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ObituaryBill Thurston (1946–2012)John H. Hubbard (Cornell University, Ithaca, US)Photo courtesy of theCornell Math DepartmentWilliam Thurston (30 October1946–21 August 2012) wasa geometer: he taught a wholegeneration a new way to thinkabout geometry. In all the fieldsin which he worked, the “afterThurston’’ landscape is nearlyunrecognisable from what itwas “before Thurston’’.His influence still dominatesthese fields, through his ownresults and through his manystudents: he supervised 33 thesesand many of these former students are now majormathematicians in their own right. At last count (April2014), he had 177 students, grand-students and greatgrand-students.Brief biographyThurston received his bachelor’s degree from New College(now New College of Florida) in 1967. For his undergraduatethesis he developed an intuitionist foundationfor topology. Following this, he earned a doctorate inmathematics from the University of California, Berkeley,in 1972. His PhD advisor was Morris W. Hirsch and hisdissertation was on Foliations of Three-Manifolds whichare Circle Bundles.After completing his PhD, he spent a year at the Institutefor Advanced Study (where he worked with JohnMilnor and started Milnor’s interest in dynamical systems),then another year at MIT as an assistant professor.In 1974, he was appointed as a professor of mathematicsat Princeton University. In 1991, he returned toUC Berkeley as a professor of mathematics and in 1993became Director of the Mathematical Sciences ResearchInstitute. In 1996, he moved to University of California,Davis. In 2003, he became a professor of mathematics atCornell University.He did revolutionary work in foliation theory, lowdimensionaltopology, dynamics and geometric grouptheory.Foliation TheoryHis early work, in the early 1970s, was mainly about foliations.He solved so many problems that the field was“tsunamied’’: graduate students were discouraged fromits study because it appeared that Thurston would solveall the problems. Only now is the field catching up withhis contributions.At the time, finding a codimension one foliation of amanifold was a major result in its own right. He solvedthe problem completely: a compact manifold has a codi-mension one foliation if and only if its Euler characteristicis 0.He also found that any real number could be a Godbillon-Veyinvariant, a major open problem at the time.With John Mather, he showed that the cohomology ofthe group of homeomorphisms of a manifold is the samewhether one gives the group the discrete topology or thetopology of uniform convergence on compact sets. This resultwas prescient: at the time no one thought about suchquestions, but today they are central to a whole field.Results involving complex analysisIn the late 1970s and early 1980s, Thurston found a collectionof results that appear to be unrelated but areall closely connected; the connecting thread was Teichmüllertheory and complex analysis. This led Lars Ahlfors,a professor at Harvard, arguably the greatest complexanalyst of the 20th century and one of the two firstField’s Medallists, to write as his complete NSF proposalin the early 1980s: “I will continue to study the work ofBill Thurston.’’ Ahlfors was indeed awarded the grant.And Al Marden, of Minnesota, another great complexanalyst, claimed that “everyone saw that Thurston wasthe best complex analyst in the world’’, and created theGeometry Center as a playground for Thurston’s ideas.Many great things came out of the Geometry Center, inparticular the two videos Not Knot and Inside out, thatset a whole new standard for mathematical videos.The results that so electrified the mathematical communitywere the following.1. Homeomorphisms of surfaces.Every homeomorphism of a compact surface is eitherof finite order, reducible or pseudo-Anosov.2. Hyperbolization of 3-manifolds that fiber over thecircle.A compact 3-manifold that fibers over the circle hasa hyperbolic structure if and only if its monodromy ispseudo-Anosov.3. Hyperbolization of Haken manifolds.A compact Haken 3-manifold admits a hyperbolicstructure if and only if it contains no incompressibletori.4. Topological characterization of rational functions.A post-critically finite branched map of the 2-sphereto itself is equivalent to a rational function if and onlyif it admits no Thurston obstructions.Proving just one of these results requires an entire graduatecourse; each involves a multitude of totally new ideasand techniques. There are international conferences everyyear about just aspects of each of them.36 EMS Newsletter June 2014