A structural answer for three-dimensional spaces

What changed

Three-dimensional spaces can be understood through a proved geometric decomposition, resolving the Poincaré conjecture along the way.

Scientific scope

The closed three-manifold setting of geometrization. This S placement belongs to three-dimensional topology; it is not a civilization-wide comparison with medicine or energy.

Evidence

CMI marks the problem solved and describes the broader geometrization result. The linked 2002 paper introduces central Ricci-flow tools; that one abstract alone is not the complete proof.

Contributors

• Grigori Perelman · SCIENCE: Proof of geometrization and the resulting Poincaré conclusion.
• Richard Hamilton · SCIENCE: Pioneering Ricci-flow program, a distinct precursor contribution.
• Henri Poincaré; William Thurston · SCIENCE: The Poincaré problem and geometrization framework, respectively.

• CMI: Poincaré conjecture
• Perelman: entropy and Ricci flow

Provisional WRS assessment, edition 2026-10-16.1. Independent expert calibration is pending. This grade does not certify correctness or assign ownership.

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