The Mathocalypse

A breakthrough wave of machine-generated mathematics has produced hundreds of purported proofs and algorithms, including a Lean-verified proof of Subhash Khot’s Unique Games Conjecture - work that has occupied many researchers for years - and a string of other notable results: L=BPL, sub-O(n log n) Fourier transform and integer multiplication, a positive solution to the Unitary Synthesis Problem, parity not in QAC0, near-fourth-power randomized vs. quantum query separations, superquadratic sensitivity separations, an area law for 2D gapped Hamiltonians, randomized nearly-linear-time maximum-matching algorithms, matrix multiplication in O(n9/4), stronger permanent lower bounds, randomized approximate counting of perfect matchings, and uncomputability for solving polynomial equations over the rationals, along with partial progress on major number-theory conjectures. Many of the manuscripts are messy, hard to parse without AI help, and require human teams to verify and translate into standard mathematical exposition; Scott Aaronson relays a complexity theorist’s visceral reaction that the UGC write-up reads like “alien craziness,” while also noting the personal and communal upheaval when longstanding goals are suddenly claimed solved.

The results emerged via two dissemination patterns: an OpenAI dump of ≈372 solutions (roughly 5% success from ~8,000 attempts, using a few hours of compute per problem) and an Anthropic-mediated route that let human authors refine and announce solutions - each model poses tradeoffs in credit, curation, and verification. Researchers worldwide are racing to understand, formalize, and salvage ideas from the AI outputs; metaphors range from teleportation to a luxury resort arriving beside a hunter-gatherer to capture the abrupt change in how mathematical discovery and craftsmanship will proceed going forward. Notably absent are resolutions of P vs NP and other deepest TCS barriers, leaving core open problems intact.