在2026年5月至7月的短短三个月间，多个大型语言模型在数学领域取得了突破性进展，通过发现反例推翻了多个困扰数学界多年的重大猜想。[1]
ChatGPT率先在5月20日推翻了Erdős单位距离猜想，随后Logical Intelligence系统将其自动形式化在Lean编程语言中。[1]6月26日，OpenAI研究员Boris Alexeev利用新模型Sol完成了该反例的完整形式化，生成了120万行代码。[1]
随着这些工具的进一步应用，更多长期未解的难题被攻克。7月11日，Akhi Mathew使用Sol发现了Grothendieck关于阶为n的有限自由群方案的猜想存在反例，该反例随后由自动化系统Fable形式化验证。[1]此外，Levent Alpöge指出Fable还发现了已开放100年的Jacobian猜想的反例。[1]
这些成果表明AI在生成和验证大规模数学代码方面已具备极高能力。当前，博士生每月需支付200美元以访问Sol和Fable等工具，而哈佛大学已向其数学系免费开放Fable的使用权限，反映出数学界对AI辅助研究的广泛投入和关注。[1]
Between May and July 2026, major language models made significant breakthroughs in mathematical research by discovering counterexamples to long-standing conjectures. [1] On May 20, 2026, ChatGPT disproved the Erdős unit distance conjecture, which was subsequently automatically formalized in Lean by the Logical Intelligence system. [1]
OpenAI researcher Boris Alexeev used a new model called Sol to complete a full formalization of the Erdős counterexample, generating 1.2 million lines of code, which was finished by June 26, 2026. [1] The same model enabled further discoveries: on July 11, 2026, Akhi Mathew identified a counterexample to Grothendieck's conjecture about finite free group schemes of order n, which was then automatically verified and formalized by Fable. [1]
Beyond these specific breakthroughs, Levent Alpöge noted that Fable has also discovered a counterexample to the Jacobian conjecture, which had remained open for 100 years. [1] These developments demonstrate that AI systems have achieved substantial capability in generating and verifying large-scale mathematical code.
The practical implications are reshaping mathematical research. According to the available information, doctoral students must pay $200 per month to access tools such as Sol and Fable, though Harvard University has made Fable available free of charge to its mathematics department. [1]