Wednesday, August 16, 2006

Poincare Conjecture

The following article gives a very nice and accurate wrte up on the solution of the Poinacre conjecture and mathematician who is different:
http://www.nytimes.com/2006/08/15/science/15math.html?_r=2&8dpc=&oref=slogin&pagewanted=print&oref=slogin
Suddenly, the topic seems to be in several blogs; may be again the influence of mainstream news. Despite the recent disquiet in several blogs about the rise of anti-scientic attitudes in USA, USA is still a power house in science and mathematics. Though Perelmam came from a Russian tradition which seems to be weakening, many of the mathematicians who contributed to the solution are Americans or educated in USA. The Americans took to Toplogy when it was young and many of the big names and large number of mathematicians working in Toplogy starting with Veblen, Alexander have been Americans. Thurston popularized Hyperbolic Geometry since the late 70's and formulated the Geometrization Conjecture of which Poincare Conjecture is a special case. The Geomtrization Conjecture is much more wide ranging and (now known to be true after Perelman) elucidates the structure of all compact three manifolds. Richard Hamilton started developing the Ricci flow techinque in the 80's specially for the purpose of attacking the Geometrzation Conjecture. Even after Perelman's three papers improving Hamilton's techniques, it took a number of powerful mathematicaians (mostly Americans) three and half years to complete the programme.
George Szpiro, who earlier wrote a popular book on the Kepler Problem is writing a popular book on the Poincare Conjecture and may come out in an year. If the preliminary chapters are any indication, it should be a very readable book.

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