Mathematical Digest

Short Summaries of Articles about Mathematics
in the Popular Press

"If it looks like a sphere...," by Erica Klarreich. Science News, 14 June 2003.

Klarreich's article chronicles the many attempts to settle Poincaré's conjecture, posed 99 years ago, and reports that the most recent results of Russian Grigory Perelman have yet to be verified by colleagues. Perelman claims to have found that there is a classification of three-dimensional shapes like the simple breakdown of two-dimensional shapes into spheres and tori, which, in Klarreich's words, "gives a way to identify whether a complicated shape is a distorted version of a sphere. He also claims to have proved the much broader Thurston geometrization conjecture, which considers all closed three-dimensional shapes." Perelman (Steklov Institute of Mathematics in St. Petersburg) worked mainly in self-supported seclusion and has declined to talk to the press himself until his proof is verified. Other mathematicians---Jeff Cheeger of the Courant Institute at New York University and John Milnor of SUNY Stony Brook---are quoted, praising the mathematician and his work. If Perelman has in fact proven the conjecture, he will be awarded the US$1 million prize from the Clay Mathematics Institute in Cambridge MA.

--- Annette Emerson

American Mathematical Society