Proof of the Poincaré conjecture
Henri PoincaréGrigori PerelmanRichard Hamilton
This page delivers no verdict; it presents claims and evidence with their sources. No theory in science is absolute. Method
For everyone
In 1904 Poincaré posed a conjecture characterising three-dimensional "sphere-like" spaces. Grigori Perelman proved it in three papers posted to arXiv in 2002–2003. He declined the Clay Institute's million-dollar prize and the Fields Medal. It is the only Millennium Prize Problem solved to date.
For specialists
The conjecture states that every simply connected closed 3-manifold is homeomorphic to S³. Perelman completed Hamilton's Ricci-flow programme with surgery and proved Thurston's geometrisation conjecture, of which the Poincaré conjecture is a corollary. The proof was verified in detail by Kleiner–Lott, Morgan–Tian and Cao–Zhu.
Claims
Evidence
Supporting
Perelman's preprints were verified by several independent teams in detailed expositions running to hundreds of pages.[4]
Challenging
—
Connections
Sources
- Preprint (2002). The entropy formula for the Ricci flow and its geometric applicationsarXiv:math/0211159archive
- Preprint (2003). Ricci flow with surgery on three-manifoldsarXiv:math/0303109archive
- Preprint (2003). Finite extinction time for the solutions to the Ricci flow on certain three-manifoldsarXiv:math/0307245archive
- WebPoincaré Conjecture. Clay Mathematics Instituteclaymath.orgarchive
Search the literature
Look for scholarly work on this topic in other indexes:
Cite this page
Athena contributors. (2026). Proof of the Poincaré conjecture. Athena: The tree of human knowledge. Retrieved November 1, 2026, from https://latifkedi.github.io/athena/en/d/poincare/
@misc{athena_poincare,
title = {Proof of the Poincaré conjecture},
author = {{Athena contributors}},
year = {2026},
howpublished = {\url{https://latifkedi.github.io/athena/en/d/poincare/}},
note = {Athena: The tree of human knowledge. Accessed: 2026-11-01}
}Added: September 27, 2026 · Last changed: September 27, 2026 · Page history