Two leading AI systems have independently cracked a challenging problem in number theory linked to the absolute Galois group of 2-adic numbers, a puzzle that would normally keep human mathematicians busy for months. Anthropic's Claude Fable 5 first delivered a verified solution on June 9, 2026, followed by OpenAI's GPT-5.5 Pro fifteen days later. Both models' answers passed an automated checker used by Epoch AI's FrontierMath benchmark, which focuses on genuinely unsolved problems from professional mathematicians.
The absolute Galois group relates to the symmetries inherent in solutions of polynomial equations, and the 2-adic numbers form a special numerical system tied to properties of the prime number 2. While similar problems for other primes have been solved before, the 2-adic case remained open until now. Mathematicians consider this achievement a solid step forward, with MIT’s David Roe estimating a very high likelihood that such problems can eventually be solved.
Verification and Implications
The FrontierMath community, responsible for maintaining the benchmark, highlighted that although these AI solutions passed automated validation, the rigorous process of full peer-reviewed proof is still ongoing as of early July. This reflects the caution typical in pure mathematics, where automated checks cannot yet replace human scrutiny.
This breakthrough raises questions about AI’s expanding role across research fields such as pure math and cryptography, where complex problem-solving is essential. It follows growing interest and investment in AI development, as seen in recent debates over Nvidia's AI spending and new AI toolkits.
