— quote-tweeting @polynoamial — saved image
Kevin Roose @kevinroose · 3h almost nobody is pricing in the possibility that the models just keep plowing through every discipline the way they're plowing through math [Quoted tweet] Noam Brown @polynoamial · 14h An internal version of Astra, @OpenAI's next major model family, solved 10 major open problems in mathematics, quantum complexity, and theoretical computer science. ... [Embedded list image, white background:] 1. High-dimensional sphere packing. The asymptotic strength of the Cohn–Elkies linear program is determined exactly. This gives an improved general packing bound in high dimensions and settles the corresponding Fourier sign-uncertainty problem asymptotically. 2. Binary and spherical codes. Classical upper bounds for fixed-distance binary and spherical codes are improved by exponential factors for all parameters. The spherical construction also recovers the sphere-packing exponent of Chapter 1. 3. Non-sofic groups. An explicit non-sofic group is constructed, resolving the question of whether every countable group admits finite permutation approximations. The argument uses property-(T) expanders and the binary Leavitt algebra. 4. Connes's rigidity conjecture. Infinitely many pairwise nonisomorphic property-(T) groups are constructed with the same group von Neumann algebra, disproving Connes's conjecture and answering a related finite-to-one question. 5. Arithmetic circuit complexity. For the permanent, division-free circuits require Ω(n²log log n) gates, while formulas require Ω(n⁴/log n) leaves. 6. Quantum parallel repetition. Exponential parallel repetition is proved for every finite two-player entangled game, extending the classical repetition principle beyond previously treated special classes of quantum games. 7. Closest vector problem. A direct reduction from 3SAT gives n^(1/400)-factor hardness for Euclidean closest vector, with related consequences for binary decoding and other lattice norms. 8. Ehrhart's volume conjecture. The sharp bound (n+1)^n/n! is proved in every dimension for convex bodies whose barycenter is their only interior lattice point. 9. Multicolor Ramsey numbers. A superexponential lower bound proves R_k(3) = k^Θ(k). 10. Compactness and degeneracy. Separate bipartite graph constructions disprove two conjectures in extremal graph theory: the compactness conjecture of Erdős and Simonovits and a degeneracy conjecture of Erdős. 81 54 564 62K xlr8harder @xlr8harder · 2h Math has the benefit of being easily verifiable. I still think progress will be fast, but it's still hard in less verifiable domains.
Note from Claude Sonnet 5
Twitter thread reacting to Noam Brown's (OpenAI) claim that an internal 'Astra' model solved 10 major open problems in math, quantum complexity, and theoretical computer science, with the full itemized list of claimed results shown. Kevin Roose comments that nobody is pricing in models plowing through every discipline; xlr8harder notes math's verifiability advantage over less verifiable domains.