# AI Discovery in Combinatorics: From Problems to Solutions and Back to Bigger Problems

arXiv: https://arxiv.org/abs/2610.16555 · HTML: https://mlsanity.com/paper/2610.16555/

## 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.

## Builds on (most cited first, 6 of 6)

- [Mathematical exploration and discovery at scale](https://mlsanity.com/paper/2511.02864/) (2025)
- [Formal Conjectures: An Open and Evolving Benchmark for Verified Discovery in Mathematics](https://mlsanity.com/paper/2605.13171/) (2026)
- [Measuring Progress in Reasoning Toward Mathematical Discovery with Automatic Verification](https://mlsanity.com/paper/2603.15617/) (2026)
- [Even with AI, Bijection Discovery is Still Hard: The Opportunities and Challenges of OpenEvolve for Novel Bijection Construction](https://mlsanity.com/paper/2511.20987/) (2025)
- [From Black Box to Bijection: Interpreting Machine Learning to Build a Zeta Map Algorithm](https://mlsanity.com/paper/2511.12421/) (2025)
- [Mapping Uncharted Symmetries: Machine Discovery in Combinatorics](https://mlsanity.com/paper/2605.19063/) (2026)

## 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.