Feature

AI

2026-09-14 00:13:13

Two high school students use AI to push forward an open problem linked to June Huh’s Lorentzian polynomial work

A research result circulating in UCLA’s math community has drawn unusual attention: two high school students, Aayush Bathija and Prince Rohatgi, working under UCLA postdoctoral scholar Daniel Soskin, posted a 75-page paper on arXiv titled Bounded Ratios for Lorentzian Polynomials. The report says the paper advances a problem tied to work by June Huh, the 2022 Fields Medalist, in a direction that had not previously been completed. The paper focuses on a technical question inside Lorentzian polynomial theory: which ratios formed from polynomial coefficients stay uniformly bounded, which can grow without limit, and, when a bound exists, what the sharp bound is. According to the report, the paper’s main structural theorem extends earlier quadratic results to arbitrary degree and gives a full criterion based on discrete convexity conditions. The story also stands out because of how the work was done. The authors wrote in the acknowledgments that Claude Opus 5 and GPT-5.6 Sol were core tools in the project, used for computation, proof ideas, and editing support. They also stated that some AI suggestions were useful while others were misleading, and that all computations were independently verified by the authors, who take responsibility for the paper’s contents. The timing added another layer of debate, coming just a day after a public letter signed by 25 Fields Medalists warning about AI’s impact on mathematics.

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Claude

2026-08-24 13:00:10

Harvard researcher and Claude present an S6 complex-structure construction in a 78-year math problem

A 108-page proof by Harvard mathematician Levent Alpöge and Claude claims to answer one of the longest-running questions in differential and complex geometry: whether the six-dimensional sphere, S⁶, admits a complex structure. The result, described in the source article as a direct construction rather than another attempt along older lines, builds a compact complex threefold X and then identifies it with S⁶ through calculations of the fundamental group, homology arguments, and a chain of classical theorems. The article says mathematician Qiaochu Yuan had GPT-5.6 Sol examine the manuscript. After an initial six-minute pass and another 15 minutes of review, the model reportedly found no flaw. Sol’s view, as cited in the piece, is that if the proof holds up, it may stand as the most important AI-assisted mathematical result so far. The report places this work alongside two earlier Claude-linked advances from July 20 and Aug. 10, and argues that the S⁶ case is different because the geometric object was constructed outright rather than found through search or recombination.

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