The Shape of Space.

The article looks at Russian mathematician Grigori Perelman, who may have proved a theorem known as the Poincaré conjecture. Space is represented by a 3-manifold. The branch of mathematics that studies manifolds is topology. Perelman's analysis also completes a major research program that classifies all possible three-dimensional manifolds. A major step in closing the three-dimensional problem came in November 2002, when Perelman posted a paper on the www.arxiv.org Web server that is widely used by physicists and mathematicians as a clearinghouse of new research. The Poincaré conjecture has a $1-million reward on offer for its proof: it is one of seven such "Millennium Problems" singled out in 2000 by the Clay Mathematics Institute in Cambridge, Massachusetts.