Fermat's proof, Claudeforce, and the US-China AI summit

Claude formalizes Fermat's Last Theorem in eleven days

Andrew Wiles' celebrated 1995 proof of Fermat's Last Theorem stretched to 129 pages of dense graduate mathematics, and finding a subtle gap took the world's best number theorists an additional year to close. Now Anthropic has done something that large community of experts could not: in just eleven days, a swarm of Claude agents produced the first full, machine-verified formalization of that proof in the Lean theorem prover.

The scale was extraordinary. The agents generated six billion tokens of output and wrote more than thirteen million lines of Lean code—the largest computer-verified proof ever produced—establishing 29,500 intermediate theorems along the way. The swarm ran largely without human intervention, guided only by high-level mathematical direction from Anthropic researchers and by access to Prove2ME, an open-source tool that helps AI agents find the most efficient next step in lengthy proof workflows.

Anthropics formalization follows Wiles' original logical path: the Frey curve construction, Ribet's level-lowering theorem, and the modularity theorem for semistable elliptic curves. Lean's type-checker issued a formal certificate confirming each step follows incontestably from the axioms of mathematics.

The mathematical community is divided on what the milestone means. Critics note that translating an existing proof is fundamentally different from discovering new mathematics—the creative leap connecting elliptic curves to modular forms was Wiles' alone. But that translation work, which experts estimated would occupy a coordinated human team for several years, was completed autonomously in under a fortnight. The episode is a landmark for AI-assisted formal verification, and it raises an obvious next question: which unsolved conjectures might be accessible to the same approach?

Claudeforce: Salesforce bets its stack on Claude

In one of the more consequential enterprise AI deals of the year, Salesforce and Anthropic unveiled Claudeforce—a deep integration that makes Claude the default reasoning model across Salesforce's full product suite. Announced August 26 and entering open beta in September, the deal covers Agentforce (Salesforce's autonomous agent platform), Slack AI, Slackbot, Headless 360, and Agentforce Coworker. Claude Code and Claude Enterprise are now the preferred AI tools for Salesforce's entire workforce.

The commercial centrepiece is Salesforce in Claude—a plugin that gives Claude governed access to live CRM data and 37 prebuilt sales skills, enabling sellers to trigger pipeline updates, draft proposals, and take CRM actions directly from the Claude interface. Anthropic becomes the first LLM provider integrated fully within Salesforce's Trust Boundary, meaning customer data can move between platforms under Salesforce's enterprise data-protection controls without leaving its governance perimeter.

For Anthropic, the deal delivers instant distribution across a vast installed base of enterprise Salesforce customers. For Salesforce, it is a bet that superior reasoning is now more commercially valuable than proprietary model control—a significant philosophical shift for a company that has historically preferred to build core AI capabilities in-house. The September open beta's uptake will be watched closely as an indicator of enterprise willingness to standardize on a single frontier model provider across an entire workflow stack.

US and China prepare their first bilateral AI safety talks

Washington and Beijing are quietly organizing what would be their first meeting devoted exclusively to AI safety. U.S. Treasury Secretary Scott Bessent is expected to lead the American delegation; on the Chinese side, Vice Premier He Lifeng or Politburo Standing Committee member Ding Xuexiang—Xi Jinping's senior technology policy coordinator—may chair the session. The talks are expected in mid-September, ahead of a Trump-Xi summit on September 24.

The agenda is still under negotiation. The U.S. side wants to address AI-directed cyberattacks and the alleged distillation of American frontier models by Chinese actors. China's reported precondition is that both sides first settle on a shared definition of AI safety—a philosophically loaded term: Washington primarily frames safety around catastrophic and military risks, while Beijing's definition extends to social stability and information control.

Both governments are expected to propose voluntary self-monitoring standards for AI labs and frameworks for sharing information about emerging threats. No binding agreements are expected to emerge from the September session. Analysts argue the talks' value lies in creating a communication channel before an AI-related incident forces reactive diplomacy. If the September discussions hold, they could lay the groundwork for a permanent bilateral AI commission—an equivalent of the Cold War nuclear hotline adapted for an era of autonomous systems.

California joins the OpenAI investigation over the Hugging Face hack

California Attorney General Rob Bonta announced this week that his office has launched an investigation into OpenAI in connection with the Hugging Face security incident, joining more than a dozen states already scrutinizing the company. The probe focuses on whether OpenAI acted unlawfully during an incident in which threat actors infiltrated Hugging Face's platform—the same breach that prompted Nvidia's $12.9 billion acquisition of Hugging Face announced on September 3.

Nvidia's rationale for the acquisition turned partly on the security compromise: a well-resourced acquirer could harden the world's largest open-model repository and integrate it into Nvidia's software ecosystem, while also giving the chipmaker a direct relationship with the open-source AI community. California's investigation adds legal exposure to what is already a fraught post-acquisition transition. The coordinated state enforcement push—now spanning California, Texas, New York, and others—is emerging as a de facto regulatory substitute in the absence of comprehensive federal AI legislation.