HorizonMath：基于自动验证的数学发现AI进展评估框架

HorizonMath: Measuring AI Progress Toward Mathematical Discovery with Automatic Verification

March 16, 2026

作者: Erik Y. Wang, Sumeet Motwani, James V. Roggeveen, Eliot Hodges, Dulhan Jayalath, Charles London, Kalyan Ramakrishnan, Flaviu Cipcigan, Philip Torr, Alessandro Abate

cs.AI

摘要

人工智能能否在重要的未解数学问题上取得突破？当前大语言模型已具备复杂的数学与科学推理能力，但其能否开展创新性研究仍存在广泛争议且探索不足。我们推出HorizonMath基准测试集，涵盖计算数学与应用数学8大领域的百余个未解难题，并配套开源自动化验证框架。该基准聚焦于一类发现困难（需要深刻数学洞察力）、但验证计算高效简捷的问题。由于这些问题的解决方案尚未可知，HorizonMath能有效避免数据污染问题，目前最先进模型的得分率接近0%。现有研究级基准依赖形式化证明验证或人工评审，均难以规模化应用。通过该平台，我们发现GPT 5.4 Pro针对两个问题提出的解决方案优于已知最佳公开结果，可能构成创新性贡献（待专家评审）。我们将HorizonMath作为开放性挑战和持续更新的社区资源发布，其中未解问题类的正确答案有望成为数学文献中的新发现。

English

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.