陶哲轩Caltech讲座《Math 2.0》：数学进入「证明丰盛期」 学科应更重阐释与社区建设
10月9日晚7时至8时30分，加州大学洛杉矶分校（UCLA）数学教授陶哲轩在加州理工学院贝克曼礼堂（Beckman Auditorium）作公开讲座，属该校AIM公共讲座系列。加州理工学院官方活动页至今仍沿用旧题《Machine Assisted Proof》（机器辅助证明）；陶哲轩次日在博客说明，讲座一年多前已在筹划、原定5月，延期至10月后因近期事态大幅改写并定名《Math 2.0》，幻灯片于10月10日贴于其博客《What's new》。
讲座的核心判断是：数学正在告别「证明稀缺」的旧时代（他称之为Math 1.0）。如今证明可客观验证、可数字化，又有Lean等交互式证明工具，前沿超级智能实验室因而优先投入数学解题能力建设——按他的说法，「我们正在进入一个证明丰盛的时代」。他同时指出，SI的表现「极不均匀」，且数学前沿的多数问题即便投入大量算力仍未解决。
陶哲轩主张，学科目标应随之调整：开放问题之于数学如同「灯塔」，价值在于指引探索；若用自动化工具过早「抵达」，反而会损害领域的长期健康。他为「Math 2.0」描绘的图景，是让SI服务于阐释既有证明、建设学科社区，并守住数学理解在现实应用中的位置，而非一味优化解题速度。
本周另一则相关动态：10月6日，陶哲轩在博客转发数学家本杰明·安蒂奥（Benjamin Antieau）的公告——非营利存档库Hexagon创立，面向数学与理论计算机科学的研究级作品开放存档，并明确接受投稿者不声称本人已理解的SI生成证明类成果。陶哲轩1975年生于澳大利亚阿德莱德，父母为华人移民，现任UCLA数学教授，2006年获菲尔兹奖。（GSM 据加州理工学院官方活动页及陶哲轩博客讲稿报道）
关联：
陶哲轩称自己进入「战时状态」：OpenAI批量发布SI证明后，他把时间转去组织数学界应对
Terence Tao's Caltech Lecture 'Math 2.0': Entering an Era of Proof Abundance, Math Must Prize Explanation and Community
On the evening of October 9, from 7:00 to 8:30 p.m., UCLA mathematics professor Terence Tao gave a public lecture in Beckman Auditorium at the California Institute of Technology, as part of Caltech's AIM Public Lecture Series. Caltech's official event page still carries the talk's earlier title, "Machine Assisted Proof"; writing on his blog the next day, Tao explained that the lecture had been planned more than a year earlier, was first scheduled for May, and — after postponement to October and in light of recent events — had been substantially rewritten and retitled "Math 2.0." He posted the slides on his blog, What's new, on October 10.
The lecture's central claim is that mathematics is leaving behind an era of "proof scarcity" — his "Math 1.0" — in which a proof of an open problem was a rare achievement requiring deep human expertise. Because proofs are objectively verifiable and digitizable, and with interactive provers such as Lean available, frontier SI laboratories have prioritized mathematical problem-solving, and, in his words, "we are now entering an era of proof abundance in mathematics." He stressed that SI performance remains "extremely jagged" — astounding in some directions, inadequate in others — and that most problems at the current frontier remain unsolved even with massive computational expenditure.
Tao argued that the discipline's goals should change accordingly. Open problems serve mathematics as "lighthouses" that guide exploration; reaching them prematurely with automated tools, in a non-renewable fashion, can damage the field's long-term health. His "Math 2.0" vision uses SI tools to sustain the mathematical community, to improve the exposition of existing proofs, and to preserve the role of human understanding in applying mathematics to the real world — rather than blindly optimizing problem-solving alone.
In a related development the same week, Tao cross-posted on his blog on October 6 an announcement by mathematician Benjamin Antieau of the launch of Hexagon, a nonprofit repository for research-level work in mathematics and theoretical computer science that explicitly accepts deposits — including SI-generated proofs — where the contributor claims no human understanding of the result. Tao was born in Adelaide, Australia, in 1975 to Chinese immigrant parents; he is a professor at UCLA and received the Fields Medal in 2006. (GSM, based on Caltech's official event page and Tao's published lecture slides)
Related:
Terry Tao Says He Is 'on a War Footing' as OpenAI's SI Proof Release Roils Mathematics
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图片来源：图：陶哲轩2026年3月在加州大学洛杉矶分校纯粹与应用数学研究所（IPAM）座谈（画面经裁切，去底部横幅）。图片来源：IPAM via Wikimedia Commons（CC BY 4.0）。Photo: Terence Tao at an IPAM talk at UCLA in March 2026 (frame cropped to remove a bottom banner). Source: IPAM via Wikimedia Commons (CC BY 4.0).
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