Three days is the headline number, but it isn’t the interesting one. The interesting part is who did the work: an automated system running a non-public Anthropic model, not a team of complexity theorists. If the claim holds, it is one of the clearest examples yet of an AI system producing real research mathematics instead of just assisting with it.
PSI, a physics research company that launched publicly in September 2026, announced that its system proved the Aaronson-Ambainis conjecture, posed in 2008. The system ran on PSI’s own infrastructure. It then improved the proof twice, and Lean accepted the final version too.
What the conjecture actually says
The conjecture asks when a quantum algorithm can be approximated by a classical one. If it holds, a broad class of quantum algorithms, run on randomly chosen inputs, could be simulated classically with only polynomial overhead. That matters because polynomial and exponential growth diverge fast as problems get bigger.
It does not kill quantum advantage. Shor’s algorithm for factoring is not ruled out. The result only narrows the conditions under which an apparent exponential speedup is real.
Why Lean matters, and where it stops
Lean is a proof assistant. It checks that every step follows logically from the stated assumptions. That is a strong guarantee against the usual failure of AI-generated math, which is confident nonsense.
But Lean can’t tell you whether the formal statement matches the original conjecture. Humans still have to check that. PSI says David Turturean led the work and takes responsibility for the paper’s correctness, Jim Halverson audited the proof, and Phiala Shanahan commented on the formalisation. A Stanford group (Guy Blanc, Jordan Docter, Carmen Strassle and Li-Yang Tan), which proved a special case in August 2026, is preparing a shorter exposition for other experts.
That is encouraging, but it is not full independent academic review.
How it fits the bigger picture
AI labs have been pushing hard on math as a proving ground. Google DeepMind has AlphaProof and AlphaEvolve, and OpenAI has made its own claims about research-level problem solving. PSI’s pitch is a bit different. It is a startup building the scaffolding around a frontier model, and the model is Anthropic’s. That suggests the value is shifting toward the systems and workflows wrapped around models, not just the models themselves.
For developers and founders, the practical takeaway is the pairing: a generative model for proof search, a formal verifier for correctness. That combination is far more trustworthy than either piece alone, and it will likely spread to other fields where answers can be checked mechanically.
Is this noise? Not entirely. A Lean-verified proof is hard to fake. But treat it as a strong claim, not a settled result, until the experts finish reading.
