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 57M40
QuestionPoincaré conjecture
Reported resolvedScope unassessed
Resolution scope has not been assessed in this publication.
Source report · observed Oct 1, 2026
Viewing pinned publication v1. 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
Reported resolvedScope unassessed
Resolution scope has not been assessed in this publication.
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 v1 · history & checksums
- Stable Problem ID
- problem-poincare-conjecture
- Publication SHA-256
- 05e49e819932dddd738ad935f50a54a81143c76b9cb49362ac94c561e6f1e64d
- Published
- 2026-09-30T20:13:42.302923+00:00
- Publication reason
- Initial checked pilot publication; source attribution, rights, wording and coverage reviewed by OpenMath staff.
- 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.