HorizonMath: Measuring AI Progress Toward Mathematical Discovery with Automatic Verification

TL;DR

HorizonMath is a new benchmark with over 100 unsolved mathematical problems designed to evaluate AI's ability to make novel discoveries, using automated verification to identify potential breakthroughs by large language models like GPT-5.4.

Contribution

It introduces a scalable, open-source platform for assessing AI-driven mathematical discovery on unsolved problems, avoiding data contamination and manual review.

Findings

GPT 5.4 Pro proposed solutions to two problems, improving on known results.

HorizonMath enables scalable, automated evaluation of AI's mathematical reasoning.

Potential for AI solutions to contribute novel results to mathematics.

Abstract

Can AI make progress on important, unsolved mathematical problems? Large language models are now capable of sophisticated mathematical and scientific reasoning, but whether they can perform novel research is still widely debated and underexplored. We introduce HorizonMath, a benchmark of over 100 predominantly unsolved problems spanning 8 domains in computational and applied mathematics, paired with an open-source evaluation framework for automated verification. Our benchmark targets a class of problems where discovery is hard, requiring meaningful mathematical insight, but verification is computationally efficient and simple. Because these solutions are unknown, HorizonMath is immune to data contamination, and most state-of-the-art models score near 0%. Existing research-level benchmarks instead rely on formal proof verification or manual review, both of which are expensive to scale. Using this platform, we find two problems for which GPT 5.4 Pro proposes solutions that improve on the best-known published results, representing potential novel contributions (pending expert review). We release HorizonMath as an open challenge and a growing community resource, where correct solutions to problems in the unsolved problem classes could constitute novel results in the mathematical literature.