitioned into pieces belonging to eight distinct model geometries.
Institutional Leadership and Later Career
Thurston served as a professor at the University of California, Berkeley from 1992 to 1997, a period during which he also directed the Mathematical Sciences Research Institute. He later joined the faculty at the University of California, Davis, from 1996 until 2003, before concluding his career at Cornell University, where he remained from 2003 until his death in 2012. He was an early proponent of utilizing computing power for mathematical research, notably encouraging the development of the SnapPea software.
Honors and Professional Legacy
Throughout his career, Thurston received numerous distinctions, including the Oswald Veblen Prize in Geometry in 1976 and the Alan T. Waterman Award in 1979. He was elected a member of the National Academy of Sciences and the American Academy of Arts and Sciences. His work remained influential long after his 2012 death, underscored by his posthumous receipt of the Steele Prize for Seminal Contribution to Research in the same year.
Fast facts
- Born: 1946, Washington, D.C.
- Died: 2012, Rochester
- Undergraduate Degree: New College of Florida, 1967
- Doctorate: University of California, Berkeley, 1972
- Fields Medal: 1982
- Notable Professorships: Princeton, UC Berkeley, Cornell
- Primary Field: Topology
- Membership: National Academy of Sciences
Questions readers ask
What is the Geometrization Conjecture?
It is a mathematical hypothesis, formulated by Thurston, stating that every three-dimensional manifold can be decomposed into pieces that each admit one of eight specific geometric structures.
Which awards did William Thurston receive?
His honors included the Oswald Veblen Prize in Geometry (1976), the Alan T. Waterman Award (1979), the Fields Medal (1982), the Joseph Doob Prize (2005), and the Steele Prize (2012).
Achievements
- Oswald Veblen Prize in Geometry — 1976
- Fields medal — 1982
- Joseph Doob Prize — 2005
- Steele Prize for Seminal Contribution to Research — 2012
- Held posts at Princeton University, University of California, Davis and University of California, Berkeley
- Fields: topology and mathematics
.jpg)