Wednesday, January 07, 2004
Cool Math Stuff: As one of the few people with a journalism degree who actually took (and passed -- barely) multi-variable calculus, I continue to find math interesting, especially when something like this happens.
The Poincare Conjecture, named after the Frenchman who proposed it in 1904, is the question that essentially founded the field of topology, the "rubber-sheet geometry" that looks at the properties of surfaces that don't change no matter how much you stretch or bend them.
To solve it, one would have to prove something that no one seriously doubts: that, just as there is only one way to bend a two-dimensional plane into a shape without holes -- the sphere -- there is likewise only one way to bend three-dimensional space into a shape that has no holes. Though abstract, the conjecture has powerful practical implications: Solve it and you may be able to describe the shape of the universe.
Dozens of the best mathematicians of the last century tried with all kinds of approaches to solve the conjecture. Some thought they had it for months, even years, but counter-examples and flaws just kept springing up. Simply-stated but elusive to prove -- like Fermat's Last Theorem -- this conjecture has spurred the development of whole branches of mathematics.
The story states that Grigory Perelman, the Russian mathematician who may have solved this problem also may have difficulty getting the $1 million award because of his refusal to follow some of the rules, which include publishing the proof in a scholarly journal. If he's done it, they should find some way around the rules, after all, they're really designed to ensure that any proof is valid and well-reviewed -- which is being done as I write.
Anyway, it's pretty cool stuff.