Wednesday, August 23, 2006

The Anti-Escultura

"Grigory Perelman, a 40-year-old native of St. Petersburg, won a Fields Medal - often described as math's equivalent of the Nobel prize - for a breakthrough in the study of shapes that experts say might help scientists figure out the shape of the universe"
The story from the Wall Street Journal
"In 2002 and 2003, he posted two papers to an online archive. Usually, a posting serves a flag-planting function - "I solved this first!" - until the paper is published in a journal, which can take years. But as the math community waited for him to follow up his postings, a realization set in. Dr. Perelman, long affiliated with the Steklov Institute of Mathematics in St. Petersburg, apparently has no intention of saying more. He probably feels he proved the Poincare conjecture, mathematicians surmise, and has no interest in the $1 million bounty. (He did not respond to emailed requests for comment.)"
"Putting his proof online rather than in a journal is only one example of Dr. Perelman's iconoclasm. He admits that he gives only "a sketch of an eclectic proof of" a more general conjecture from which Poincare's follows; he never mentions Poincare. The papers are difficult to understand, and sketchy in the extreme. He asserts that one can prove something by a variation on an earlier argument, but it isn't clear what the variation is. "Perelman's papers are written in a style rather different from what would appear in a journal," says mathematician Bruce Kleiner of Yale University."
"Others have taken it upon themselves to explicate his work - and find no major flaws. Like Torah commentaries, they dwarf the original. Dr. Perelman's 2003 paper is 22 pdf pages; the 2002 paper is 39. But "Notes on Perelman's Papers," in which Prof. Kleiner and John Lott of the University of Michigan explain them almost line-by-line, is 192 pages. A book on the papers is expected to top 300 pages. A "complete proof" of Poincare, based on Dr. Perelman's breakthrough and published last month in the Asian Journal of Mathematics (which Prof. Milnor describes as throwing "a monkey wrench" into the question of who gets credit), is 328 pages long."
He put his proof online and did not answer questions nor defend it, yet other mathematicians recognized the worth of his work continued it and still gave most of the credit to Mr. Perelman. so much so that he won a Fields Medal.

Meanwhile the Gauss Prize that Dr. Escultura has claimed he won was awarded for the first time to Kiyoshi Itô

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