OpenAI在2026年9月8日宣布利用人工智能生成了纳维-斯托克斯方程存在性和光滑性问题的解决方案，并提供了Lean形式化证明和非形式化手稿1。然而这一宣布随即引发数学界的广泛质疑。
评论指出，OpenAI提供的虽是形式化答案，但并非真正的数学解，核心在于缺乏人类能够理解和应用的可理解证明1。Clay数学研究所强调："证明不仅给予确定性，也给予理解"1。数学界认为，数学远超问题求解的范畴，还包括理论发展、理解世界、维持学术社群、培养新一代数学家以及追求审美价值等多重目标1。为此，包括25位菲尔兹奖得主在内的数学家联署声明，警告AI公司与数学社群的目标存在"严重错位"1。
On September 8, 2026, OpenAI announced the resolution of the Navier-Stokes existence and smoothness problem, one of the Millennium Prize Problems, using artificial intelligence.1 The company provided both a Lean formal proof and a non-formal manuscript as supporting materials.1
The announcement has triggered significant scrutiny regarding what constitutes a genuine mathematical solution. Critics distinguish between two types of proofs: logical proofs that can be mechanically verified, and understandable proofs that require human comprehension.1 While AI may deliver formal certainty, observers argue it fails to provide the human intelligibility that mathematics demands. The Clay Mathematics Institute emphasized that "proof gives not only certainty but also understanding."1
Twenty-five Fields Medal recipients issued a joint statement cautioning that AI companies and the mathematical community operate with "serious misalignment" in their objectives.1 Mathematician Terence Tao articulated mathematics' multifaceted purposes, including theoretical development, understanding the natural world, sustaining the mathematical community, cultivating future mathematicians, and aesthetic value.1 The debate reflects fundamental questions about whether computational solutions satisfy the deeper intellectual and cultural functions that mathematics serves within human knowledge and society.
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