BBC Science — A
solution to one of the most difficult problems in mathematics was the
most important advance of 2006, according to the prestigious journal Science.
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. Dr Perelman is said
to despise self-promotion and describes himself as isolated from the
rest of the mathematical community. But his work has set the field
alight with excitement - and controversy. Terence Tao, professor of
mathematics at the University of California, Los Angeles, called
Perelman’s result “the best piece of mathematics we have seen in the
last 10 years”. Timofey Shilkin, a former colleague of Perelman at the
Steklov Mathematics Institute in St Petersburg, Russia, told BBC News:
“He definitely deserves the Fields Medal - that is my personal opinion.
I am completely sure he is a genius.” He added: “I’m afraid he is quite
a self-enclosed person. We know about him approximately the same as you
know - not too much. … 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. Since the 19th Century,
mathematicians have known that the sphere is the only enclosed
two-dimensional space with this property; but they were uncertain about
objects with more dimensions. 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. (12/22/06)
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