William P. Thurston, 1946-2012

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William P. Thurston, whose geometric vision revolutionized topology, died August 21 at the age of 65. Within a short span of just a few years at the beginning of his career, Thurston proved so many outstanding results in foliation theory, that the whole area seemed to be finished because he had answered most of the important open problems. Then, in the mid-1970s, he turned his attention to low-dimensional topology, to which he brought a whole new set of geometric tools, most notably from hyperbolic geometry. (Photo: E. David Luria) Thurston classified surface diffeomorphisms in terms of their dynamical/geometric behavior, and he opened a new perspective on three-manifolds that became known as his geometrization program. Thurston not only formulated the framework and the crucial conjectures for this geometrization of three-manifolds, but he also proved his conjectures to be true in large classes of important cases. After further contributions by many other mathematicians, Thurston's program was finally completed around 2003 by Grigory Perelman. Thurston's geometric ideas developed initially in connection with three-dimensional topology have been extremely influential in the last few decades, both in topology and geometry, and in other fields such as group theory and complexity. Alongside Mikhael Gromov, Thurston is one of the fathers of geometric group theory.

Thurston had deep interest in mathematics teaching and communication. In the foreword to The Best Writing on Mathematics 2010 (edited by Mircea Pitici, Princeton University Press, 2011), Thurston wrote: "We humans have a wide range of abilities that help us perceive and analyze mathematical content. We perceive abstract notions not just through seeing but also by hearing, by feeling, by our sense of body motion and position. Our geometric and spatial skills are highly trainable, just as in other high-performance activities. In mathematics we can use the modules of our minds in flexible ways---even metaphorically. A whole-mind approach to mathematical thinking is vastly more effective than the common approach that manipulates only symbols."

Born in 1946, Thurston received his PhD from the University of California, Berkeley in 1972 under the direction of Morris Hirsch. He held positions at Princeton, MIT, UC Berkeley, UC Davis, and, most recently, Cornell. He served as director of the Mathematical Sciences Research Institute in Berkeley from 1992 to 1997. Thurston had a large number of outstanding students at Princeton, many of whom continue to work in the areas touched upon by his vision. He supervised 33 PhD students in total.

Thurston's honors include the Fields Medal (1982), the AMS Book Prize (2005) (since renamed the Joseph L. Doob Prize), and the AMS Steele Prize for a Seminal Contribution to Research (2012).

Wednesday August 22nd 2012 © AMS