For more than 150 years, the Riemann hypothesis has sat unsolved at the center of number theory, a $1 million Clay Millennium Prize still waiting on a working proof. Anthropic hasn't claimed that prize. But on Monday, the company said an as-yet-unreleased model had meaningfully raised the lower bound of solutions for which the hypothesis holds, work confirmed by two of its in-house mathematicians and formalized in the open-source proof assistant Lean.
The method is the real story. An Anthropic staffer without deep mathematical training simply asked the model to attempt a proof, then let it run. Over the following day and a half, it tested 650 distinct approaches across 60 coordinated subagents, spending 31 million output tokens. Two subagents developed the key ideas; thirteen contributed supporting work; thirty tried and failed; thirteen validated the logic; two wrote up the paper.
It's the latest entry in a fast-growing list of AI-assisted math results this year, following OpenAI's ten Astra-proved results and Anthropic's own disproof of the Jacobian conjecture. Mathematicians remain split: a June declaration signed by prominent researchers warned that AI could erode the norm of provable results carrying a named, accountable author. Fields medalist Timothy Gowers pushed back, suggesting math without individual attribution might simply be a different, not lesser, way of doing the field.
The standalone Gemini app has now passed 1 billion monthly active users, a figure that covers the app alone and excludes Gemini usage baked into Search's AI Mode, which has separately cleared a billion users of its own. Sixty-three percent of Gemini users talk to the assistant by voice, and the app now generates over 150 million images a day.
The number arrives right after Google's Q2 earnings call touted 950 million monthly users and daily actives tripling over the past year, and just ahead of the Made by Google event, where more Gemini-powered Pixel features are expected. The company also reports more than 100 million active iOS users, a channel entirely outside its own hardware and software stack.
Every Claude model released after August 2 will automatically watermark generated text and files, Anthropic confirmed in an updated support page, with files handled through the open C2PA standard. Older models will get the capability extended to them over time, and the tag applies model-wide, meaning it shows up no matter whether the text comes from the Claude app, the API, Claude Code, Claude Cowork, or Claude Tag.
Anthropic hasn't said exactly how much editing it takes to strip the watermark out, and TechCrunch is still waiting on that clarification. The company joins Black Forest Labs, Google, Meta, Microsoft, OpenAI, and Synthesia in committing to the EU's transparency code, a wave that follows Suno's music-watermarking announcement last week and Substack's Pangram-powered AI detection tool from July.
Lightcap joined OpenAI in 2018 and, by his own account, built out the company's first Finance, Legal, People, and GTM functions before four years as CFO and then COO. In a message to staff Tuesday, he called it "bittersweet" to leave, adding that he's spent recent months thinking about "the next horizon" and what the world will need to get right, without saying what that means yet.
He's the third notable OpenAI departure since July, following AGI lead Fidji Simo's exit and earlier moves by Sora's Bill Peebles and Science VP Kevin Weil. The company is simultaneously preparing for what reporting has called an IPO of industrywide significance, making the executive churn harder to read as routine.
General Catalyst and AMP PBC led the round, with Nvidia, AMD Ventures, Y Combinator, and Temasek all participating, an enormous check for a company that only came out of stealth in June. Babuschkin, whose résumé spans DeepMind, OpenAI, and xAI, wants to rebuild the AI stack end to end so agents behave less like rented assistants and more like, in his words, "guardian angels" that belong to the person using them.
River's first product is an API billed per million tokens that lets developers apply reinforcement learning and LoRA fine-tuning to open models, pitched as an alternative to prompt engineering a model you can't actually own. The company claims enterprises can run a complex RL job in 15 to 20 minutes without an infrastructure team, at two to four times the cost of closed-source alternatives.