Henri Poincaré v Gisha Perelman

There was an fascinating and amazing article buried in section A of today’s Chron. (Of course, I may be in a small minority thinking so.)

It’s thought that someone has solved the Poincaré Conjecture. It’s one of the seven Millennium Problems that each have a bounty of a million dollars on them. This problem was first posited 99 years ago. It would be huge to solve it!

“It is by logic we prove, it is by intuition that we invent.” – Henri Poincaré, 1904

Jan. 8, 2004, 12:24AM

Russian’s math may take prize

Associated Press

SAN FRANCISCO — A publicity-shy Russian researcher who labors in near-seclusion may have solved one of mathematics’ oldest and most abstruse problems, the Poincare Conjecture.

Evidence has been mounting since November 2002 that Grigori “Gisha” Perelman has cracked the 100-year-old problem, which seeks to explain the geometry of three-dimensional space.

If Perelman succeeded, he could be eligible for a $1 million prize offered by the Cambridge, Mass.-based Clay Mathematics Institute, formed to identify the world’s seven toughest math problems.

Mathematicians around the world have been checking Perelman’s work in search of the kind of flaws that have sunk the many other supposed solutions to a problem first presented by the French mathematician Henri Poincare in 1904.

“This is arguably the most famous unsolved problem in math and has been for some time,” said Bruce Kleiner, a University of Michigan math professor reviewing Perelman’s work.

Perelman is a researcher at St. Peterburg-based Steklov Institute of Mathematics of the Russian Academy. Colleagues describe him as brilliant and say he spent his formative years in the United States, then spent eight years quietly working in Russia without publishing any of his works in science journals.

The institute’s rules state that to collect on a proof, winners must publish their work in a science journal and withstand two years of scrutiny afterward.

Though Perelman emerged from relative seclusion last year and gave lectures to math experts at various U.S. colleges, he appears uninterested in submitting his work to a journal and has not openly discussed the prize money. He has instead posted three papers and corresponding data on a Web site.

James Carlson, the institute’s president, said that since Perelman’s work is undergoing, in effect, a peer review by the world’s brightest math minds, he may yet qualify for the prize.

Math experts are confident they soon will be able to decide if Perelman has solved the problem. They are analyzing his use of such esoteric concepts as the “Ricci flow,” “modulo diffeomorphism” and “maximal horns.”

“They are very complicated papers and there are so many moving parts to them,” said Columbia University professor John Morgan. “It’s very easy to slip up a little bit. It’s a long process.”

The Poincare Conjecture is a highly abstract problem that only the most gifted math wizards love and truly understand.

Poincare’s question was whether two-dimensional calculations could be easily modified to answer similar questions about 3-D spaces. He was pretty sure they could, but he could not prove it mathematically.

Answering the question may help scientists better understand the shape of the universe.

-b