Enough of Geometry, Let us See if Donuts are Like Frogs.

A couple of weeks ago, while Susan and I drove to San Diego, we heard a story on the radio concerning an interesting event in mathematics. You see, a prominent Russian mathematician has claimed that he has proved Poincaré's Conjecture.

Poincaré's Conjecture is a topological claim; the famous mathematician was concerned with the nature of shapes and spaces and the shapes of spaces-- topology.

While the idea of topology is a bit hard to get across, we can picture it like so: what makes a sphere a sphere and not a torus? Or, how is a donut like a frog? Well, a donut is like a frog in that each has one continuous hole through it (disregarding nostrils, I suppose (not that donuts have nostrils)).

That's the essence of Poincaré's Conjecture. Stated more mathily, if all closed lines on a surface can be contracted to a point without cutting the surface or the line, the surface is a sphere.

From this article in the Times, we learn that this fellow seems to have proved a more general result, and in the process, completes the proof of P's C. It seems to be fiendishly complicated, and 1000 pages long, so they may be a while yet in verifying it... but apparently the prognosis is excellent.

On another note, I'd like to say that this sentence is strange:

Asked about Dr. Perelman’s pleasures, Dr. Anderson said that he talked a lot about hiking in the woods near St. Petersburg looking for mushrooms.

"Asked about [his] pleasures?" Really? That phrasing sounds like someone's been reading too much high-falutin' English literature.