Poincaré Conjecture/Historical Note

Theorem

The Poincaré Conjecture was first posed in $1904$ by Jules Henri Poincaré.

For $n = 1$ and $n = 2$ the result was long known to be true.

For $n \ge 5$ it was proved by Stephen Smale in $1960$.

The case for $n = 4$ was solved by Michael Hartley Freedman in $1982$.

The remaining case for $n = 3$ was finally resolved by the work of Grigori Perelman, who solved Thurston's Geometrization Conjecture in $2003$ (although some sources say $2004$).

He did this by using the Ricci flow method.


Sources

  • 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Poincaré conjecture
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Millennium Prize problems
  • 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Poincaré conjecture
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