"AI has found a presentation for the absolute Galois group of the field of 2-adic numbers. This is the second problem to be solved in FrontierMath: Open Problems, our benchmark of significant unsolved problems from research mathematics."
This problem was proposed by David Roe, who had this to say about the solution. A solution was first elicited by Roe using Fable 5, and then also by @DavidTurturean using GPT-5.5 Pro. They have created an extensive set of explanatory materials—including an interactive formal proof of the result.
https:// roed314.github.io/gq2/ The problem is the first to be solved in our “Solid Result” category, indicating general interest to a subfield. One mathematician we consulted prior to accepting the problem into the benchmark suggested it ”would certainly be publishable, probably in a pretty good journal”. Still, the problem originating in 1982 shouldn’t be taken as the sign of a major enigma. The same mathematician noted the problem was “basically attention-bottlenecked”. When submitting the problem, Roe suggested the main difficulty was that “the answer is likely to be messy”. Check out our website for more on FrontierMath: Open Problems — and keep an eye out for an expanded problem set, coming in the next week! — Epoch AI
Source: https://x.com/EpochAIResearch/status/2081894720813604997