AI has successfully found a presentation for the absolute Galois group of the field of 2-adic numbers, becoming the second problem solved in FrontierMath: Open Problems. Proposed by David Roe, this problem, originating in 1982, had been deemed limited by attention rather than fundamental complexity. The solutions were generated using Fable 5 and GPT-5.5 Pro, and they were accompanied by extensive explanatory materials, including an interactive formal proof. This milestone marks the first solution in the “Solid Result” category, indicating significant interest in this subfield of mathematics.

Fable 5: Fable 5 is an AI model applied to complex mathematical research problems. David Roe used it to generate the initial solution for the absolute Galois group problem. In this news, it represents one of the first AI systems to address and resolve an entry in the FrontierMath: Open Problems benchmark.
David Roe: David Roe is a mathematician who proposed the problem concerning the absolute Galois group of the field of 2-adic numbers for inclusion in the benchmark. He initially used Fable 5 to elicit a solution and provided context on the problem’s origins and challenges. In the news, he is central to both submitting the problem and overseeing its AI-assisted resolution along with related materials.
GPT-5.5 Pro: GPT-5.5 Pro is an advanced AI model utilized for solving and documenting mathematical challenges. David Turturean employed it to independently derive a solution to the 2-adic Galois group problem. The news notes its role in producing detailed explanatory materials alongside the formal proof.
David Turturean: David Turturean is a researcher who independently solved the mathematical problem using GPT-5.5 Pro. He collaborated on developing extensive explanatory resources, including an interactive formal proof. The news highlights his contribution as a second successful AI-driven solution to the FrontierMath problem.
FrontierMath: Open Problems: FrontierMath: Open Problems is a benchmark featuring significant unsolved problems drawn from active research in mathematics. It tracks progress on frontier-level challenges across various subfields and difficulty categories. In this news, it serves as the platform where AI systems first solved the problem on the absolute Galois group of the 2-adic numbers field.

AI Methodology: The result involved multiple AI systems generating both solutions and supporting formal verification materials.
Problem Context: The problem, while proposed decades ago, was viewed as primarily limited by attention rather than fundamental difficulty.
Benchmark Milestone: This marks the first solution in the “Solid Result” category of FrontierMath: Open Problems, signaling general interest to a mathematical subfield.