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Tao warns AI-generated math proofs are outpacing human verification

AI summary

Fields Medalist Terence Tao amplified mathematician Thomas Hales' essay on the Lean theorem prover's reliability and AI, and on Mathstodon proposed a shift from "Math 1.0" to "Math 2.0" — valuing explanation, community and new directions over who proves a problem first. The account says OpenAI published 722 model-generated math manuscripts on GitHub on October 6, spanning 372 result families and about 4,000 test problems, with three retracted a day later, and that Lean suffered a run of soundness bugs in summer 2026, including a formally verified claim disproving the Collatz conjecture that was accepted by the kernel and an independent checker. The report says Tao co-signed a declaration by 25 Fields Medalists on AI's misalignment in mathematics and that a body he leads called for halting collaboration with OpenAI, while researchers interviewed said the AI tide is unstoppable and may lift science less than it appears.

In-depth insight

If nobody actually reads the flood of AI proofs and the verification tools themselves can be unsound, mathematics loses its core guarantee of having reliable reason to believe a result is true.

当AI开始批量生产数学证明,人类凭什么确信这些证明是可靠的?

美国当地时间10月9日,著名数学家、菲尔兹奖得主陶哲轩在其博客转发了托马斯·黑尔斯的专栏文章“《数学家应该了解的Lean定理证明器:可靠性与人工智能问题》”。

陶哲轩博客转发文章截图

这场AI数学浪潮的矛盾在于:AI正在以前所未有的速度攻克数学难题,这些难题过去需要数学家耗费数年甚至数十年才能完成的证明。

一个典型的案例是OpenAI于10月6日在GitHub上一次性放出了722篇由内部模型生成的数学手稿,涵盖372个结果系列和约4000个测试问题。

#Terence Tao#OpenAI#Lean#Thomas Hales#Microsoft Research#Leonardo de Moura#University of California, Los Angeles#GitHub#ICLR

Original · 7 min readRead the original
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