Grigori Perelman- Poincaré Conjecture

Posted by: Avanish on: July 7, 2010

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I was scanning through an online news paper when I was surprised and amused to see a new development on “Resolution of Poincaré Conjecture” that has been one of the toughest problems for mathematicians to resolve. It was pending since past 106 years. I am not a scholar in mathematics hence won’t try to explain the problem and its importance. However, below mentioned is the description of problem as described on the website of “Clay Mathematics Institute” (One of  the premier institues of Mathematics)

“Formulated in 1904 by the French mathematician Henri Poincaré, the conjecture is fundamental to achieving an understanding of three-dimensional shapes (compact manifolds). The simplest of these shapes is the three-dimensional sphere. It is contained in four-dimensional space, and is defined as the set of points at a fixed distance from a given point, just as the two-dimensional sphere (skin of an orange or surface of the earth) is defined as the set of points in three-dimensional space at a fixed distance from a given point (the center).

Since we cannot directly visualize objects in n-dimensional space, Poincaré asked whether there is a test for recognizing when a shape is the three-sphere by performing measurements and other operations inside the shape. The goal was to recognize all three-spheres even though they may be highly distorted. Poincaré found the right test (simple connectivity, see below). However, no one before Perelman was able to show that the test guaranteed that the given shape was in fact a three-sphere.”

Dr.Grigori Perelman has solved this problem and CMI has awarded him with ‘the Millenium Prize’, that is conferred by the institute to rare scholars who manage to amaze the world with their brilliance by solving age-old problems,of which 6 are still outstanding. We are all proud to see a Mathematician of such a high calibre but what moved me deeply was Dr.Perelman’s simplicity and honesty.

Dr. Perelman has declined to accept the Millenium prize worth one million dollars mainly because he thinks CMI committee should have shared this prize with Richard Hamilton whose work helped him solve this problem.

Can you imagine his greatness? We are in a world where people don’t mind being unscrupulous crooks to be famous.The New paper also mentioned that he lives almost an ascetic life. Not to mention that he lives on his mother’s small pension and yet has courage to turn down the prize of a million dollars,for honesty.His stand shows a great strength of character. He is quite unhappy about ethical standards of mathematicians which I believe is not a surprise for any of us because we are all working hard for success/money without being able to quantify “how much is too much”. There have been several occasions when he has turned similar prizes/offers down.

Such occasions are very rare and such a personality with the character intact even under tremendous pressure/temptation is always laudable. I Thank him for his contribution and wish him luck and success for his next venture.