发表机构
The Graduate Center, CUNY（纽约市立大学研究生中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文反思OpenAI宣布的纳维-斯托克斯方程爆破证明无人能读，探讨认证证明与人类理解的距离，主张以盟约约束AI产商，维护数学共同体的自主理性。
AI 中文摘要
2026年9月8日，OpenAI宣布证明了具有光滑数据和强迫项的三维纳维-斯托克斯方程的有限时间爆破：由一万个智能体在88小时内生成166页证明，经616,000行Lean代码认证，并且在撰写本文时（2026年9月20日），没有任何人类完整阅读过该证明。本文探讨这样的产物——文本、证书和公告——究竟是什么，以及接受它作为证明会带来什么后果。数学曾是启蒙运动对自主理性的存在性证明：三个世纪以来，每个经过认证的定理都能被任何遵循其论证过程的人所理解，且两者之间的距离在构造上为零。一个无人能遵循的认证证明重新打开了这一距离，而接受它的共同体在未经投票的情况下采纳了霍布斯为利维坦起草的宪法，在其中权威而非真理制定法律。本文区分了被论证的与被启示的（被认证的）；以帕诺夫斯基的术语，将即将到来的时代命名为“倒转的中世纪”，并将其权威称为“亚人类超级智能”；并将转折点定位于不是机器所生产的，而是我们所接受的。由于接受是公司无法制造的唯一的最高制裁，本文提出以盟约取代抵制或投降：共同体将其合作给予严格遵守其可读性、披露和责任实践的产商，而拒绝给予任何不遵守者，且盟约保持多元，以帝国竞争中原住民国家的历史为指南。标题中的塞壬承诺知识，而非理解。暮光是白昼两端的亮光，而这场启蒙暮光究竟是黄昏还是黎明，取决于在接受时刻所做的事情，而这一时刻尚未过去。
英文摘要
Over three centuries ago our Enlightenment forefathers brought forth in Europe--and later on this continent--a new approach to knowledge production and dissemination, conceived in distrust of authority, and dedicated to the proposition that truth is accessible to human reason. Mathematics, the Enlightenment's firstborn, was its existence proof--knowledge that compels assent without appeal to authority--because the only way to make a theorem certain was to show it to a human mind. Now we are engaged in an existential struggle testing whether mathematics, or any discipline so conceived and so dedicated, can long endure. We are met in the wake of the OpenAI press release: 166 pages, 616,000 lines of Lean, produced in 88 hours by some 10,000 software agents, and read in full--at the time of this Siren Call--by no human being. A proof has historically been two things: a certificate that a theorem is true, and a demonstration that lets another person see why. OpenAI delivered the first without the second. But, in a larger sense, what matters is not what the Silicon Leviathan (OpenAI and its peer competitors) produces but rather what we accept. By accepting the certificate without the demonstration, we adopt the Hobbesian bargain: authority, not truth, makes the law. The age that this augurs is--in Panofsky's phrase--a Middle Ages in reverse--its authority a subhuman superintelligence. The great task before us is to frame a covenant under which what has become optional--understanding--remains required: that nothing counts as mathematics until a human being has understood it--and can show the next person why. Whether we will safeguard and keep our sovereign inheritance--decided at the moment of acceptance--which is not yet past--will determine if this Aufklärungsdämmerung spells the Enlightenment's end.
Comments60 pages, 5 figures, 108 notes. The essay dated 20 September 2026. Third version; abstract rewritten. A shorter version without notes appeared as a thread on X on 18 September 2026
