AI Discovery in Combinatorics: From Problems to Solutions and Back to Bigger Problems
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Abstract (arXiv)
We introduce qtBench, 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 questions and give our views.
Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 6 of its 26 references that are in the map. First posted on arXiv 12 Oct 2026.
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6 of 26 references.
References · 6
- 2025Mathematical exploration and discovery at scalecited by 77
- 2026Formal Conjectures: An Open and Evolving Benchmark for Verified Discovery in Mathematicscited by 10
- 2026Measuring Progress in Reasoning Toward Mathematical Discovery with Automatic Verificationcited by 9
- 2025Even with AI, Bijection Discovery is Still Hard: The Opportunities and Challenges of OpenEvolve for Novel Bijection Constructioncited by 5
- 2025From Black Box to Bijection: Interpreting Machine Learning to Build a Zeta Map Algorithmcited by 3
- 2026Mapping Uncharted Symmetries: Machine Discovery in Combinatoricscited by 1
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