| Subject: The Poincare Conjecture, solved |
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Kashmir
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Date Posted: 13:29:11 05/08/03 Thu
A Russian mathematician claims to have proved the Poincare Conjecture, one of the most famous problems in mathematics.
Dr Grigori Perelman, of the Steklov Institute of Mathematics of the Russian Academy of Sciences, St Petersburg, has been touring US universities describing his work in a series of papers not yet completed.
The Poincare Conjecture, an idea about three-dimensional objects, has haunted mathematicians for nearly a century. If it has been solved, the consequences will reverberate throughout geometry and physics.
If his proof is accepted and survives two years of scrutiny, Perelman could also be eligible for a $1m prize sponsored by the Clay Mathematics Institute in Massachusetts for solving what the centre describes as one of the seven most important unsolved mathematics problems of the millennium.
Formulated by the remarkable French mathematician Henri Poincare in 1904, the conjecture is a central question in topology, the study of the geometrical properties of objects that do not change when the they are stretched, distorted or shrunk.
For example, the hollow shell of the surface of the Earth is what topologists call a two-dimensional sphere. It has the property that every lasso of string encircling it can 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 meaning that, topologically speaking, spheres and doughnuts are different.
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. But the proof of the conjecture has eluded mathematicians.
Poincare himself demonstrated that his earliest version of his conjecture was wrong. Since then, dozens of mathematicians have asserted that they had proofs until fatal flaws were found.
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