Makeev's conjecture on universal cover
Let be the difference polytope of a regular -simplex such that circumscribes a sphere of diameter 1. Then every set of diameter 1 in is covered by a rotated copy of .
- Result
- Disproved(see note)
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Metric geometry
- Posed by
- V. V. Makeev
- Year posed
- 1994
- Years open
- 32y
- Solved
- 2026-08-10
- Model
- ChatGPT 5.6 Pro
- Vendor
- OpenAI
- Collaborators
- —
- Verification
- Unreviewed
- Publication
- Announced
- Significance
- 15 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
Makeev conjectured it to be true for all dimensions. This result disproves it for dimensions 4 and 5. Dimensions 6 and above remain open.
What the AI did
AI found the counterexample in dimensions 4 and 5 and wrote the paper and code without human mathematical input.
Verification
Checked by this site on 17 August 2026: the repository is real and unusually substantial - 596 files across four independently-built verification approaches (Magma certificates, interval-arithmetic C++, tensor-polynomial certificates, Python numerics), plus the full prompts and chat transcripts, and the problem-record links verify (Makeev's conjecture in arXiv:math/9809165, Handbook chapter 21). The certificates were not run here. The submitter reports a preliminary check by two students, which is private checking, not independent review - Unreviewed stands.
Sources
Submitted by simplex4 on