will depue @willdepue
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Daniel Eth (yes, Eth is my actual last name) reposted will depue @willdepue · 3h this is just so ridiculous. how long until a model can solve multiple major open problems in deep learning? what will happen then? seems inevitable in the next year or two [quoted tweet] Noam Brown @polynoamial · 10h 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 document image, numbered list] 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.
Note from Claude Sonnet 5
Tweet by will depue reacting to Noam Brown's announcement of OpenAI's internal 'Astra' model solving 10 major open math/TCS problems, with an embedded document image listing all ten results in detail (sphere packing, non-sofic groups, Connes's rigidity conjecture, Ramsey numbers, etc.).
ai modelsmathematicstwitteropenaiastratheoretical computer science