PreprintCC BY 4.0arXiv
AI Discovery in Combinatorics: From Problems to Solutions and Back to Bigger Problems
Abstract
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.
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BibTeX
@misc{cainelli2026discovery,
title = {{AI Discovery in Combinatorics: From Problems to Solutions and Back to Bigger Problems}},
author = {Eugenio Cainelli and Lorenzo Luccioli and Alessandro Iraci and Giovanni Paolini},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16555},
eprint = {2610.16555},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16555},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - AI Discovery in Combinatorics: From Problems to Solutions and Back to Bigger Problems
AU - Eugenio Cainelli
AU - Lorenzo Luccioli
AU - Alessandro Iraci
AU - Giovanni Paolini
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16555
UR - https://arxiv.org/abs/2610.16555
AB - 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.
ER -