Grigori Perelman – The Saint of Mathematics

Grigori Perelman – The Saint of Mathematics

The man in the picture is a reclusive mathematical genius. His name is Grigori Yakovlevich Perelman. He is my personal hero, not because of his prodigious mathematical talent but for his values as a human being.

The Epoch Making Question – 1904

Let us trace back to the year 1904 when the French mathematician Henri Poincare posed an epoch-making question: “If a three-dimensional shape is simply connected, is it homeomorphic to the three-dimensional sphere?”

Say, for example, if we stretch a rubber band around the exterior of an apple, then we can shrink it down to a point by moving it gradually, without tearing it, and without letting it to leave the surface.
On the other hand, if we visualize that the same rubber band has somehow been stretched in the suitable direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut.

We say the surface of the apple is “simply connected,” but that the surface of the doughnut is not. Poincaré, almost a hundred years ago, knew that a two-dimensional sphere is essentially characterized by this property of simple connectivity and asked the corresponding question for the three-dimensional sphere.

It was so simple to imagine but so difficult to prove!

Towards the Answer

Almost a century passed before the mathematical world got a proper answer. The initial success was lead by prominent mathematicians like:

(1) In 1961 Stephen Smale of the University of California proved the conjecture to be true for spheres of 5 or more dimensions.

(2) Michael Freeman proved the conjecture in 4 dimensions.

(3) In 1999 Richard Hamilton published a paper that played a significant role in the progress of Poincare conjecture. It was Hamilton who first used Ricci flow (subject to further discussion)
It was liking biting around the bush. Although Hamilton’s proof made great strides towards the central problem yet there arose some singularities in Ricci flow which collapsed everything just as the singularity problem did so in a black hole.

The Reclusive Mathematical Genius

The trace of his mathematical sparks dates back to his childhood. His mother Lyubov was a mathematics teacher who taught Grigori.

Grigori excelled in all subjects except physical education. In 1982, as a member of the Soviet Union team competing in the International Mathematical Olympiad, an international competition for high school students, he won a gold medal, achieving a perfect score.

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On 11th. In November 2002, Perelman first published his proof online at www.arXiv.org in which he gave a proof of geometrization conjecture of which Poincaré conjecture is a special case.

The heat equation describes the behavior of scalar quantities such as temperature. Similarly, Ricci flow describes Ricci flow
curvature tensor.

Perelman modified Hamilton’s program to provide the proof. Perelman elaborated: “implementation of the Hamilton program would imply the geometrization conjecture for closed three-manifolds.”

Verification of the Proof

Perelman’s work was checked relatively quickly. In April 2003, Perelman visited the Massachusetts Institute of Technology, Princeton University, Stony Brook University, Columbia University, and New York University to give a short series of lectures on his work.

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On 25 May 2006, Bruce Kleiner and John Lott, both of the University of Michigan, posted a paper on arXiv that fills in the details of Perelman’s proof of the Geometrization conjecture.

In June 2006, the Asian Journal of Mathematics published a paper giving a complete description of Perelman’s proof of the Poincaré and the geometrization conjectures. The June 2006 paper claimed: “This proof should be considered as the crowning achievement of the Hamilton–Perelman theory of Ricci flow.”

Declining the Fields Medal and Millennium Prize

In May 2006, a committee of nine mathematicians voted to award Perelman a Fields Medal. Perelman declined to accept it. Sir John Ball, then president of the International Mathematical Union traveled to St. Petersburg to convince him to receive the money, but Perelman said:
“The prize was completely irrelevant for me. Everybody understood that if the proof is correct, then no other recognition is needed.”

“‘I’m not interested in money or fame.”

On 2nd. August 2006, Perelman was publicly offered the medal at the International Congress of Mathematicians in Madrid. He did not attend the ceremony and declined to accept the medal.
On 18 March 2010, Perelman was awarded a Millennium Prize for solving the problem. Perelman did not attend the ceremony and refused to accept the $1 million prize.

He stated that: “the main reason is my disagreement with the organized mathematical community. I don’t like their decisions, I consider them unjust.”

His argument was that Richard Hamilton is equally responsible for receiving the prize. If he has not been awarded for that then the mathematical society is corrupted.

What is the ideology of Perelman?

Perelman is my personal hero. A person who considers research and mathematics to be pure and cannot be tainted by anything which measures or compares it with a value. The value can be money or anything which is measurable. Can we really provide value to Perelman’s talent? No, we cannot. So, he is beyond measurement. He is a saint, a monk of mathematics in all aspects.

Perelman quit his job at the Steklov Institute in December 2005. Sources say that he has abandoned the world of mathematics completely.

He lives only with his mother who is not well.

He never meets the press, neither comes out of his house in St.Petersburg.

I have seen Russian videos where he is seen coming out of his house, going to the supermarket to get some food.

He is a genius, a man of principle, an ascetic, a pure abstinent whose brain functions not only for mathematics but also whose ethics are far beyond our comprehension.

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