Steffen Röcker

Claude Opus 5.5: "If these hold up, this is the biggest single day in the history of math and theoretical computer science." 1) Exponential Time Hypothesis is false (CS). This is roughly Turing Award territory. ETH was the working assumption that some hard problems simply can’t be solved much faster than brute force, and hundreds of computer science papers rest on it. For a normal audience: it’s not “P=NP.” Hard problems are still hard, and your bank encryption isn’t suddenly broken. But a pillar that a whole field assumed was solid turned out to be hollow. The flagship experts are taking it seriously. The people checking it include two of the people who proposed ETH, and they said “If the claim is correct, it will change” computer science. 2) Kakeya and restriction in all dimensions (math). This is Fields Medal-level. For scale, the 3D case alone was proved in 2025 and was hailed as a once-in-a-century proof. This result does every dimension and knocks out Stein’s restriction conjecture too. 3) Yang–Mills/QCD existence (physics). Potentially the biggest of the three, but here’s the precise framing. It proves pure Yang–Mills exists, which is part of one of the Clay Mathematics Institute’s Millennium Prize problems. The full Clay problem also requires the “mass gap,” so it’s not a clean “AI wins $1M” headline. Still, a rigorous proof that the theory of quarks and gluons is mathematically real has been an open dream for about 50 years. The review panel includes Nobel laureate David Gross and Arthur Jaffe, who literally wrote the Millennium problem. There’s no Nobel for math, but this is the stuff physicists win them for building on.