AI cracks second FrontierMath benchmark problem on absolute Galois groups, signaling a shift for computational research

Two of the world’s most advanced AI models just solved the same unsolved math problem within two weeks of each other. The problem involves the absolute Galois group of the 2-adic numbers. Epoch AI’s FrontierMath benchmark recorded its second verified solution on June 24, 2026. Anthropic’s Claude Fable 5 got there first on June 9, followed by OpenAI’s GPT-5.5 Pro fifteen days later. Both solutions were accepted by the benchmark’s verifier, though the broader mathematical community notes that full proof verification is still ongoing as of July 6. What exactly did these models solve The absolute Galois group of ℚ₂ (the 2-adic numbers) sits at the intersection of number theory and abstract algebra. Galois groups describe the symmetries of solutions to polynomial equations. The 2-adic numbers are an alternative number system that mathematicians use to study properties related to the prime number 2. While solutions are known for other prime cases, the case of ℚ₂ had eluded resolution until these AI developments. The problem is classified as a “solid result” in number theory. Human experts would typically need one to three months to produce a solution. David Roe from MIT, who contributed ...