A HUNDRED years after it was posed, it seems a mathematician has finally solved one of the hardest problems known to humanity. April saw the publication of a proof of the notorious Poincar茅 conjecture, a prize that could make its author $1 million richer. What鈥檚 more, the solution may solve an even wider mathematical statement called the geometrisation conjecture, revolutionising the branch of mathematics called topology.
The Poincar茅 conjecture is based on a simple idea. If you tie a piece of elastic around the two-dimensional surface of a sphere, it can always be pulled tight to a point. This is true for no other shape of object with a 2D surface. Henri Poincar茅 claimed the analogous statement also holds true for spheres with 3D surfaces.
The geometrisation conjecture is even more ambitious, covering all 3D surfaces. If you can prove the geometrisation conjecture, Poincar茅鈥檚 conjecture is also solved.
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Grigori Perelman from the Steklov Institute of Mathematics in St Petersburg in Russia claims to have done just that. But as with all great problems, the solution is not straightforward. Months later, independent mathematicians have yet to find fault with his proof, but the prize money will only be awarded if it stands up to two years of scrutiny.
