The blog post recounts how Scott Aaronson’s 9‑year‑old son taunted his wife, complexity theorist Dana Moshkovitz, saying a robot had solved the math problem she had worked on her whole career. Aaronson writes that yesterday was “surely one of the biggest days in mathematical history” because OpenAI released 372 huge results, among them a proof of Subhash Khot’s Unique Games Conjecture (UGC). The UGC implies that many optimization problems are NP‑hard even for approximations better than those obtainable from semidefinite programming, a central tool in approximation theory. In addition to UGC, the release claimed results such as L=BPL (probabilistic logspace equals deterministic logspace), integer multiplication and the Fourier Transform in less than O(n log n) time, a positive solution to the Unitary Synthesis Problem, and that Parity is not in QAC0. Further claims included a nearly 4th‑power separation between randomized and quantum query complexity for total Boolean functions, a superquadratic separation between sensitivity and block sensitivity, an area law for 2D gapped Hamiltonians, matrix multiplication in n^{9/4+o(1)} time, an Ω(n^3) lower bound on the determinantal complexity of the permanent, and randomized algorithms for approximately counting perfect matchings and finding maximum matchings in general graphs.
The blog emphasizes that while many of the results are accompanied by Lean certificates, the papers are extraordinarily hard to read. Dana Moshkovitz told Aaronson the papers feel “like something written by someone who’s on psychedelics,” with unclear arguments, excessive name‑dropping without justification, and that they are “impossible to read … without AI help.” He notes that the race to understand these proofs has just begun, and that humans have not yet grasped any of them in depth. This illustrates the immediate barrier: even though the AI claims to have solved longstanding open problems, the mathematical community cannot yet verify or build upon the proofs without substantial AI‑assisted explanation.
Aaronson also discusses the practical side of this AI‑driven surge: the model apparently used about three hours of GPT‑Pro level compute per problem, and was tried on roughly 8,000 problems, solving about 5 % of the longstanding open questions it was asked about. This yields a rough cost of about $810 per solved problem under current API pricing. He contrasts two emerging models for AI‑generated math breakthroughs: the “OpenAI model” that dumps messy proofs and forces a competitive, thankless scramble among humans to digest them, versus the “Anthropic model” that selects specific mathematicians to act as emissaries for the AI’s work, as illustrated by the Williams‑Alman results that solved 3SUM and All‑Pairs Shortest Paths the day before the OpenAI dump. He concludes that, despite the flood, the true inner sanctum of human creativity remains untouched, and that the mathematical community is now faced with the task of clearing the fog and figuring out the paths using AI as a guide, while still relying on human collaboration and intuition.