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Article

Title: Making apples from oranges

Author: Staff Article Type: Product Analysis
Source: The Economist, v380 n8492 p64(1) Publication Date: Aug 26, 2006
  ISSN: 0013-0613
URL of Publication: http://www.economist.com

Dr. Grigori Perelman of Russia has been awarded the Fields medal, the highest honor awarded by the International Congress of Mathematicians, for his solution of the conjecture of a late 19th century French polymath, Henri Poincare. Dr. Perelmans solution has stood for three years and is deemed correct. The conjecture is important because much math work assumes its validity. Dr. Perelman proved Poincare's conjecture with an equation usually used to model heat dissipation in 3D objects, which is called Ricci flow. Richard Hamilton of Columbia University had also learned the practicality of the heatflow model but found that under the transformation, the object could stretch out to form singularities, or spikes that were not easily manipulated into a sphere. Dr. Perelman resolved the problem by cutting off singularities, continuing with the Ricci-flow application, and then rejoining the transformed objects subsequently. He applied the Ricci flow to the rejoined piece and this smoothed the complete object into a spherea piece of lateral thinking that would surely have delighted Poincare himself. The other three medals awarded at the August 22nd ceremony went to Andrei Okhounkov of Princeton University, Terence Tao of the University of California, Los Angeles, and Wendelin Werner of the University of Paris.

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