超越精选突破：在随机抽样的数学猜想上评估语言模型
Beyond Selected Breakthroughs: Evaluating Language Models on Randomly Sampled Mathematical Conjectures
Helen Jenne, Davis Brown, Jesse He, Henry Kvinge
AI 速览：作者构建 OpenConjecture 数据集，用随机抽样的 200 条 arXiv 猜想以可复现协议测试前沿 GPT 模型，并分析候选解的类型与特征而非做专家验证。
The last year has seen a shift in AI-assisted mathematics, with frontier language models producing proofs of and counterexamples to long-standing open conjectures. However, studying only the current set of major breakthroughs provides an incomplete picture of LLM capabilities and the computational resources needed to achieve reported results. To address this, we introduce a new dataset, OpenConjecture, which collects conjectures from mathematics papers published on the arXiv since February 2026. We use these conjectures as a source of open mathematical problems, and apply frontier GPT models to a random sample of 200 of these conjectures over three passes using a reproducible protocol without problem-specific mathematical guidance. Rather than attempt expert verification of these candidate solutions, we analyze the types of problems for which LLMs produce solutions and the characteristics of these solutions. The models we test produce candidate solutions for roughly 60% of the conjectures, with counterexamples about 1.3 times more common than proofs. We estimate solution novelty, assess how solutions cite and relate to existing literature, and analyze whether the proposed resolution relies on either an error in or underspecification of the conjecture. We find that models sometimes propose resolutions that are outside the authors' intent (e.g., proposing the trivial group as a counterexample) and that a number of proofs follow closely from existing results, but that some resolutions exhibit at least moderate novelty. Our findings underscore the need for evaluations that go beyond correctness to assess fidelity to the intended statement, attribution, and the nature of the mathematical contribution.