Daily AI CatchupAI Agents Formalize Proof, May Refute Complexity Conjecture
Anthropic says an internal research version of Claude, without human input, found a deterministic algorithm solving 3-SAT in subexponential time, which would refute the widely believed Exponential Time Hypothesis. The result, including a Lean 4 formal proof, landed within hours of a similar claim from OpenAI. Separately, Axiom Math used dozens of AI agents over 24 days to produce the first complete computer-checked proof of the Classification of Finite Simple Groups, a human proof that spans roughly 15,000 pages.
Why it matters
💻 Developer · Lean formalization at this scale, 43 million lines of generated proof code, shows agent swarms can tackle formal verification tasks that used to be purely academic grind work.
📦 Product · Not product-ready, but a signal that AI-assisted formal methods could eventually speed up verification work in compilers, crypto, and safety-critical software.
🎨 Design · Not directly relevant, though it's a preview of how AI tooling could reshape workflows in rigorous, proof-heavy technical fields.
📈 Business · Two frontier labs independently claiming major math results within hours of each other says more about competitive pressure between Anthropic and OpenAI than about near-term commercial impact.
🤔 Just Curious · AI systems just helped crack two famously hard math problems: one so long humans could barely check it, and one that could upend a 50-year-old assumption about computer science.
Sources: Anthropic's Claude Refutes the Exponential Time Hypothesis, With a Lean Proof, Formalizing the Enormous Theorem