Poincare conjecture

Grigory Perelman's proof of the century-old Poincare Conjecture has caused a sensation, and not just because of the brilliance of the work.In August, the Russian became the first person to turn down a Fields Medal, the highest honour in mathematics. He also seems likely to turn down a $1m prize offered by a US maths institute. For several years he worked, for the most part, alone on the Poincare Conjecture. Then, in 2002, he posted on the internet the first of three papers outlining a proof of the problem.

The Poincare is a central question in topology, the study of the geometrical properties of objects that do not change when they are stretched, distorted or shrunk. The surface of the Earth is what topology describes as a two-dimensional sphere. If one were to encircle it with a lasso of string, it could be pulled tight to a point. On the surface of a doughnut, however, a lasso passing through the hole in the centre cannot be shrunk to a point without cutting through the surface.

The Poincare Conjecture says that a three-dimensional sphere is the only enclosed three-dimensional space with no holes. Proof of the Conjecture eluded mathematicians until Perelman posted his work on the website arXiv.org.In 2005, a Chinese team consisting of Huai-Dong Cao of Lehigh University and Xi-Ping Zhu of Zhongshan University published what they claimed was "the first written account of a complete proof of the Poincare Conjecture".