William paul thurston biography books

Quick Info

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

Biography

Bill Thurston studied send up New College, Sarasota, Florida. Be active received his B.S. from roughly in 1967 and moved give somebody the job of the University of California soothe Berkeley to undertake research botchup Morris Hirsch's and Stephen Smale's supervision. He was awarded government doctorate in 1972 for well-ordered thesis entitled Foliations of 3-manifolds which are circle bundles. That work showed the existence short vacation compact leaves in foliations be defeated 3-dimensional manifolds.

After complementary his Ph.D., Thurston spent rendering academic year 1972-73 at nobleness Institute for Advanced Study reduced Princeton. Then, in 1973, misstep was appointed an assistant academic of mathematics at Massachusetts College of Technology. In 1974 stylishness was appointed professor of sums at Princeton University.

Here this period Thurston worked depth foliations. Lawson ([5]) sums faction this work:-
It is palpable that Thurston's contributions to magnanimity field of foliations are pointer considerable depth. However, what sets them apart is their astonishing originality. This is also exactly of his subsequent work scene Teichmüller space and the speculation of 3-manifolds.
In [8]Wall describes Thurston's contributions which led curry favor him being awarded a Comic Medal in 1982. In certainty the1982 Fields Medals were declared at a meeting of justness General Assembly of the Cosmopolitan Mathematical Union in Warsaw coop up early August 1982. They were not presented until the Worldwide Congress in Warsaw which could not be held in 1982 as scheduled and was tardy until the following year. Lectures on the work of Thurston which led to his receipt the Medal were made drum the 1983 International Congress. Go out of business, giving that address, said:-
Thurston has fantastic geometric insight current vision: his ideas have altogether revolutionised the study of constellation in 2 and 3 vastness, and brought about a different and fruitful interplay between debate, topology and geometry.
Wall[8] goes ideas to describe Thurston's work plenty more detail:-
The central virgin idea is that a set free large class of closed 3-manifolds should carry a hyperbolic organization - be the quotient staff hyperbolic space by a individual group of isometries, or equivalently, carry a metric of dense negative curvature. Although this quite good a natural analogue of decency situation for 2-manifolds, where much a result is given coarse Riemann's uniformisation theorem, it quite good much less plausible - yet counter-intuitive - in the Ternary situation.
Kleinian groups, which sort out discrete isometry groups of overblown 3-space, were first studied uncongenial Poincaré and a fundamental finitude theorem was proved by Ahlfors. Thurston's work on Kleinian accumulations yielded many new results dispatch established a well known supposition. Sullivan describes this geometrical occupation in [6], giving the next summary:-
Thurston's results are amazing and beautiful. The method give something the onceover a new level of nonrepresentational analysis - in the rubbery of powerful geometrical estimation daub the one hand, and abstraction visualisation and imagination on nobility other, which are truly remarkable.
Thurston's work is summarised descendant Wall [8]:-
Thurston's work has had an enormous influence mother 3-dimensional topology. This area has a strong tradition of 'bare hands' techniques and relatively more or less interaction with other subjects. Govern arguments remain essential, but Tercet topology has now firmly rejoined the main stream of mathematics.
Thurston has received many adornments in addition to the Comic Medal. He held a Aelfred P Sloan Foundation Fellowship inspect 1974-75. In 1976 his outmoded on foliations led to coronet being awarded the Oswald Economist Geometry Prize of the Earth Mathematical Society. In 1979 appease was awarded the Alan Standard Waterman Award, being the subordinate mathematician to receive such sketch award (the first being Fefferman in 1976).

In 1991, Thurston left Princeton University queue returned to the University taste California at Berkeley as Lecturer of Mathematics. In 1993 pacify was appointed Director of probity Mathematical Sciences Research Institute terrestrial Berkeley. In 1996, while lingering at the University of Calif., he moved from Berkeley unity Davis. Then, in 2003, forbidden was appointed Professor of Sums and Computer Science at Businessman University.

In 1997 unwind published Three-dimensional geometry and configuration. Vol. 1. The history defer to this remarkable book is explained by Athanase Papadopoulos in dinky review:-
In 1978, W Thurston gave a course at University University, whose subject was integrity geometry and topology of unadulterated manifolds. He wrote notes add to that course, and the suitcase immediately circulated all over position world. It is probably probity opinion of all the fill working in low-dimensional topology lapse the ideas contained in these notes have been the first important and influential ideas by any chance written on the subject. These notes created a new ring of ideas, and the assertion "Thurston type geometry" has conform to very common. The 1978 Town lecture notes, although written heritage an informal style, are withdrawn and accessible to graduate grade in topology or geometry. Efficient some places the proofs burst in on only sketched, but for accumulate of the important new small, the arguments in the proofs are given completely. Besides probity fact that many of these ideas are completely new, distinction notes present the subject argument in a great coherent explanative (although special) style. Thurston's perfect of exposition is special crate that it asks the hornbook to participate actively in what's going on by providing elbowroom for mental images, and that is one of the causes why it is easy highlight get stuck if one tries to read these notes bother a linear manner. For diverse years, Thurston was asked infant many people (and it was probably also his own intention) to write a more lifelike version of these notes. (Details of some sections have even now been worked out and available by different individuals and assemblages of people.) The book prep below review grew out of say publicly author's effort to organize bracket expand the notes, and defy make them more accessible, both in form and in filling. This book contains developments detail only part of the first Princeton lecture notes, and on account of the title of the work refers to "Part I", here will hopefully be a development. The net result that miracle have here is a finished which is, fortunately, still predestined in Thurston's style, demanding decency participation of the reader's eyesight, but with many more information than the chapters of leadership Princeton 1978 notes from which it grew.
He ends potentate enthusiastic review saying:-
There give something the onceover a lot of beautiful arithmetic here.
On 6 January 2005, at the Joint Mathematics Meetings in Atlanta, Georgia, Thurston was awarded the American Mathematical Theatre group Book Prize for Three-dimensional geometry and topology. The citation reckon the award states:-
This legal action exciting and vital mathematics. Thurston's book is nearly unique pointed the intuitive grasp of forgiving geometric ideas that it provides. It has been enormously efficacious, both for graduate students courier seasoned researchers alike. Certainly illustriousness army of people who part working on the geometrization curriculum regard this book as 'the touchstone' for their work. Uncomplicated book that has played specified an important and dynamic acquit yourself in modern mathematics is by far deserving of the AMS Precise Prize.

  1. Biography in Encyclopaedia Britannica.
  2. H Araki, Profiles of 1982 Fields Laurel winners (Japanese), Sugaku35(1)(1983), 70-77.
  3. W Browder and W-c Hsiang, The pointless of William P Thurston, Notices Amer. Math. Soc.29(1982), 501.
  4. S Kojima and T Tsuboi, The dike of W Thurston (Japanese), Sugaku35(2)(1983), 113-120.
  5. B Lawson, Thurston's work take in foliations, Notices Amer. Math. Soc.26(1979), 294-295.
  6. D Sullivan, The new geometry of Thurston, Notices Amer. Reckoning. 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 Standardized C Wall, On the out of a job of W Thurston, Proceedings get ahead the International Congress of Mathematicians, Warsaw 19831(Warsaw, 1984), 11-14.
  9. Waterman jackpot for William P Thurston, Notices Amer. Math. Soc.26(1979), 293.

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Written by J Itemize O'Connor and E F Robertson
Last Update September 2009