Grigori Perelman

• 1. The Boy From Leningrad

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  Grigori Yakovlevich Perelman was born on the 13th of June 1966 in Leningrad, Soviet Union. His mother Lyubov gave up her own graduate work in mathematics to raise him. The family lived in a small apartment where his mathematical talent became apparent at age ten. He joined Sergei Rukshin's after-school training program and excelled in all subjects except physical education. In 1982, not long after his sixteenth birthday, he won a gold medal as part of the Soviet team at the International Mathematical Olympiad held in Budapest. He achieved a perfect score that year.

• 2. Foundations Of Alexandrov Spaces

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  In the late 1980s and early 1990s, Perelman collaborated with Yuri Burago and Mikhael Gromov. They established modern foundations for Alexandrov spaces using Gromov, Hausdorff convergence as an organizing principle. A very well-known paper coauthored by these three men defined this field. Perelman later proved his stability theorem in an unpublished follow-up. This theorem asserted that elements within any sufficiently small metric ball around a compact space are mutually homeomorphic. Vitali Kapovitch described Perelman's article as being very hard to read but wrote a detailed version himself. Perelman also developed a version of Morse theory on Alexandrov spaces despite their lack of smoothness.

• 3. The Ricci Flow Breakthrough

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  Richard Hamilton introduced his theory of the Ricci flow in the 1980s. It was a prescription for how to deform a Riemannian metric on a manifold. Hamilton proved that his equation could spread extreme curvatures and uniformize a Riemannian metric in certain geometric settings. In November 2002 and March 2003, Perelman posted two preprints to arXiv claiming to outline a proof of Thurston's conjecture. His first preprint contained a novel adaptation of Peter Li and Shing-Tung Yau's differential Harnack inequalities. By carrying out the proof of the Bishop, Gromov inequality, Perelman established his celebrated noncollapsing theorem. This result asserted that local control of curvature implies control of volumes. The canonical neighborhoods theorem followed as the second main result of his first paper. It achieved the quantitative understanding of singularities which had eluded Hamilton.

• 4. Verification By The Mathematical Community

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  Perelman's preprints quickly gained attention from the mathematical community though they were widely seen as hard to understand. Many technical details had been omitted against usual academic style. In April 2003, Perelman visited Massachusetts Institute of Technology, Princeton University, Stony Brook University, Columbia University, and New York University to give lectures. Bruce Kleiner and John Lott posted notes filling in details of Perelman's first preprint on the 14th of June 2003. Their notes were updated to include Perelman's second preprint by September 2004. They posted a version to arXiv on the 25th of May 2006. At the 2006 International Congress of Mathematicians, Lott stated that all indications showed his arguments were correct. John Morgan and Gang Tian posted a paper on the 18th of July 2006 providing a detailed presentation of the proof. Morgan declared at an the 24th of August 2006 lecture in Madrid that Perelman's work had been thoroughly checked.

• 5. Rejection Of Prestigious Awards

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  In May 2006, a committee of nine mathematicians voted to award Perelman a Fields Medal for his work on Ricci flow. Sir John Ball approached him in Saint Petersburg in June 2006 to persuade him to accept. After ten hours of attempted persuasion over two days, Ball gave up. On the 22nd of August 2006, Perelman was offered the medal at the International Congress of Mathematicians in Madrid. He did not attend the ceremony and declined to accept it. This made him the only person to have ever declined the prize. On the 18th of March 2010, he was awarded a Millennium Prize for solving the problem. On the 8th of June 2010, he did not attend a ceremony in Paris to accept his one million dollar prize. He refused the money because he considered the Clay Institute decision unfair for not sharing the prize with Richard S. Hamilton. He stated that his main reason was disagreement with the organized mathematical community.

• 6. Withdrawal From Professional Mathematics

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  Perelman quit his job at the Steklov Institute in December 2005. His friends stated that he found mathematics a painful topic to discuss by 2010. Some even said he had entirely abandoned mathematics. A 2006 article in The New Yorker quoted him as saying he was disappointed with ethical standards in the field. He claimed that Shing-Tung Yau tried to downplay his role while playing up the work of Cao and Zhu. In 2007, Yakov Eliashberg said Perelman confided that he was working on other things but it was too premature to discuss them. Russian media reported in 2014 that he was working in nanotechnology in Sweden. Shortly thereafter, he was spotted again in Saint Petersburg taking care of his elderly mother.

• 7. Media Encounters And Public Legacy

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  Perelman has avoided journalists and other members of the media since 2006. Masha Gessen author of a biography about Perelman was unable to meet him. A reporter who called him was told you are disturbing me I am picking mushrooms. A Russian documentary titled Maverick: Perelman's Lesson released in 2011 discussed his work with leading mathematicians including Mikhail Gromov and Ludwig Faddeev. Aleksandr Zabrovsky claimed in April 2011 to have held an interview with Perelman under the tentative title The Formula of the Universe. Many journalists believe this interview is most likely fake due to contradictions in statements supposedly made by Perelman. Brett Forrest briefly interacted with Perelman in 2012. He lives in seclusion in Saint Petersburg and has declined requests for interviews since 2006.