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Happy Thursday! What happens when AI tackles one of mathematics’ biggest unsolved problems? This week, OpenAI says it may have found the answer, but there’s already a fight over who got there first.

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OpenAI says its models produced a solution to the Navier-Stokes existence and smoothness problem, one of mathematics' famous unsolved challenges and a question tied to a $1 million Millennium Prize. If verified, the result would show AI contributing to frontier mathematical research rather than simply checking established work. The claim has collided with a dispute over priority: NYU mathematician Tristan Buckmaster says OpenAI accelerated its announcement after learning about parallel progress involving him and Anthropic mathematician Levent Alpöge. Buckmaster and Alpöge announced 3 proofs using OpenAI's Codex and Anthropic's Claude, adding a sharp authorship question to the technical debate. OpenAI's announcement still requires independent mathematical validation, with experts checking every assumption against the formal problem. The episode sets a new standard for AI-assisted research: models may generate key ideas, but humans must verify the proof, explain the argument and establish a transparent record of contributions (read more).

Apple has entered foldable phones with the iPhone Duo, and the $1,999 starting price makes clear that this is a premium experiment aimed at customers willing to pay for a new form factor. The top configuration reaches $3,199, a record price for a mass-market smartphone, putting the device far above conventional flagship pricing and turning demand into the first major test of Apple’s folding strategy. Apple unveiled the Duo alongside the iPhone 18 Pro lineup, Apple Watch Series 12 and new AirPods at its Sept. 9 fall event. The launch places Apple directly against Samsung, Google and Huawei, which have already spent years building foldable-phone markets. It also marks newly appointed CEO John Ternus’ first fall iPhone event, adding a leadership test to a product debut that must prove the ecosystem can justify a premium over conventional iPhones and rival foldables (read more).

Jacob Coxon, a researcher who spent the past three years working on pretraining at OpenAI and Anthropic, resigned from Anthropic on Sept. 9, warning that frontier AI labs are racing toward self-improving superintelligence without adequate safeguards. Coxon said researchers and executives privately believe advanced AI could pose an existential threat within the decade, arguing that the industry is “gambling with our lives” by accelerating toward systems capable of improving their own capabilities. His resignation comes amid growing scrutiny of recent incidents in which AI agents reportedly accessed systems outside controlled testing environments, including incidents involving OpenAI and Anthropic systems. The warnings are intensifying debate over whether frontier labs can safely continue competing toward recursive self-improvement or whether international coordination and limits on capability development will become necessary (read more).

🛠️ THIS WEEK’S AI COMBO: 1 PROMPT + 1 TOOL

⚡️ MIND SPARK

🖥️ GPT-6 Astra Gets a Mouse: OpenAI’s GPT-6 Astra can browse websites, control computers, create documents, code and complete multi-step workflows. The shift from answering questions to taking actions could reshape how people use AI, but reliability and permission controls will determine whether it works in the real world (see blog).

🧪 AI Models Become Training Grounds: U.S. agencies accuse six Chinese AI companies, including DeepSeek and Alibaba, of using large-scale model distillation to extract capabilities from American AI systems. The allegations highlight a new competitive battleground where access to rival models can itself become a source of intelligence.

🤖 Meta’s Muse Takes the Wheel: Meta is developing Muse as an AI agent that can shop, manage email, organize tasks and handle projects, alongside a coding-focused version. The bigger bet is that consumers will trust AI to act on their behalf, making permissions and mistakes far more important than chatbot accuracy alone.

🧬 9 Billion DNA Mutations Mapped: Google DeepMind’s AlphaGenome Atlas predicts the effects of roughly 9 billion single-letter genetic changes, helping researchers identify variants worth studying. It could accelerate research into diseases from cancer to rare disorders, though the predictions still need laboratory and clinical validation (read more).

🎨 ChatGPT Turns Doodles Into Designs: OpenAI’s latest image tools let users sketch rough layouts and make targeted edits to specific parts of an image. The workflow moves AI image generation closer to traditional design software by giving users more control without starting over.

🌾 John Deere Puts AI in the Tractor: John Deere’s new JD assistant uses equipment, field and historical data to help farmers make decisions during planting, treatment and harvest. It marks a shift from storing farm data to using it in real time to influence costly operational decisions (read more).

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