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First Clay Mathematics Institute Millennium Prize Announced Today
Source of package cmi.poincare · claymath.org/wp-content/uploads/2022/06/Poincare-press-release.pdf
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- urn:org:cmi:poincare#CMI_PRESS_RELEASE_2010
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- claymath.org/wp-content/uploads/2022/06/Poincare-press-release.pdf
- kind
- urn:org:cmi:poincare#treatise
CMI_PRESS_RELEASE_EDITION
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- urn:org:cmi:poincare#CMI_PRESS_RELEASE_EDITION
- language
- en
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- official
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| URI | Type | documentHash | Retrieved |
|---|---|---|---|
| https://www.claymath.org/wp-content/uploads/2022/06/Poincare-press-release.pdf | text/plain; charset=utf-8 | sha256:ea81ef4ade7600b54f3ff140745f31414d61b01131fbc51bf1e05599a32f94a1 | 2026-09-17T00:00:00Z |
Fragments — 10
announcement-2002-2003 · lemma · referenced by: 1
en · official · sha256:ae91fd2ff1c556b74a618a8c7b1d97c3a0eeeb6ca392b11358270ae22082e775
It was thus a huge surprise when Grigoriy Perelman announced, in a series of preprints posted on ArXiv.org in 2002 and 2003, a solution not only of the Poincare conjecture, but also of Thurston's geometrization conjecture [P1, P2, P3].Referencing norms: names-perelman-preprints
award-citation · lemma · referenced by: 1
en · official · sha256:463549413af7cbbbece13e0a411dda213915dd7eafb63bc81ff2901ec56d170e
The Clay Mathematics Institute hereby awards the Millennium Prize for resolution of the Poincare conjecture to Grigoriy Perelman.Referencing norms: press-reports-solved
headline · defn · referenced by: 1
en · official · sha256:ba22f178efd0af18ec47af0ec4bebce5fbc71a40e509d3fc14af47b2b3dc255b
Prize for Resolution of the Poincare Conjecture Awarded to Dr. Grigoriy PerelmanReferencing norms: CmiPressReleaseSource
perelman-entropy · defn
en · official · sha256:f09b8e8359ba51b81d8b062f06c6b260ee61a3a8ab5977d21f4860ea03756bfa
He introduced a new quantity, the entropy, which instead of measuring disorder at the atomic level, as in the classical theory of heat exchange, measures disorder in the global geometry of the space.ref-ha1 · defn
en · official · sha256:630bb3419f68c8a87e47bf0340a653898486cf70c7bfab73afb1412e5ffdb53b
[Ha1] R. Hamilton, Three-manifolds with positive Ricci curvature, Journal of Differential Geometry, vol. 17:255-306 (1982)ref-p1 · defn
en · official · sha256:18d01c889e1564a477f5c9412dfd5c33ee8800325d1847704a163c549d28f83c
[P1] G. Perelman, The entropy formula for the Ricci flow and its geometric applications, arXiv.org, November 11, 2002ref-p2 · defn
en · official · sha256:6c209c26142905d0967be7287776075efd25a305b1fa4c79bf101e1d2965a90c
[P2] G. Perelman, Ricci flow with surgery on three-manifolds, arXiv.org, March 10, 2003ref-p3 · defn
en · official · sha256:9a69c3c5e1ecec939629c2119b265d61c18fc4b2e064ba4ae67f189fbda34ce7
[P3] G. Perelman, Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, arXiv.org, July 17, 2003ricci-flow-1982 · defn · referenced by: 1
en · official · sha256:69958d0afa82e53464a72da55ee060725f096f29baa33a9939ff4770760be050
Around 1982, however, a new line of attack was opened. This was the Ricci flow method pioneered and developed by Richard Hamilton.Referencing norms: names-hamilton-ricci-flow
settled · lemma · referenced by: 1
en · official · sha256:abef2023267c6ba83c4930162733305fa7042eb2312986cb84b2cd756e33d714
Perelman had solved the Poincare conjecture. After a century's wait, it was settled!Referencing norms: names-settled
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