Grigori excelled in all subjects except physical education. In the late s and early s, with a strong recommendation from the geometer Mikhail Gromov ,  Perelman obtained research positions at several universities in the United States. After having proved the soul conjecture in , he was offered jobs at several top universities in the US, including Princeton and Stanford , but he rejected them all and returned to the Steklov Institute in Saint Petersburg in the summer of for a research-only position. Then the soul of M is a point; equivalently M is diffeomorphic to Rn.
|Published (Last):||20 November 2012|
|PDF File Size:||8.25 Mb|
|ePub File Size:||9.92 Mb|
|Price:||Free* [*Free Regsitration Required]|
In November , a Russian mathematician named Grigori Perelman posted the first of three short preprints to the arXiv an online repository for drafts of academic papers in math and science , offering a proof for the famous Poincare conjecture —one of the toughest remaining unsolved problems in mathematics, although partial solutions had been made over the decades since it was first proposed in Rumor had it that Perelman did not even plan to publish a formal paper.
It was such a momentous achievement that in , Perelman was awarded the Fields Medal, the highest honor in mathematics. All sought to answer the burning question: What would drive a man to shun all fame and recognition—well-deserved, I might add—and withdraw from the world altogether?
Certainly, Perelman had always been eccentric. It was his best shot, as a Jewish boy, of getting into the prestigious Leningrad University, which only accepted two Jewish candidates per year.
By the time he entered university, he had long curling fingernails and already evinced hermit tendencies, preferring to hole up in his room to work, subsisting on black bread and fermented milk. He labored in relative obscurity until , when he shot to mathematical fame with his proof of a topological conundrum known as the soul conjecture, and was offered positions at both Stanford and Princeton in the US. He returned to Russian and a position at the Steklov Institute.
When the European Mathematical Society considered awarding Perelman a prize for his work, he threatened to cause a nasty scene. Apparently he thought the work was incomplete and he was the best judge of when it would be deserving of a prize. From the few public statements made by Perelman and close colleagues, it seems he had become disillusioned with the entire field of mathematics. He was the purest of the purists, consumed with his love for mathematics, and completely uninterested in academic politics, with its relentless jockeying for position and squabbling over credit.
He denounced most of his colleagues as conformists. Now when I become a very conspicuous person, I cannot stay a pet and say nothing. That is why I had to quit. But since she did not interview Perelman, nor has the man undergone professional evaluation, this is little more than an armchair diagnosis, albeit a compelling one. It is still an unanswered, and possibly unanswerable, question. Most Recent Entries.
Donate to arXiv
In Perelman had left academia and apparently had abandoned mathematics. He was the first mathematician ever to decline the Fields Medal. Perelman earned a doctorate from St. Petersburg State University and then spent much of the s in the United States, including at the University of California , Berkeley. He was still listed as a researcher at the Steklov Institute of Mathematics, St. Petersburg University, until Jan.
He was particularly interested in what topological properties characterized a sphere. In this way he was able to conclude that these two spaces were, indeed, different. Is it possible that the fundamental group of V could be trivial, even though V is not homeomorphic to the 3-dimensional sphere? Here is the standard form of the conjecture: Every simply connected , closed 3- manifold is homeomorphic to the 3-sphere. Note that "closed" here means, as customary in this area, the condition of being compact in terms of set topology, and also without boundary 3-dimensional Euclidean space is an example of a simply connected 3-manifold not homeomorphic to the 3-sphere; but it is not compact and therefore not a counter-example. Attempted solutions[ edit ] This problem seemed to lie dormant until J. Whitehead revived interest in the conjecture, when in the s he first claimed a proof and then retracted it.