AlphaEvolve 发现，在某些排列群中的 Bruhat intervals 具有一种特殊结构，在研究者的研究中，这些结构形成了称为 hypercubes 的更高维立方体。Libedinsky 说：「如果它是人类，那会是极其有创造力的人类。」Ellenberg 说：「我们并没有要求 AlphaEvolve 去找大的 hypercubes，」Williamson 则说那是「一种已经在我们鼻子前面摆了 50 年的结构。」Williamson 还说：「我可以突然在 20 分钟内做一个实验，而 2 年前这本来要花我两周，」尽管「大多数时候它都行不通。」
Ravi Vakil、Balázs Elek 和 Jim Bryan 研究了球面如何嵌入称为 flag varieties 的特殊空间，并找到了例子，显示它与所有连续嵌入空间的预期相似性会非常快地出现。他们与 Freddie Manners 和 George Salafatinos 合作，使用 DeepThink 和 FullProof。2026 年 1 月 12 日的一份 preprint 中，AI 在一个更简单的情形下先给出了一个「非常优雅、正确、写得很美」的证明，之后又成功补全了一般性证明的细节。Vakil 说：「论证的清晰度给了我们一个新想法。」
Litt 警告说，「有大量由 AI 生成的胡言乱语在污染公共领域」，而 Joel David Hamkins 说他「对这片淹没我们期刊系统的垃圾海洋感到绝望。」Tao 说：「没有验证的 AI 太不可靠，无法用于任何严肃应用，」并补充说：「第一次，我确实觉得我们可以透过 AI 形式化数学的一个重要部分。」Tao 把当前的 AIs 比作「跳跃机器人」，它们可以「用跑酷的方式爬上 6 英尺高的墙顶」，而 Litt 说：「我预期 20 年后，我们会看到 AI 工具生成的数学，在许多可衡量的方面都比每一位人类数学家更好。」
AlphaEvolve found that the Bruhat intervals in certain permutation groups had a special structure and, in the researchers’ study, formed higher-dimensional cubes called hypercubes. Libedinsky said, “If it was a human, it would be an extremely creative human.” Ellenberg said, “We didn’t ask AlphaEvolve to find big hypercubes,” and Williamson said it was “a structure that’s been sitting there for 50 years in front of our nose.” Williamson also said, “I can suddenly do an experiment in 20 minutes that two years ago would have taken me two weeks,” even though “most of the time it doesn’t work.”
Ravi Vakil, Balázs Elek, and Jim Bryan studied how spheres can be embedded in special spaces called flag varieties, and they found examples suggesting that the expected resemblance to the space of all continuous embeddings happens very quickly. They worked with Freddie Manners and George Salafatinos using DeepThink and FullProof. In a preprint on January 12, 2026, the AI succeeded in filling in the details of a general proof after giving a “very elegant, correct, beautifully written” proof in a simpler case. Vakil said, “The clarity of the argument gave us a new idea.”
Litt warned that “there is a lot of pollution of the commons by AI-generated nonsense,” and Joel David Hamkins said he is “despairing of this ocean of slop that is overwhelming our journal systems.” Tao said, “AI without validation is too unreliable to be of use in any serious application,” and he added, “For the first time, it does feel like we could formalize a significant fraction of mathematics through AI.” Tao compared current AIs to “jumping robots” that can “parkour their way to the top of a 6-foot wall,” while Litt said, “My expectation is surely in 20 years we are going to see AI tools generating mathematics that in many measurable ways are better than every human mathematician.”