Proof of the Poincaré and geometrization conjectures
Prueba de la conjetura de Poincaré y de la geometrización
- Date
- 2002-2003 · confidence high
- Place
- St Petersburg (Steklov Institute), Russia
- Credited to
- Grigori Perelman; Richard Hamilton's Ricci flow (1982); Thurston's geometrisation conjecture (1982)
- People
- 👤 Grigori Perelmán1966–
- Field
- Knowledge & symbols
What was discovered
Using Ricci flow with surgery, Perelman proved that every 3-manifold decomposes into pieces with one of eight geometries, which implies the Poincaré conjecture. The only Millennium Problem solved.
Published only on arXiv; Perelman turned down the Fields Medal (2006) and the Millennium Prize (2010).
What it led to
- geometric analysis
- the complete classification of 3-manifolds
- geometric flow techniques