Actually, four mathematicians received the coveted Fields Medal for work in a variety of areas. The NY Times carries a story today that lists all of them. However, the big news concerns Grigory Perelman, a Russian mathematician, who was one of the four named today, but refused the prize.
And while the Times article gives a little more background on the problem than the AP story carried by CNN and the Wall Street Journal, they all leave something out that is of interest to mathematicians. (But of course the mathematicians are not getting their news on this subject from the AP.)
Perelman may have actually succeeded in proving Thurston's Geometrization Conjecture which includes Poincaré's Conjecture as a special case. If the proof holds, it would be quite an achievement. However, according to the Mathematical Association of America's FOCUS newsletter this month, Perelman does not seem intent on publishing his result. In fact, the preprints are not complete to the standards of mathematical literature. Two other mathematicians, Bruce Kleiner and John Lott, have attempted to fill in some of the details Perelman left out.
The Clay Mathematics Institute is offering a million dollar prize for the solution to this and other famous math problems. (The link has an even better description of the conjecture.) However, the rules state that the work must be published and withstand two years of scrutiny. So Perelman receives (but turns down) the Fields Medal, but will he win the million dollar prize from the Clay Institute? That remains to be seen.
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