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Grigory Perelman (1966– )

Solver of the Poincaré Conjecture

Grigory Perelman is a Russian mathematician who solved one of the most profound and long-standing problems in mathematics—the Poincaré conjecture—via Perelman’s proof using Ricci flow with surgery. Born in Leningrad, his breakthrough work in the early 2000s earned global acclaim, but he famously declined both accolades and the million-dollar Millennium Prize.

Contributions

• Geometric analysis: introduced a Ricci flow equation \[ \frac{\partial g_{ij}}{\partial t} = -2R_{ij} \] smoothing out irregularities in geometry over time.
• Topological conclusion: showed that a closed three-manifold with finite extinction under Ricci flow is a 3-sphere.

Legacy

Perelman’s proof unified deep geometry, topology, and analysis. His refusal of fame and prizes accentuates his philosophical purity and the intrinsic motivation of mathematics. He remains one of the most enigmatic and respected figures in modern mathematics.