Grigori Yakovlevich Perelman
Born	June 13, 1966 (1966-06-13) (age 41) Leningrad, USSR
Fields	Mathematician
Known for	Riemannian geometry and geometric topology
Notable awards	Fields Medal (2006), declined

Grigori Yakovlevich Perelman (Russian: Григорий Яковлевич Перельман), born 13 June 1966 in Leningrad, USSR (now St. Events 1525 - Martin Luther marries Katharina von Bora, against the Celibacy rule decreed by the Roman Catholic Church for Year 1966 ( MCMLXVI) was a Common year starting on Saturday (link will display full calendar of the 1966 Gregorian calendar. Saint Petersburg ( tr: Sankt-Peterburg,) is a city and a federal subject of Russia located on the Neva River The Union of Soviet Socialist Republics (USSR was a constitutionally Socialist state that existed in Eurasia from 1922 to 1991 A mathematician is a person whose primary area of study and research is the field of Mathematics. Elliptic geometry is also sometimes called Riemannian geometry. In Mathematics, geometric topology is the study of Manifolds and their Embeddings Low-dimensional topology, concerning questions of dimensions The Fields Medal is a prize awarded to two three or four Mathematicians not over 40 years of age at each International Congress of the International Mathematical Russian ( transliteration:,) is the most geographically widespread language of Eurasia, the most widely spoken of the Slavic languages Events 1525 - Martin Luther marries Katharina von Bora, against the Celibacy rule decreed by the Roman Catholic Church for Year 1966 ( MCMLXVI) was a Common year starting on Saturday (link will display full calendar of the 1966 Gregorian calendar. Saint Petersburg ( tr: Sankt-Peterburg,) is a city and a federal subject of Russia located on the Neva River The Union of Soviet Socialist Republics (USSR was a constitutionally Socialist state that existed in Eurasia from 1922 to 1991  Petersburg, Russia), sometimes known as Grisha Perelman, is a Russian mathematician who has made landmark contributions to Riemannian geometry and geometric topology. A mathematician is a person whose primary area of study and research is the field of Mathematics. Elliptic geometry is also sometimes called Riemannian geometry. In Mathematics, geometric topology is the study of Manifolds and their Embeddings Low-dimensional topology, concerning questions of dimensions In particular, he proved Thurston's geometrization conjecture. Thurston's geometrization conjecture states that compact 3-manifolds can be decomposed into Submanifolds that have geometric structures This solves in the affirmative the famous Poincaré conjecture, posed in 1904 and regarded as one of the most important and difficult open problems in mathematics until it was solved. In Mathematics, the Poincaré conjecture (French pwɛ̃kaʀe is a Theorem about the characterization of the three-dimensional sphere among

In August 2006, Perelman was awarded the Fields Medal,^[1] for "his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow". Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. The Fields Medal is a prize awarded to two three or four Mathematicians not over 40 years of age at each International Congress of the International Mathematical In Differential geometry, the Ricci flow is an intrinsic Geometric flow —a process which deforms the metric of a Riemannian manifold —in this case in The Fields Medal is widely considered to be the top honor a mathematician can receive. The Fields Medal is a prize awarded to two three or four Mathematicians not over 40 years of age at each International Congress of the International Mathematical However, he declined to accept the award or appear at the congress. The International Congress of Mathematicians (ICM is the largest congress in the Mathematics community He is the only person ever to refuse the award.

On December 22, 2006, the journal Science recognized Perelman's proof of the Poincaré Conjecture as the scientific "Breakthrough of the Year," the first such recognition in the area of mathematics. Events 1790 - The Turkish fortress of Izmail is stormed and captured by Suvorov and his Russian armies Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. Science is the Academic journal of the American Association for the Advancement of Science and is considered one of the world's most prestigious Scientific The Breakthrough of the Year is an annual award made by the journal Science for the most significant development in scientific research ^[2]

Contents 1 Early life and education 2 Geometrization and Poincaré conjectures 2.1 The problem 2.2 Perelman's proof 2.3 Verification 3 The Fields Medal and Millennium Prize 4 Withdrawal from mathematics 5 Bibliography 6 Notes 7 References 8 See also 9 External links

Early life and education

Grigori Perelman was born in Leningrad (now Saint Petersburg) to a Jewish family on June 13, 1966. PLEASE TAKE NOTE************ Events 1525 - Martin Luther marries Katharina von Bora, against the Celibacy rule decreed by the Roman Catholic Church for Year 1966 ( MCMLXVI) was a Common year starting on Saturday (link will display full calendar of the 1966 Gregorian calendar. His early mathematical education occurred at the Leningrad Secondary School #239, a specialized school with advanced mathematics and physics programs. Saint Petersburg Lyceum 239 (физико-математический лицей №239 is a public high school in Saint Petersburg, Russia that specializes For the equivalent in the UK see Specialist school. Schools for students with special needs are discussed in the " Special school " article Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. In 1982, as a member of the USSR team competing in the International Mathematical Olympiad, an international competition for high school students, he won a gold medal, achieving a perfect score. The Union of Soviet Socialist Republics (USSR was a constitutionally Socialist state that existed in Eurasia from 1922 to 1991 The International Mathematical Olympiad ( IMO) is an annual six-problem 42-point Mathematical olympiad for pre- collegiate students and is the oldest of ^[3] In the late 1980s, Perelman went on to earn a Candidate of Science degree (the Russian equivalent to the Ph. Kandidat nauk or Candidate of Sciences (Кандидат наук is a first post-graduate scientific degree in the former USSR and in some Post-Soviet D. ) at the Mathematics and Mechanics Faculty of the Leningrad State University, one of the leading universities in the former Soviet Union. Saint Petersburg State University ( Санкт-Петербургский государственный университет) is a Russian federal state-owned higher His dissertation was entitled "Saddle surfaces in Euclidean spaces". A dissertation (also called thesis or disquisition) is a document that presents the author's Research and findings and is submitted in support of candidature A saddle surface is a Smooth surface containing one or more Saddle points The term derives of the peculiar shape of historical Saddles evolved

After graduation, Perelman began work at the renowned Leningrad Department of Steklov Institute of Mathematics of the USSR Academy of Sciences, where his advisors were Aleksandr Danilovich Aleksandrov and Yuri Dmitrievich Burago. Steklov Institute of Mathematics or Steklov Mathematical Institute ( Russian: Математический институт имени В The Russian Academy of Sciences (Российская Академия Наук Rossi'iskaya Akade'miya Nau'k, shortened to PAH RAN) consists of the National Aleksandr Danilovich Aleksandrov ( Алекса́ндр Дани́лович Алекса́ндров, alternative Transliterations Yuri Dmitrievich Burago (Юрий Дмитриевич Бураго is a Russian Mathematician. In the late 80s and early 90s, Perelman held posts at several universities in the United States. The United States of America —commonly referred to as the In 1992, he was invited to spend a semester each at New York University and Stony Brook University. New York University ( NYU) is a private, Nonsectarian, Coeducational Research University in New York City. State University of New York at Stony Brook, commonly known as Stony Brook University, is a public research university located in Stony Brook, New York From there, he accepted a two-year fellowship at the University of California, Berkeley in 1993. The University of California Berkeley (also referred to as Cal, Berkeley and UC Berkeley) is a major research university located in Berkeley 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 the summer of 1995.

Perelman is a talented violinist and also plays table tennis. ^[4]

Geometrization and Poincaré conjectures

Until the autumn of 2002, Perelman was best known for his work in comparison theorems in Riemannian geometry. Elliptic geometry is also sometimes called Riemannian geometry. Among his notable achievements was the proof of the soul conjecture. In Mathematics, the soul theorem is the following theorem of Riemannian geometry: If ( M, g) is a complete non

The problem

Main article: Poincaré conjecture

The Poincaré conjecture, proposed by French mathematician Henri Poincaré in 1904, was the most famous open problem in topology. In Mathematics, the Poincaré conjecture (French pwɛ̃kaʀe is a Theorem about the characterization of the three-dimensional sphere among In Mathematics, the Poincaré conjecture (French pwɛ̃kaʀe is a Theorem about the characterization of the three-dimensional sphere among This article is about the country For a topic outline on this subject see List of basic France topics. Jules Henri Poincaré ( 29 April 1854 &ndash 17 July 1912) (ˈʒyl ɑ̃ˈʁi pwɛ̃kaˈʁe was a French Mathematician Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of Loosely speaking, the conjecture surmises that if a closed three-dimensional manifold is sufficiently like a sphere in that each loop in the manifold can be tightened to a point, then it is really just a three-dimensional sphere. A manifold is a mathematical space in which every point has a neighborhood which resembles Euclidean space, but in which the global structure may be In Mathematics, a path in a Topological space X is a continuous map f from the Unit interval I = to The analogous result has been known to be true in higher dimensions for some time, but the case of three-manifolds had turned out to be the hardest of them all. Roughly speaking, this is because in topologically manipulating a three-manifold, there are too few dimensions to move "problematic regions" out of the way without interfering with something else.

In 1999, the Clay Mathematics Institute announced the Millennium Prize Problems – a one million dollar prize for the proof of several conjectures, including the Poincaré conjecture. The Clay Mathematics Institute (CMI is a private Non-profit foundation, based in Cambridge, Massachusetts. The Millennium Prize Problems are seven problems in Mathematics that were stated by the Clay Mathematics Institute in 2000 There is universal agreement that a successful proof would constitute a landmark event in the history of mathematics, fully comparable with the proof by Andrew Wiles of Fermat's Last Theorem, but possibly even more far-reaching. Sir Andrew John Wiles KBE FRS (born 11 April 1953 is a British Mathematician and a professor at Princeton University Fermat's Last Theorem is the name of the statement in Number theory that It is impossible to separate any power higher than the second into two like

Perelman's proof

In November 2002, Perelman posted to the arXiv the first of a series of eprints in which he claimed to have outlined a proof of the geometrization conjecture, a result that includes the Poincaré conjecture as a particular case. The arXiv ( pronounced " Archive " as if the "X" were the Greek letter Chi, χ is an Archive for electronic An eprint is a digital version of a research document (usually a journal article but could also be a Thesis, conference paper book chapter or a book that is accessible online In Mathematics, a proof is a convincing demonstration (within the accepted standards of the field that some Mathematical statement is necessarily true Thurston's geometrization conjecture states that compact 3-manifolds can be decomposed into Submanifolds that have geometric structures In Mathematics, the Poincaré conjecture (French pwɛ̃kaʀe is a Theorem about the characterization of the three-dimensional sphere among See the Solution of the Poincaré conjecture for a layman's description of the mathematics. This entry describes the solution of the Poincaré conjecture at a level intended for the general public

Perelman modifies Richard Hamilton's program for a proof of the conjecture, in which the central idea is the notion of the Ricci flow. Richard Streit Hamilton (born 1943 is professor of Mathematics at Columbia University. In Differential geometry, the Ricci flow is an intrinsic Geometric flow —a process which deforms the metric of a Riemannian manifold —in this case in Hamilton's basic idea is to formulate a "dynamical process" in which a given three-manifold is geometrically distorted, such that this distortion process is governed by a differential equation analogous to the heat equation. The heat equation is an important Partial differential equation which describes the distribution of Heat (or variation in temperature in a given region over time The heat equation describes the behavior of scalar quantities such as temperature; it ensures that concentrations of elevated temperature will spread out until a uniform temperature is achieved throughout an object. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature Similarly, the Ricci flow describes the behavior of a tensorial quantity, the Ricci curvature tensor. History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually In Differential geometry, the Ricci curvature tensor, named after Gregorio Ricci-Curbastro, provides one way of measuring the degree to which the geometry determined Hamilton's hope was that under the Ricci flow, concentrations of large curvature will spread out until a uniform curvature is achieved over the entire three-manifold. If so, if one starts with any three-manifold and lets the Ricci flow work its magic, eventually one should in principle obtain a kind of "normal form". According to William Thurston, this normal form must take one of a small number of possibilities, each having a different flavor of geometry, called Thurston model geometries. William Paul Thurston (born October 30, 1946) is an American Mathematician. Thurston's geometrization conjecture states that compact 3-manifolds can be decomposed into Submanifolds that have geometric structures

This is similar to formulating a dynamical process which gradually "perturbs" a given square matrix, and which is guaranteed to result after a finite time in its rational canonical form. In Linear algebra, the Frobenius normal form, Turner binormal projective form or rational canonical form of a Square matrix A is a

Hamilton's idea had attracted a great deal of attention, but no one could prove that the process would not "hang up" by developing "singularities", until Perelman's eprints sketched a program for overcoming these obstacles. An eprint is a digital version of a research document (usually a journal article but could also be a Thesis, conference paper book chapter or a book that is accessible online According to Perelman, a modification of the standard Ricci flow, called Ricci flow with surgery, can systematically excise singular regions as they develop, in a controlled way.

It is known that singularities (including those which occur, roughly speaking, after the flow has continued for an infinite amount of time) must occur in many cases. However, mathematicians expect that, assuming that the geometrization conjecture is true, any singularity which develops in a finite time is essentially a "pinching" along certain spheres corresponding to the prime decomposition of the 3-manifold. In Mathematics, the prime decomposition theorem for 3-manifolds states that every compact orientable 3-manifold is the Connected sum of a unique (up to If so, any "infinite time" singularities should result from certain collapsing pieces of the JSJ decomposition. In Mathematics, the JSJ decomposition, also known as the toral decomposition, is a Topological construct given by the following theorem Perelman's work apparently proves this claim and thus proves the geometrization conjecture.

Verification

Since 2003, Perelman's program has attracted increasing attention from the mathematical community. In April 2003, he accepted an invitation to visit Massachusetts Institute of Technology, Princeton University, State University of New York at Stony Brook, Columbia University and Harvard University, where he gave a series of talks on his work. Princeton University is a private Coeducational research university located in Princeton, New Jersey. State University of New York at Stony Brook, commonly known as Stony Brook University, is a public research university located in Stony Brook, New York Columbia University is a private University in the United States and a member of the Ivy League. ^[3]

Three independent groups of scholars have verified that Perelman's papers contain all the essentials for a complete proof of the geometrization conjecture:

1. 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. Events 1085 - Alfonso VI of Castile takes Toledo Spain back from the Moors. Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. The University of Michigan Ann Arbor ( U of M, U-M, UM or simply Michigan) is a top-ranked Coeducational public research The arXiv ( pronounced " Archive " as if the "X" were the Greek letter Chi, χ is an Archive for electronic ^[5] As John Lott said in ICM2006, "It has taken us some time to examine Perelman's work. This is partly due to the originality of Perelman's work and partly to the technical sophistication of his arguments. All indications are that his arguments are correct. "
2. In June 2006, the Asian Journal of Mathematics published a paper by Xi-Ping Zhu of Sun Yat-sen University in China and Huai-Dong Cao of Lehigh University in Pennsylvania, giving a complete description of Perelman's proof of the Poincaré and the geometrization conjectures. Award In December 2004, Zhu won the Morningside Medal of Mathematics at the Third International Congress of Chinese Mathematicians (ICCM a triennial congress hosted by This article is about the Sun Yat-sen University located in the People's Republic of China; see also National Sun Yat-sen University in Taiwan China ( Wade-Giles ( Mandarin) Chung¹kuo² is a cultural region, an ancient Civilization, and depending on perspective a National Selected bibliography Huai-Dong Cao and Xi-Ping Zhu " A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory Lehigh University is a private, co-educational University located in Bethlehem, Pennsylvania, in the Lehigh Valley region of The Commonwealth of Pennsylvania ( often colloquially referred to as PA (its abbreviation by natives and Northeasterners is a state located in the Northeastern ^[6]
3. In July 2006, John Morgan of Columbia University and Gang Tian of the Massachusetts Institute of Technology posted a paper on the arXiv titled, "Ricci Flow and the Poincaré Conjecture. John Willard Morgan is an American Mathematician, well-known for his contributions to Topology and Geometry. Tian Gang ( 1958 &ndash  is a Chinese Mathematician and an Academician of the Chinese Academy of Sciences. " In this paper, they provide a detailed version of Perelman's proof of the Poincaré Conjecture. ^[7] On 24 August 2006, Morgan delivered a lecture at the ICM in Madrid on the Poincaré conjecture. Events 49 BC - Julius Caesar 's General Gaius Scribonius Curio is defeated in the Second Battle of the Bagradas River Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. ^[8]

Nigel Hitchin, professor of mathematics at Oxford University, has said that "I think for many months or even years now people have been saying they were convinced by the argument. Nigel Hitchin (b 2 August 1946 in Holbrook Derbyshire) is a British Mathematician working in the fields of Differential I think it's a done deal. "^[9]

The Fields Medal and Millennium Prize

In May 2006, a committee of nine mathematicians voted to award Perelman a Fields Medal for his work on the Poincaré conjecture. The Fields Medal is a prize awarded to two three or four Mathematicians not over 40 years of age at each International Congress of the International Mathematical ^[3] The Fields Medal is the highest award in mathematics; two to four medals are awarded every four years.

Sir John Ball, president of the International Mathematical Union, approached Perelman in Saint Petersburg in June 2006 to persuade him to accept the prize. Sir John Macleod Ball, FRS (born 1948 is Sedleian Professor of Natural Philosophy at the University of Oxford. The International Mathematical Union is an international Non-governmental organization devoted to international cooperation in the field of Mathematics. Saint Petersburg ( tr: Sankt-Peterburg,) is a city and a federal subject of Russia located on the Neva River After 10 hours of persuading over two days, he gave up. Two weeks later, Perelman summed up the conversation as: "He 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. From the very beginning, I told him I have chosen the third one. " He went on to say that the prize "was completely irrelevant for me. Everybody understood that if the proof is correct then no other recognition is needed. "^[3]

On August 22, 2006, Perelman was publicly offered the medal at the International Congress of Mathematicians in Madrid, "for his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow". Events 392 - Arbogast has Eugenius elected Western Roman Emperor. Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. The International Congress of Mathematicians (ICM is the largest congress in the Mathematics community Madrid (pronounced in English in Spanish and colloquially in Spain) is the Capital and largest city of Spain. ^[10] He did not attend the ceremony, and declined to accept the medal, making him the first person in history to decline this prestigious prize. ^[11][12]

He had previously turned down a prestigious prize from the European Mathematical Society,^[12] allegedly saying that he felt the prize committee was unqualified to assess his work, even positively. The European Mathematical Society (EMS is a European organization dedicated to the development of Mathematics in Europe. ^[9]

Perelman may also be due to receive a share (or the totality) of a Millennium Prize. The Millennium Prize Problems are seven problems in Mathematics that were stated by the Clay Mathematics Institute in 2000 The rules for this prize - which can be changed, as stated by a member of the advisory board of the Clay Mathematics Institute - require his proof to be published in a peer-reviewed mathematics journal. The Clay Mathematics Institute (CMI is a private Non-profit foundation, based in Cambridge, Massachusetts. Peer review (also known as refereeing) is the process of subjecting an author's scholarly work research or Ideas to the scrutiny of others who are While Perelman has not pursued publication himself, other mathematicians have published papers about the proof. This may make Perelman eligible to receive a share or the whole of a prize. Perelman has stated that "I’m not going to decide whether to accept the prize until it is offered. "^[3]

Terence Tao spoke about Perelman's work on the Poincaré Conjecture during the 2006 Fields Medal Event [1]:

“

They [the Millennium Prize Problems] are like these huge cliff walls, with no obvious hand holds. Terence Chi-Shen Tao FRS (陶哲軒 (born July 17, 1975, Adelaide, South Australia) is an Australian Mathematician In Mathematics, the Poincaré conjecture (French pwɛ̃kaʀe is a Theorem about the characterization of the three-dimensional sphere among The Millennium Prize Problems are seven problems in Mathematics that were stated by the Clay Mathematics Institute in 2000 I have no idea how to get to the top. [Perelman's proof of the Poincare Conjecture] is a fantastic achievement, the most deserving of all of us here in my opinion. In Mathematics, the Poincaré conjecture (French pwɛ̃kaʀe is a Theorem about the characterization of the three-dimensional sphere among Most of the time in mathematics you look at something that's already been done, take a problem and focus on that. But here, the sheer number of breakthroughs. . . well it's amazing.

”

Withdrawal from mathematics

As of the spring of 2003, Perelman no longer works at the Steklov Institute. ^[4] His friends are said to have stated that he currently finds mathematics a painful topic to discuss; some even say that he has abandoned mathematics entirely. ^[13] According to a 2006 interview, Perelman is currently jobless, living with his mother in Saint Petersburg. ^[4]

Although Perelman says in a The New Yorker article that he is disappointed with the ethical standards of the field of mathematics, the article implies that Perelman refers particularly to Yau's efforts to downplay his role in the proof and play up the work of Cao and Zhu. The New Yorker is an American Magazine that publishes reportage commentary criticism essays fiction satire cartoons and poetry Shing-Tung Yau ( born April 4, 1949) is a Chinese American Mathematician working in Differential geometry, and involved Selected bibliography Huai-Dong Cao and Xi-Ping Zhu " A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory Award In December 2004, Zhu won the Morningside Medal of Mathematics at the Third International Congress of Chinese Mathematicians (ICCM a triennial congress hosted by Perelman has said that "I can’t say I’m outraged. Other people do worse. Of course, there are many mathematicians who are more or less honest. But almost all of them are conformists. They are more or less honest, but they tolerate those who are not honest. "^[3] He has also said that "It is not people who break ethical standards who are regarded as aliens. It is people like me who are isolated. "^[3]

This, combined with the possibility of being awarded a Fields medal, led him to quit professional mathematics. He has said that "As long as I was not conspicuous, I had a choice. Either to make some ugly thing" (a fuss about the mathematics community's lack of integrity) "or, if I didn’t do this kind of thing, to be treated as a pet. Now, when I become a very conspicuous person, I cannot stay a pet and say nothing. That is why I had to quit. ”^[3]

Bibliography

• Перельман, Григорий Яковлевич (1990). Седловые поверхности в евклидовых пространствах:Автореф. дис. на соиск. учен. степ. канд. физ. -мат. наук (in Russian). Ленинградский Государственный Университет.   (Perelman's dissertation)

• Perelman, G. ; Yu. Burago, M. Gromov (1992). "Aleksandrov spaces with curvatures bounded below". Russian Math Surveys 47 (2): 1-58.  

• Perelman, G. (1993). "Construction of manifolds of positive Ricci curvature with big volume and large Betti numbers" (PDF). Comparison Geometry 30: 157-163.  

• Perelman, G. (1994). "Proof of the soul conjecture of Cheeger and Gromoll". J. Differential Geom. 40: 209-212.  

• Perelman, G. (1994). "Elements of Morse theory on Aleksandrov spaces". St. Petersbg. Math. J. 5 (1): 205-213.  

• Perelman, G. Ya. ; Petrunin, A. M. (1994). "Extremal subsets in Alexandrov spaces and the generalized Liberman theorem". Saint Petersburg Math. J. 5 (1): 215-227.  

Perelman's proof of the geometrization conjecture:

• Perelman, Grisha (November 11, 2002). Events 308 - The Congress of Carnuntum: Attempting to keep peace within the Roman Empire, the leaders of the Tetrarchy declare See also 2002 (disambiguation Year 2002 ( MMII) was a Common year starting on Tuesday of the Gregorian calendar. "The entropy formula for the Ricci flow and its geometric applications". arXiv:math.DG/0211159. The arXiv ( pronounced " Archive " as if the "X" were the Greek letter Chi, χ is an Archive for electronic  
• Perelman, Grisha (March 10, 2003). Events 241 BC - First Punic War: Battle of the Aegates Islands - The Romans sink the Carthaginian fleet bringing Year 2003 ( MMIII) was a Common year starting on Wednesday of the Gregorian calendar. "Ricci flow with surgery on three-manifolds". arXiv:math.DG/0303109. The arXiv ( pronounced " Archive " as if the "X" were the Greek letter Chi, χ is an Archive for electronic  
• Perelman, Grisha (July 17, 2003). Events 180 - Twelve inhabitants of Scillium in North Africa are executed for being Christians Year 2003 ( MMIII) was a Common year starting on Wednesday of the Gregorian calendar. "Finite extinction time for the solutions to the Ricci flow on certain three-manifolds". arXiv:math.DG/0307245. The arXiv ( pronounced " Archive " as if the "X" were the Greek letter Chi, χ is an Archive for electronic  

Notes

References

See also

• Homology sphere
• Manifold Destiny (On The New Yorker article)
• Soul theorem
• Uniformization theorem

External links

• Grigori Perelman at the Mathematics Genealogy Project
• Fields Medals awarded at the 2006 IMU
• International Congress of Mathematicians 2006
• Perelman's arXiv eprints (link to APS mirror due to server strain on arxiv. In Algebraic topology, a homology sphere is an n -manifold X having the Homology groups of an n - Sphere, for some integer "Manifold Destiny" is an article in The New Yorker written by Sylvia Nasar and David Gruber and published in the August 28 2006 issue of the The New Yorker is an American Magazine that publishes reportage commentary criticism essays fiction satire cartoons and poetry In Mathematics, the soul theorem is the following theorem of Riemannian geometry: If ( M, g) is a complete non In Mathematics, the uniformization theorem for Surfaces says that any surface admits a Riemannian metric of constant Gaussian curvature. The Mathematics Genealogy Project is a web-based Database that gives an Academic genealogy based on Dissertation supervision relations org re Perelman)
• Staff listing for Perelman at Petersburg Department of Steklov Institute of Mathematics
• Mathematics & Mechanics Faculty of Saint Petersburg State University
• Petersburg Department of Steklov Institute of Mathematics
• Notes and commentary on Perelman's Ricci flow papers
• International Mathematical Olympiad 1982 (Budapest, Hungary)
• Maths solution tops science class (Link to BBC News page)
• BREAKTHROUGH OF THE YEAR: The Poincaré Conjecture--Proved
• Perelman refuses a million dollars to live in complete poverty

Persondata
NAME	Perelman, Grigori Yakovlevich
ALTERNATIVE NAMES
SHORT DESCRIPTION	Mathematician
DATE OF BIRTH	June 13, 1966
PLACE OF BIRTH	Leningrad, USSR
DATE OF DEATH
PLACE OF DEATH

Events 1525 - Martin Luther marries Katharina von Bora, against the Celibacy rule decreed by the Roman Catholic Church for Year 1966 ( MCMLXVI) was a Common year starting on Saturday (link will display full calendar of the 1966 Gregorian calendar. Saint Petersburg ( tr: Sankt-Peterburg,) is a city and a federal subject of Russia located on the Neva River The Union of Soviet Socialist Republics (USSR was a constitutionally Socialist state that existed in Eurasia from 1922 to 1991

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