Using mostly my voice, I solved one of @EpochAIResearch’s FrontierMath Open Problems: finding an explicit presentation of the 2-adic Absolute Galois Group—open for more than forty years, now with a full proof in collaboration with David Roe, the problem’s proposer.
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”.
2026/07/30 | Tencent Hy—Not sure what is the name of this thing
Tencent Hy: For a finite set of integers (A), how much faster can (|A+A|) grow than (|A-A|)?
A 1969 theorem gave an upper bound of 2 for the exponent. For more than 50 years, the best constructions barely exceeded 1.1.
With help from our research agent Hyra and the Hy3 model, we found an explicit construction showing that the optimal exponent is exactly 2.
Two notable AI math results recently
2026/07/28 | mainly GPT 5.6 Pro—David Turturean’s Proof of The 2-adic Absolute Galois Group (FrontierMath Open Problems: Solid Result):
Epoch AI:
2026/07/30 | Tencent Hy—Not sure what is the name of this thing