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An AI helped break a math problem that had stood since 1939, and the whole answer fits in a tweet.
The counterexample runs 216 characters. The same week, the best AI agent scored just 24% on real job tasks, ten public health agencies signed on to pilot OpenAI and Anthropic tools, and Anthropic opened $50,000 rare-disease grants.
The same models solving problems no human could still fail the ordinary work most people do every day, and we are wiring them into hospitals anyway.
A note: this issue is drafted with Claude, an Anthropic model, and Anthropic turns up in several stories below. Primary sources are linked throughout so you can weigh them yourself.
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Fable 5 Broke an 87-Year-Old Conjecture
On Sunday night, Anthropic mathematician Levent Alpöge posted a counterexample that disproves the Jacobian conjecture, open since 1939, and credited Fable 5.
Its Jacobian determinant is a constant -2, the condition the conjecture said guaranteed reversibility. Yet three inputs hit the same output, so it cannot be reversed.
Hard to find, easy to check: Timothy Gowers and others verified it by hand within a day. It disproves the conjecture in dimension three and up, but the two-dimensional case is still open, with no peer-reviewed paper yet.
Anthropic Opens $50K Grants for Rare Disease
Anthropic opened a call for researchers to point Claude at rare genetic diseases, with up to $50,000 in credits over six months. Two tracks: academic labs chasing disease mechanisms, and early-stage biotechs speeding up drug development.
About 400 million people live with one of more than 7,000 rare diseases, most studied in isolation. The bet is that a model can spot mechanisms shared across them that no single team would catch. Applications close August 2.
Source: Anthropic
Lead Analysis
Ten Health Agencies Are Piloting AI
The Coalition for Health AI launched PULSE with OpenAI, Anthropic, and Accenture, donating licenses for up to 2,000 practitioners across 10 jurisdictions. The pilots cover biosurveillance, translation, and clinical-data retrieval.
The coalition has not yet published evaluation, privacy, or human-review rules for any of the five use cases. Pilots begin this fall; the guidance meant to govern them arrives in 2027.
Quick Hits
NVIDIA leaned into world models. At SIGGRAPH, NVIDIA showed neural rendering and its Cosmos 3 world-foundation models, pitching simulated environments as training grounds for robots and other physical AI. Read more→
YouTube stopped paying for AI slop. A clarified monetization policy names three kinds of "inauthentic" content that can no longer earn ad revenue, including AI personas dispensing health or finance advice. It took effect July 16 for all Partner Program members. Read more→
Samsung launched a Health Assistant. Its new beta pulls sleep, activity, nutrition, mindfulness, and vitals into one view and answers questions with recommendations it says physicians vetted. US only, for now. Read more→
