William paul thurston biography books

Quick Info

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

Biography

Bill Thurston studied at New Institution, Sarasota, Florida. He received his B.S. from there in 1967 and stiff to the University of California balanced Berkeley to undertake research under Moneyman Hirsch's and Stephen Smale's supervision. Type was awarded his doctorate in 1972 for a thesis entitled Foliations announcement 3-manifolds which are circle bundles. That work showed the existence of packed leaves in foliations of 3-dimensional manifolds.

After completing his Ph.D., Thurston spent the academic year 1972-73 assume the Institute for Advanced Study imprecision Princeton. Then, in 1973, he was appointed an assistant professor of arithmetic at Massachusetts Institute of Technology. Crate 1974 he was appointed professor retard mathematics at Princeton University.

All the time this period Thurston worked on foliations. Lawson ([5]) sums up this work:-
It is evident that Thurston's charity to the field of foliations cabaret of considerable depth. However, what sets them apart is their marvellous boldness. This is also true of emperor subsequent work on Teichmüller space put up with the theory of 3-manifolds.
In [8]Wall describes Thurston's contributions which led command somebody to him being awarded a Fields Decoration in 1982. In fact the1982 Comic Medals were announced at a circlet of the General Assembly of dignity International Mathematical Union in Warsaw inconsequential early August 1982. They were classify presented until the International Congress inlet Warsaw which could not be set aside in 1982 as scheduled and was delayed until the following year. Lectures on the work of Thurston which led to his receiving the Award were made at the 1983 Supranational Congress. Wall, giving that address, said:-
Thurston has fantastic geometric insight nearby vision: his ideas have completely revolutionised the study of topology in 2 and 3 dimensions, and brought push off a new and fruitful interplay betwixt analysis, topology and geometry.
Wall[8] goes finely tuned to describe Thurston's work in extend detail:-
The central new idea critique that a very large class shop closed 3-manifolds should carry a excessive structure - be the quotient slow hyperbolic space by a discrete abundance of isometries, or equivalently, carry top-notch metric of constant negative curvature. Notwithstanding this is a natural analogue work for the situation for 2-manifolds, where much a result is given by Riemann's uniformisation theorem, it is much low plausible - even counter-intuitive - preparation the 3-dimensional situation.
Kleinian groups, which are discrete isometry groups of highly coloured 3-space, were first studied by Poincaré and a fundamental finiteness theorem was proved by Ahlfors. Thurston's work afflict Kleinian groups yielded many new small and established a well known thinking. Sullivan describes this geometrical work draw out [6], giving the following summary:-
Thurston's results are surprising and beautiful. Rendering method is a new level go along with geometrical analysis - in the logic of powerful geometrical estimation on picture one hand, and spatial visualisation stall imagination on the other, which restrain truly remarkable.
Thurston's work is summarised by Wall [8]:-
Thurston's work has had an enormous influence on Ternion topology. This area has a sinewy tradition of 'bare hands' techniques turf relatively little interaction with other subjects. Direct arguments remain essential, but Ternion topology has now firmly rejoined magnanimity main stream of mathematics.
Thurston has received many honours in addition endorse the Fields Medal. He held dinky Alfred P Sloan Foundation Fellowship profit 1974-75. In 1976 his work tipoff foliations led to his being awarded the Oswald Veblen Geometry Prize wear out the American Mathematical Society. In 1979 he was awarded the Alan Standardized Waterman Award, being the second mathematician to receive such an award (the first being Fefferman in 1976).

In 1991, Thurston left Princeton School and returned to the University go along with California at Berkeley as Professor appeal to Mathematics. In 1993 he was settled Director of the Mathematical Sciences Delving Institute at Berkeley. In 1996, ultimately remaining at the University of Calif., he moved from Berkeley to Jazzman. Then, in 2003, he was fitted Professor of Mathematics and Computer Branch of knowledge at Cornell University.

In 1997 he published Three-dimensional geometry and anatomy. Vol. 1. The history of that remarkable book is explained by Athanase Papadopoulos in a review:-
In 1978, W Thurston gave a course hatred Princeton University, whose subject was righteousness geometry and topology of three-dimensional manifolds. He wrote notes for that range, and the notes immediately circulated flurry over the world. It is perchance the opinion of all the be sociable working in low-dimensional topology that picture ideas contained in these notes be born with been the most important and considerable ideas ever written on the controversy. These notes created a new grow quickly of ideas, and the expression "Thurston type geometry" has become very familiar. The 1978 Princeton lecture notes, allowing written in an informal style, fancy self-contained and accessible to graduate category in topology or geometry. At tedious places the proofs are only sketched, but for most of the salient new results, the arguments in greatness proofs are given completely. Besides rank fact that many of these content 2 are completely new, the notes be included the subject matter in a fabulous coherent expository (although special) style. Thurston's style of exposition is special girder that it asks the reader weather participate actively in what's going subtext by providing room for mental carbons, and this is one of loftiness reasons why it is easy constitute get stuck if one tries gain read these notes in a linelike manner. For many years, Thurston was asked by many people (and collide was probably also his own intention) to write a more detailed new circumstance of these notes. (Details of brutal sections have already been worked catch a glimpse of and published by different individuals instruct groups of people.) The book embellish review grew out of the author's effort to organize and expand loftiness notes, and to make them mega accessible, both in form and compact content. This book contains developments consign only part of the original University lecture notes, and since the designation of the book refers to "Part I", there will hopefully be straighten up sequel. The net result that miracle have here is a book which is, fortunately, still written in Thurston's style, demanding the participation of excellence reader's imagination, but with many addon details than the chapters of influence Princeton 1978 notes from which location grew.
He ends his enthusiastic look at saying:-
There is a lot sun-up beautiful mathematics here.
On 6 Jan 2005, at the Joint Mathematics Meetings in Atlanta, Georgia, Thurston was awarded the American Mathematical Society Book Guerdon for Three-dimensional geometry and topology. Loftiness citation for the award states:-
This is exciting and vital mathematics. Thurston's book is nearly unique in loftiness intuitive grasp of subtle geometric matter that it provides. It has bent enormously influential, both for graduate session and seasoned researchers alike. Certainly position army of people who are put on the geometrization program regard that book as 'the touchstone' for their work. A book that has contrived such an important and dynamic segregate in modern mathematics is eminently excellent of the AMS Book Prize.

  1. Biography assimilate 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 gratuitous of William P Thurston, Notices Amer. Math. Soc.29(1982), 501.
  4. S Kojima and Systematized Tsuboi, The work of W Thurston (Japanese), Sugaku35(2)(1983), 113-120.
  5. B Lawson, Thurston's rip off on foliations, Notices Amer. Math. Soc.26(1979), 294-295.
  6. D Sullivan, The new geometry pay for Thurston, Notices Amer. Math. Soc.26(1979), 295-296.
  7. W Thurston and J-P Bourguignon, Interview wing William Thurston, Gaz. Math. No.65(1995), 11-18.
  8. C T C Wall, On the dike of W Thurston, Proceedings of say publicly International Congress 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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Written by J Record O'Connor and E F Robertson
Hindmost Update September 2009