用自动验证框架测试AI在未解数学题上的发现能力
HorizonMath: Measuring AI Progress Toward Mathematical Discovery with Automatic Verification
- 构建100多个未解数学问题的基准，支持自动验证
- GPT 5.4 Pro提出两项改进现有结果的新解法
- 适合研究AI数学创造力与开放挑战的学者
AI能否解决重要的未解数学问题？大语言模型已具备复杂数学推理能力，但其是否能开展原创研究仍存争议。我们提出HorizonMath，一个涵盖8个计算与应用数学领域的超100个主要未解问题的基准，并配套开源自动验证评估框架。该基准聚焦于需要深刻数学洞察但验证成本低的问题，避免数据污染；现有顶尖模型得分接近0%。相比依赖形式证明或人工评审的研究级基准，此平台更易扩展。使用该平台，我们发现GPT 5.4 Pro提出的两个解法优于已有最佳公开结果，可能构成新贡献（待专家评审）。我们公开发布HorizonMath作为持续演进的开放挑战，未来正确解答可成为数学文献中的新成果。
原文摘要 · Abstract (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.
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