"Science's Breakthrough of the Year: The Poincare Theorem Solved: In 2006, researchers closed a major chapter in mathematics, reaching a consensus that the elusive Poincare Conjecture, which deals with abstract shapes in three-dimensional space, had finally been solved....
"The Poincare Conjecture is part of a branch of mathematics called topology, informally known as "rubber sheet geometry" because it involves surfaces that can undergo arbitrary amounts of stretching. The conjecture, proposed in 1904 by Henri Poincare, describes a test for showing that a space is equivalent to a "hypersphere," the three-dimensional surface of a four-dimensional ball.
"In 2002, Russian mathematician Grigori Perelman, who had been working mostly incommunicado for seven years [other than the DON'T DISTRACT ME!!!!! sign on his office door--JA], posted on the Internet the first of three papers that outlined a proof of Poincare's conjecture as part of an even more ambitious result. But, after a visit to the United States in 2003, the reclusive mathematician returned to Russia and stopped replying to phone calls and emails [and cut back on blogging to just one post a day--JA]. By 2006, the others finally caught up.
Three separate teams wrote papers that filled in key missing details of Perelman's proof, and there was little doubt among his colleagues that he had solved the famous problem."
Hypersphere it is, then.
"The Poincare Conjecture is part of a branch of mathematics called topology, informally known as "rubber sheet geometry" because it involves surfaces that can undergo arbitrary amounts of stretching. The conjecture, proposed in 1904 by Henri Poincare, describes a test for showing that a space is equivalent to a "hypersphere," the three-dimensional surface of a four-dimensional ball.
"In 2002, Russian mathematician Grigori Perelman, who had been working mostly incommunicado for seven years [other than the DON'T DISTRACT ME!!!!! sign on his office door--JA], posted on the Internet the first of three papers that outlined a proof of Poincare's conjecture as part of an even more ambitious result. But, after a visit to the United States in 2003, the reclusive mathematician returned to Russia and stopped replying to phone calls and emails [and cut back on blogging to just one post a day--JA]. By 2006, the others finally caught up.
Three separate teams wrote papers that filled in key missing details of Perelman's proof, and there was little doubt among his colleagues that he had solved the famous problem."
Hypersphere it is, then.
