AI Discovery in Combinatorics: From Problems to Solutions and Back to Bigger Problems
We introduce $qt$Bench, a benchmark of 29 open problems in algebraic combinatorics. These problems ask for a simple combinatorial algorithm that explains given polynomial coefficients or identities. To help AI agents search for such algorithms, we provide a scaffold for playing with combinatorial objects, countering cheating attempts, and testing candidate solutions. To explore how far frontier AI systems can go on these problems, we collaborated with OpenAI, whose researchers obtained proposed solutions to several of them. This highlights bigger meta-problems: is AI discovery at scale ethical? How should these results be released? How should proof digestion be organized? We discuss these...
| Authors | Eugenio Cainelli, Lorenzo Luccioli, Alessandro Iraci et al. |
|---|---|
| Primary category | cs.AI |
| Published | 12 October 2026 |
| Last updated at source | 12 October 2026 |
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