The Aluffi-Chen-Marcolli Real-Rootedness Conjecture
Aluffi, Chen and Marcolli conjectured that the Poincare polynomial of the Deligne-Mumford moduli space of stable -pointed rational curves has only real roots. True, with simple roots and strict interlacing between consecutive .
- Result
- Proved
- Status
- Resolved
- AI contribution
- AI co-developed
- Method
- Argument
- Field
- Algebraic geometry
- Posed by
- Paolo Aluffi, Wenxuan Chen, Matilde Marcolli
- Year posed
- —
- Years open
- —
- Solved
- 2026-05-27
- Model
- Co-Mathematician
- Vendor
- —
- Collaborators
- Gergely Berczi, Young-Hoon Kiem
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 20 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What the AI did
The paper says the proof was found with the assistance of Co-Mathematician, a frontier agentic LLM-based system for mathematical research described in a separate paper, and its title calls the result an AI-assisted proof.
Verification
arXiv preprint; not yet peer-reviewed.
Source
arXiv:2605.29151 - Real-rootedness of the Poincare polynomials of M(0,n): an AI-assisted proof