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A mathematician quietly ended an 87-year-old debate in a single social media post. Anthropic’s Levent Alpöge used Claude Fable 5 to find a polynomial counterexample that disproves the Jacobian conjecture — a rule about reversible functions that’s stood unresolved since 1939.
The proof is short enough to fit in one X post and simple enough for other mathematicians to check by hand. If a frontier model can generate genuinely new math this fast, how many other “settled” open problems are actually one good prompt away from falling?
Today in AI Brief:
Claude helps disprove an 87-year-old math conjecture
OpenAI launches Presence, its enterprise agent platform
Alphabet’s cloud revenue jumps 82% as AI spending soars
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Claude Helps Disprove an 87-Year-Old Math Conjecture
In Brief: Anthropic mathematician Levent Alpöge used Claude Fable 5 to find a polynomial counterexample disproving the Jacobian conjecture, a rule about invertible polynomial maps that had stood open since 1939.
The Details:
Alpöge’s counterexample is a three-dimensional polynomial map with a constant Jacobian determinant of -2 that still sends multiple inputs to the same output — proof the map isn’t invertible.
The proof is short enough to fit in a single X post, and mathematicians say it’s easy to verify independently — no lengthy formal paper required.
Alpöge said the model did the key work during the World Cup final, adding to a growing list of AI-assisted proofs that already includes several Erdős problems and an 80-year-old unit-distance puzzle.
Take Away:
A single social post now carries the weight of a mathematical proof, at least until peer review catches up. It’s the clearest sign yet that frontier models can generate genuinely new mathematical objects, not just recall known ones.
OpenAI Launches Presence, a Platform for Enterprise AI Agents
In Brief: OpenAI introduced Presence, a managed platform that helps large companies deploy AI agents for customer support, sales, and internal workflows across voice and chat.
The Details:
OpenAI runs its own English-language phone support line on Presence, where the system resolves 75% of inbound issues without a human.
Deployments are led by OpenAI’s own forward-deployed engineers or select systems integrators — there’s no self-service tier at launch.
Presence pairs model reasoning with a company’s own policies, guardrails, and escalation rules so agent behavior stays predictable as products and customer needs shift.
Take Away:
OpenAI is moving from selling raw model access to selling outcomes, competing directly with contact-center vendors and consultancies. The white-glove approach suggests enterprises still don’t trust agents enough to deploy them at scale on their own.
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Alphabet’s Cloud Revenue Jumps 82% as AI Spending Hits $205B
In Brief: Alphabet posted 24% revenue growth to $119.8 billion in its second quarter, powered by Google Cloud revenue surging 82% — but shares fell after the company raised its 2026 capital spending forecast to as much as $205 billion.
The Details:
Google Cloud’s operating margin expanded to 35.6% even as the unit keeps turning away outside customers because Google needs the compute for its own AI models.
Quarterly capital expenditures jumped to $44.9 billion, roughly double a year ago, pushing free cash flow negative for the quarter.
Operating income still rose 30% to $40.8 billion, with the operating margin holding at 34% despite the spending increase.
Take Away:
Wall Street’s mixed reaction shows investors still can’t agree on whether AI infrastructure spending is fuel for growth or overreach. Alphabet is betting the compute crunch is real enough to justify negative free cash flow today for cloud market share tomorrow.
Everything else in AI
The White House accused Chinese startup Moonshot AI of secretly distilling Anthropic’s Fable model to build its Kimi K3 system, with Treasury now threatening sanctions.
OpenAI unveiled Project Camellia, a $30 billion, 3.2-gigawatt data center campus near Savannah, Georgia, expected to create up to 1,000 permanent jobs.
Google plans a new “Frozen v2” chip that bakes Gemini’s architecture directly into silicon for 6-10x better power efficiency per token.
Meta piloted StoryKit, an app that turns a photo of a child’s favorite toy into an illustrated, narrated bedtime story with built-in safety filters.