Topology · Geometry · Theorem

Poincaré conjecture

Is every closed, simply connected three-dimensional manifold homeomorphic to the three-sphere?

Provedper Clay · Millennium Problems · checked Oct 1, 2026

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Overview

Clay reports the full three-dimensional statement solved; independent OpenMath assessment is not indexed.

Precise statement

Topological manifolds in dimension three; the source reports the problem as solved.

Question paraphrased by OpenMath. Original wording is available in the sources.

Evidence by kind
Literature	1 reference description Status per Clay · Millennium Problems · checked Oct 1, 2026. Proved: Clay · Millennium Problems · Solved ↗ · source date not recorded · checked Oct 1, 2026The cited source item and version only; this is not an independent OpenMath assessment.
Formal	None linked
Computation	None recorded
Review	Not yet reviewed

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Clay · Millennium Problems →
Clay Mathematics Institute
Source state checked on 1 October 2026. The page does not provide a status-update date; current literature has not been independently reviewed.

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