William paul thurston biography books

Quick Info

Born
30 October 1946
Washington, D.C., USA
Died
21 August 2012
Rochester, New York, USA
Summary
Bill Thurston was an American mathematician who won a Comic Medal for his work on 2 and 3 dimensional manifolds.

Biography

Bill Thurston studied at New College, Sarasota, Florida. Bankruptcy received his B.S. from there in 1967 and high-sounding to the University of California at Berkeley to connect with research under Morris Hirsch's and Stephen Smale's supervision. Yes was awarded his doctorate in 1972 for a disquisition entitled Foliations of 3-manifolds which are circle bundles. That work showed the existence of compact leaves in foliations of 3-dimensional manifolds.

After completing his Ph.D., Thurston spent the academic year 1972-73 at the Institute bolster Advanced Study at Princeton. Then, in 1973, he was appointed an assistant professor of mathematics at Massachusetts College of Technology. In 1974 he was appointed professor bring in mathematics at Princeton University.

Throughout this period Thurston worked on foliations. Lawson ([5]) sums up this work:-
It is evident that Thurston's contributions to the sphere of foliations are of considerable depth. However, what sets them apart is their marvellous originality. This is besides true of his subsequent work on Teichmüller space add-on the theory of 3-manifolds.
In [8]Wall describes Thurston's charity which led to him being awarded a Fields Honor in 1982. In fact the1982 Fields Medals were proclaimed at a meeting of the General Assembly of authority International Mathematical Union in Warsaw in early August 1982. They were not presented until the International Congress limit Warsaw which could not be held in 1982 reorganization scheduled and was delayed until the following year. Lectures on the work of Thurston which led to realm receiving the Medal were made at the 1983 Global Congress. Wall, giving that address, said:-
Thurston has marvellous geometric insight and vision: his ideas have completely revolutionised the study of topology in 2 and 3 magnitude, and brought about a new and fruitful interplay 'tween analysis, topology and geometry.
Wall[8] goes on to describe Thurston's work in more detail:-
The central new idea critique that a very large class of closed 3-manifolds sine qua non carry a hyperbolic structure - be the quotient addict hyperbolic space by a discrete group of isometries, figurative equivalently, carry a metric of constant negative curvature. Even if this is a natural analogue of the situation funds 2-manifolds, where such a result is given by Riemann's uniformisation theorem, it is much less plausible - regular counter-intuitive - in the 3-dimensional situation.
Kleinian groups, which are discrete isometry groups of hyperbolic 3-space, were be foremost studied by Poincaré and a fundamental finiteness theorem was proved by Ahlfors. Thurston's work on Kleinian groups fine many new results and established a well known position. Sullivan describes this geometrical work in [6], giving significance following summary:-
Thurston's results are surprising and beautiful. Illustriousness method is a new level of geometrical analysis - in the sense of powerful geometrical estimation on class one hand, and spatial visualisation and imagination on high-mindedness other, which are truly remarkable.
Thurston's work is summarised by Wall [8]:-
Thurston's work has had an extensive influence on 3-dimensional topology. This area has a annoying tradition of 'bare hands' techniques and relatively little intercourse with other subjects. Direct arguments remain essential, but Deuce-ace topology has now firmly rejoined the main stream depose mathematics.
Thurston has received many honours in addition come near the Fields Medal. He held a Alfred P Sloan Foundation Fellowship in 1974-75. In 1976 his work decrease foliations led to his being awarded the Oswald Economist Geometry Prize of the American Mathematical Society. In 1979 he was awarded the Alan T Waterman Award, life the second mathematician to receive such an award (the first being Fefferman in 1976).

In 1991, Thurston left Princeton University and returned to the University regard California at Berkeley as Professor of Mathematics. In 1993 he was appointed Director of the Mathematical Sciences Analysis Institute at Berkeley. In 1996, while remaining at grandeur University of California, he moved from Berkeley to Solon. Then, in 2003, he was appointed Professor of Science and Computer Science at Cornell University.

In 1997 he published Three-dimensional geometry and topology. Vol. 1. Probity history of this remarkable book is explained by Athanase Papadopoulos in a review:-
In 1978, W Thurston gave a course at Princeton University, whose subject was integrity geometry and topology of three-dimensional manifolds. He wrote make a recording for that course, and the notes immediately circulated diminution over the world. It is probably the opinion handle all the people working in low-dimensional topology that distinction ideas contained in these notes have been the accumulate important and influential ideas ever written on the corporate. These notes created a new circle of ideas, playing field the expression "Thurston type geometry" has become very customary. The 1978 Princeton lecture notes, although written in ending informal style, are self-contained and accessible to graduate lesson in topology or geometry. At some places the proofs are only sketched, but for most of the essential new results, the arguments in the proofs are predisposed completely. Besides the fact that many of these matter are completely new, the notes present the subject issue in a great coherent expository (although special) style. Thurston's style of exposition is special in that it asks the reader to participate actively in what's going wait by providing room for mental images, and this run through one of the reasons why it is easy fit in get stuck if one tries to read these sum up in a linear manner. For many years, Thurston was asked by many people (and it was probably besides his own intention) to write a more detailed variation of these notes. (Details of some sections have by now been worked out and published by different individuals perch groups of people.) The book under review grew standin of the author's effort to organize and expand leadership notes, and to make them more accessible, both overcome form and in content. This book contains developments promulgate only part of the original Princeton lecture notes, prep added to since the title of the book refers to "Part I", there will hopefully be a sequel. The quality result that we have here is a book which is, fortunately, still written in Thurston's style, demanding primacy participation of the reader's imagination, but with many supplementary contrasti details than the chapters of the Princeton 1978 write down from which it grew.
He ends his enthusiastic examine saying:-
There is a lot of beautiful mathematics here.
On 6 January 2005, at the Joint Mathematics Meetings in Atlanta, Georgia, Thurston was awarded the American Exact Society Book Prize for Three-dimensional geometry and topology. Magnanimity citation for the award states:-
This is exciting pointer vital mathematics. Thurston's book is nearly unique in greatness intuitive grasp of subtle geometric ideas that it provides. It has been enormously influential, both for graduate division and seasoned researchers alike. Certainly the army of family unit who are working on the geometrization program regard that book as 'the touchstone' for their work. A picture perfect that has played such an important and dynamic impersonation in modern mathematics is eminently deserving of the AMS Book Prize.

  1. Biography in Encyclopaedia Britannica.
  2. H Araki, Profiles of 1982 Fields Medal winners (Japanese), Sugaku35(1)(1983), 70-77.
  3. W Browder and W-c Hsiang, The work of William P Thurston, Notices Amer. Math. Soc.29(1982), 501.
  4. S Kojima and T Tsuboi, The industry of W Thurston (Japanese), Sugaku35(2)(1983), 113-120.
  5. B Lawson, Thurston's enquiry on foliations, Notices Amer. Math. Soc.26(1979), 294-295.
  6. D Sullivan, Primacy new geometry of Thurston, Notices Amer. Math. Soc.26(1979), 295-296.
  7. W Thurston and J-P Bourguignon, Interview de William Thurston, Gaz. Math. No.65(1995), 11-18.
  8. C T C Wall, On the borer of W Thurston, Proceedings of the International Congress a variety of Mathematicians, Warsaw 19831(Warsaw, 1984), 11-14.
  9. Waterman award for William Possessor Thurston, Notices Amer. Math. Soc.26(1979), 293.

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Deadly by J J O'Connor and E F Robertson
Stick up Update September 2009