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The Mathocalypse
Hraness wrote this summary from a saved copy of the source. Quotations are taken word for word from the source.
gist
Scott Aaronson calls OpenAI’s release of 372 AI-generated results one of the biggest days in mathematical history, centered on a claimed proof of the Unique Games Conjecture that his wife Dana Moshkovitz spent her career on. He surveys the complexity-theory haul, contrasts OpenAI’s raw dump with Anthropic’s digested 3SUM release, and argues the human job now is to understand, explain, and keep caring about the paths up these mountains.
ideas
- Unique Games falls, unread. A Lean-certified UGC proof arrives that no human yet understands; Moshkovitz describes an alien recursive code with a noise test and irrelevant citations.
- A complexity-theory treasure list. L = BPL, sub-n log n Fourier transform and integer multiplication, unitary synthesis, parity outside QAC0, a near-quartic quantum query separation, a 2D area law, n^(9/4) matrix multiplication, and Hilbert’s tenth problem over the rationals.
- What is missing matters. P versus NP, P = BPP, and cryptography are absent; Aaronson adds that labs are now quietly testing models against cryptographic primitives, and he rebukes critics who will call it all slop.
- Two release models. OpenAI posts undigested proofs and triggers a human race to explain them; Anthropic let Williams and Alman write up a 3SUM and APSP breakthrough for compensation.
- Cheap, general, not bespoke. The results reportedly came from OpenAI’s latest internal model at about three hours of Pro-level compute per solved problem, roughly 5% of about 8,000 attempted.
quotes
“yesterday was surely one of the biggest days in mathematical history.”
“It’s not the long code, not the short code – some alien craziness”
“The “OpenAI model” sets up a crazy race among humans to digest and explain a messy AI proof”
“right now it “merely” solves ~5% of the longstanding open mathematical problems that it’s asked about”