The Kinoshita Conjecture and Kirby Problem 4.37
Kinoshita conjectured that every embedded projective plane in is reducible. False: an irreducible embedded projective plane exists in . The construction also answers both parts of Problem 4.37 of the Kirby problem list.
- Result
- Disproved
- Status
- Resolved
- AI contribution
- AI-assisted
- Method
- Construction
- Field
- 4-manifold topology
- Posed by
- Shin'ichi Kinoshita; Problem 4.37 of the Kirby list
- Year posed
- —
- Years open
- —
- Solved
- 2026-05-13
- Model
- ChatGPT, Cursor and Gemini
- Vendor
- —
- Collaborators
- Mark Hughes, Seungwon Kim, Maggie Miller, Gheehyun Nahm
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 35 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
Deliberately bounded, and the authors draw the boundary themselves: they acknowledge using ChatGPT, Cursor and Gemini during initial exploration and computation, and state that all final computations were performed and verified by the authors without the use of AI. So the models were exploratory instruments and none of the standing mathematics rests on them.
Verification
The authors state they performed and verified all final computations themselves without AI. The result is an explicit construction plus a computation, so it is checkable by hand. arXiv preprint, not peer-reviewed.
Source
arXiv:2605.12921 - An irreducible real projective plane in the 4-sphere