Source label: Solved
Source status date unavailable · Observed Oct 1, 2026
The cited source item and version only; this is not an independent OpenMath assessment.
Topology · Geometry MSC2020 57K30 / 57R60
theoremPoincaré conjecture
ProvedFull statement
Clay reports the full three-dimensional statement solved; independent OpenMath assessment is not indexed.
Source report · observed Oct 1, 2026
Viewing pinned publication v3. View the current publication →
Question & scope
Is every closed, simply connected three-dimensional manifold homeomorphic to the three-sphere?
Topological manifolds in dimension three; the source reports the problem as solved.
Question paraphrased by OpenMath. Use the cited source and locator for authoritative wording.
Research state
ProvedFull statement
Clay reports the full three-dimensional statement solved; independent OpenMath assessment is not indexed.
Source report · observed Oct 1, 2026 · Clay · Millennium Problems
This is a discovery entry. OpenMath has checked the linked source and attribution; it has not independently assessed the present mathematical status.
Literature & sources
Clay problem page and official description ↗
Source state checked on 1 October 2026. The page does not provide a status-update date; current literature has not been independently reviewed.
Provenance & coverage
Published after staff preview and source checks. This page covers the cited items; it does not represent a complete list of problems or a literature-wide review.
- No exhaustive literature or source-list coverage.
- Independent mathematical assessment has not been performed.
Clay · Millennium Problems ↗
Clay Mathematics Institute · metadata-link · Not established; links and OpenMath paraphrases only
Store metadata and original OpenMath paraphrases; follow the original source for authoritative wording. Rights / source terms
1 cited entry · exact source identity
- Version
- clay-millennium@observed-2026-10-01
- Revision
- observed-2026-10-01
- Content SHA-256
- No upstream byte snapshot retained; linked metadata only
- Source update
- Unavailable
- Observed
- 2026-10-01
- Check cadence
- 30 days
- https://www.claymath.org/millennium/poincare-conjecture/ ↗
poincare-conjecture:entry:0:v1
Publication v3 · history & checksums
- Stable Problem ID
- problem-poincare-conjecture
- Publication SHA-256
- bffc56f4510c69ce8b073816161a77146b4204167d9b9870fd99f2a16185758c
- Published
- 2026-10-10T06:01:24.763945+00:00
- Publication reason
- Add cited resolution scope and consolidate equivalent prime formulations and supporting Claims; mathematical evidence and execution review remain distinct.
- v1 · publish · Sep 30, 2026
Initial checked pilot publication; source attribution, rights, wording and coverage reviewed by OpenMath staff.
- v2 · publish · Sep 30, 2026
Correct classification to MSC2020 57K30 and 57R60 after checking the official AMS/zbMATH taxonomy; retain the attributed Clay status.
- v3 · publish · Oct 10, 2026
Add cited resolution scope and consolidate equivalent prime formulations and supporting Claims; mathematical evidence and execution review remain distinct.
- v4 · publish · Oct 11, 2026
Publish checked pilot curation with canonical Claims and scoped progress; preserve exact source revisions, assumptions, coverage limits and historical publications. External artifacts and OpenMath execution remain distinct.
- v5 · publish · Oct 12, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- v6 · publish · Oct 12, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- v7 · publish · Oct 12, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- v8 · publish · Oct 12, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- v9 · publish · Oct 13, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- v10 · publish · Oct 14, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- v11 · publish · Oct 15, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- v12 · publish · Oct 20, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
- v13 · publish · Oct 20, 2026
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.