35 Facts About Grigori Perelman

In 2005, Perelman resigned from his research post in Steklov Institute of Mathematics and in 2006 stated that he had quit professional mathematics, owing to feeling disappointed over the ethical standards in the field.

The full details of Grigori Perelman's work were filled in and explained by various authors over the following several years.

Grigori Perelman had previously rejected the prestigious prize of the European Mathematical Society in 1996.

Grigori Yakovlevich Perelman was born in Leningrad, Soviet Union on June 13,1966, to Jewish parents, Yakov and Lyubov.

In 1991, Grigori Perelman won the Young Mathematician Prize of the Saint Petersburg Mathematical Society for his work on Aleksandrov's spaces of curvature bounded from below.

Grigori Perelman's first published article studied the combinatorial structures arising from intersections of convex polyhedra.

Grigori Perelman proved that any such metric on the plane which is complete can be continuously immersed as a polyhedral surface.

Previous examples of such surfaces were known, but Grigori Perelman's was the first to exhibit the saddle property on nonexistence of locally strictly supporting hyperplanes.

Grigori Perelman developed a version of Morse theory on Alexandrov spaces.

In further unpublished work, Grigori Perelman studied DC functions on Alexandrov spaces and established that the set of regular points has the structure of a manifold modeled on DC functions.

In 1994, Grigori Perelman gave a short proof of Cheeger and Gromoll's conjecture by establishing that, under the condition of nonnegative sectional curvature, Sharafutdinov's retraction is a submersion.

Grigori Perelman's theorem is significant in establishing a topological obstruction to deforming a nonnegatively curved metric to one which is positively curved, even at a single point.

Some of Grigori Perelman's work dealt with the construction of various interesting Riemannian manifolds with positive Ricci curvature.

Grigori Perelman found Riemannian metrics on the connected sum of arbitrarily many complex projective planes with positive Ricci curvature, bounded diameter, and volume bounded away from zero.

Grigori Perelman's proposal, known as the Thurston geometrization conjecture, posited that given any closed three-dimensional manifold whatsoever, there is some collection of two-dimensional spheres and tori inside of the manifold which disconnect the space into separate pieces, each of which can be endowed with a uniform geometric structure.

In November 2002 and March 2003, Grigori Perelman posted two preprints to arXiv, in which he claimed to have outlined a proof of Thurston's conjecture.

Roughly speaking, Grigori Perelman showed that on a microscopic level, every singularity looks either like a cylinder collapsing to its axis, or a sphere collapsing to its center.

Grigori Perelman's proof of his canonical neighborhoods theorem is a highly technical achievement, based upon extensive arguments by contradiction in which Hamilton's compactness theorem is applied to construct self-contradictory manifolds.

Grigori Perelman was unable to resolve Hamilton's 1999 conjecture on long-time behavior, which would make Thurston's conjecture another corollary of the existence of Ricci flow with surgery.

Nonetheless, Grigori Perelman was able to adapt Hamilton's arguments to the precise conditions of his new Ricci flow with surgery.

Since then, various parts of Grigori Perelman's work have appeared in a number of textbooks and expository articles.

Two weeks later, Grigori Perelman summed up the conversation as follows:.

Grigori Perelman proposed to me three alternatives: accept and come; accept and don't come, and we will send you the medal later; third, I don't accept the prize.

Nevertheless, on 22 August 2006, at the International Congress of Mathematicians in Madrid, Grigori Perelman was offered the Fields Medal "for his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow".

Grigori Perelman did not attend the ceremony and the presenter informed the congress that Perelman declined to accept the medal, which made him the only person to have ever declined the prize.

Grigori Perelman has rejected a prestigious prize from the European Mathematical Society.

On 18 March 2010, Grigori Perelman was awarded a Millennium Prize for solving the problem.

Grigori Perelman quit his job at the Steklov Institute in December 2005.

Grigori Perelman's friends are said to have stated that he currently finds mathematics a painful topic to discuss; by 2010, some even said that he had entirely abandoned mathematics.

Grigori Perelman is quoted in a 2006 article in The New Yorker saying that he was disappointed with the ethical standards of the field of mathematics.

The article implies that Grigori Perelman refers particularly to alleged efforts of Fields medalist Shing-Tung Yau to downplay Grigori Perelman's role in the proof and play up the work of Cao and Zhu.

Yakov Eliashberg, another Russian mathematician, said that in 2007 Grigori Perelman confided to him that he was working on other things, but that it was too premature to discuss them.

In 2014, Russian media reported that Grigori Perelman was working in the field of nanotechnology in Sweden.

Grigori Perelman has avoided journalists and other members of the media.

Zabrovsky says that in the interview, Grigori Perelman explained why he rejected the one million dollar prize.