Century-old Brain-twister Now Solved: Poincare Conjecture

... Grigory Perelman, 40, snared a Fields Medal, regarded as the equivalent of the Nobel Prize for mathematics, organisers at the 25th International Congress of Mathematicians in Madrid announced Tuesday.....

however he's refused to accept the award. he didn't even attend the recent Mathematicians Summit in Spain where 3 other scientists were given Fields Medal by Spain's King.

why ?

... he's a real sage, who is only interested in truth and not the chatter around it ...

read more :

Russia's beautiful mind: Reclusive life of a maths genius

Perelman went on to complete a doctorate in mathematics, specialising in topology, a geometry-related branch of mathematics that analyzes the shape of objects in space.

He then taught at US universities, including the prestigious Massachusetts Institute of Technology (MIT), before returning to Russia in the mid-1990s.

In 1996, he won an award at the Second European Congress of Mathematics in Budapest. Russian newspapers said that he turned down the prize because he considered the jury insufficiently qualified.

But Perelman's international fame in the mathematics world came in 2002 and 2003 when he published two papers online that appeared to solve the Poincare Conjecture.

Russian refuses math's highest honor

... John Ball, president of the International Mathematical Union, said that he had urged Perelman to accept the medal, but Perelman said he felt isolated from the mathematics community and "does not want to be seen as its figurehead." Ball offered no further details of the conversation.

Besides shunning the award for his work in topology, Perelman also seems uninterested, according to colleagues, in a separate $1 million prize he could win for proving the Poincare conjecture, a theorem about the nature of multidimensional space....

The Fields medal was founded in 1936 and named after Canadian mathematician John Charles Fields. It come with a $13,400 stipend.

Perelman is eligible for far more money from a private foundation called The Clay Mathematics Institute in Cambridge, Mass.

In 2000, the institute announced bounties for seven historic, unsolved math problems, including the Poincare conjecture.

If his proof stands the test of time, Perelman will win all or part of the $1 million prize money. That prize should be announced in about two years.

...

Proving the conjecture — an exercise in acrobatics with mindboggling imaginary doughnuts and balls — is anything but trivial. Colleagues say Perelman's work gives mathematical descriptions of what the universe might look like and promises exciting applications in physics and other fields.

"It is very important indeed because it really gives us an insight into geometry and in particular the geometry of the space we live in," said Oxford University math professor Marcus du Sautoy. "It does not say what the shape (of the universe) is. It just says, 'look, these are the things it could be.'"

Academics have been studying Perelman's proof since he left the first of three papers on it on a math Web site in Nov. 2002. Normal procedure would have been to seek publication in a peer-approved journal.

Century-old brain-twister now solved

The Poincare conjecture involves topology, a branch of math that studies shapes.

It essentially says that in three dimensions you cannot transform a doughnut shape into a sphere without ripping it, although any shape without a hole can be stretched or shrunk into a sphere.

There is a catch: the space has to be finite. Imagine an ant crawling on an apple in a straight line. It can only walk so far before it's back where it started.

Even though the apple has three dimensions, its surface is two-dimensional. The ant can walk backward, forward and sideways on the surface but not up and down. In three dimensions, shapes are harder to determine because people cannot directly 'see' them and there are many more possible types of holes.

The conjecture is named for French mathematician and physicist Henri Poincare, who proposed it in 1904.

An analogous conjecture was proved for spaces of more than three dimensions over 20 years ago. But the specific 3-D case flummoxed mathematicians for years.

In 1982, Columbia University's Richard Hamilton developed a technique called Ricci flow that mathematically ironed out wrinkles in 3-D surfaces and provided a blueprint for cracking the Poincare conundrum.

A problem was posed by puzzling, dense spots called singularities, which exhibited sudden, uncontrolled change.

Perelman's breakthrough was to understand how to analyze these singularities, essentially neutralizing them for a while and allowing the Ricci flow to proceed smoothly and show what a given space is really like, topologically speaking.