OpenAI says an internal AI model, more capable than GPT-6 Astra, generated a solution to part of the Navier–Stokes existence and smoothness problem, one of the Millennium Prize Problems. The proof demonstrates that three-dimensional incompressible fluid dynamics governed by these equations can develop a singularity—unbounded speed growth—in finite time, even from smooth initial conditions. OpenAI released both a written explanation of the proof and a formal verification built in the Lean proof assistant.
OpenAI claims its internal AI model, paired with 10,000 concurrent agents, solved the century-old Navier-Stokes equation, one of the seven Millennium Prize Problems worth $1 million. However, NYU professor Tristan Buckmaster says he and Anthropic researcher Levent Alpöge had been developing a nearly identical proof using OpenAI's Codex tool, and he suspects OpenAI may have drawn on their unpublished work without clear confirmation from the company.
Labor force participation among Americans 65 and older has climbed to 19.2%, up from roughly 12% in 2000, and 42% of sitting CEOs are now 60 or older—an unusually high share, according to executive recruiter Cowen Partners. Companies like Boeing, Verizon and Cracker Barrel have repeatedly brought back older or previously retired executives rather than promoting younger leaders.
OpenAI announced on 8 September that its latest AI model produced a proof showing that the Navier-Stokes equations, which model fluid motion, can break down and predict a fluid reaching infinite speed in finite time. This addresses one of the seven unsolved Clay Mathematics Institute Millennium Problems, which carries a $1 million prize for a full solution. OpenAI researchers say they focused their AI on this problem after hearing that two academic mathematicians were close to solving related aspects.
An essay examines why Shakespeare's Macbeth, despite its cultural notoriety and superstition-laden reputation, is uniquely difficult to produce well onstage. The piece argues that unlike 'actor-proof' scripts that survive weak performances or direction, Macbeth demands that every element—acting, design, pacing—align perfectly or the production collapses. Central to this difficulty is the play's embedded supernatural elements, starting with the witches, which set a challenging tone that productions must sustain throughout.
A long-time foldable phone user argues that Apple's upcoming iPhone Ultra, expected to launch September 9, will likely carry over many of the same compromises seen in Android foldables. These include a soft plastic folding display prone to scratches, a factory-applied screen protector users typically cannot remove, and other durability and design tradeoffs common to the foldable category.
Caltech is organizing a 40-hour event called Mathathon, running October 30 to November 1, where about 100 teams will use frontier AI models with over $2 million in compute credits to tackle open mathematical conjectures. Teams will present their findings to leading mathematicians, who will judge their understanding and rigor, with prizes awarded initially and again later once results are independently verified by the math community.
Oura has acknowledged in SEC paperwork filed ahead of its IPO that some Ring 4 units suffered battery performance problems, which contributed to an $84.4 million rise in warranty expenses during fiscal 2025. The company replaced affected rings free of charge, sometimes even after the standard one-year warranty had lapsed. Oura has not specified which production batches were affected.
A troubleshooting guide outlines fixes for frequent Apple Wallet and Apple Pay issues, such as cards being declined due to expiration or reissue, outdated iOS software, and regional restrictions. The recommended fixes include removing and re-adding cards, updating iOS through Settings, and verifying that the device's region matches supported Apple Pay markets.
Slate, the young EV startup backed by roughly $1.4 billion in funding including from Jeff Bezos' family office, is building its truck exclusively for the US market at launch. The company will sell direct-to-consumer, manufacture in a converted Indiana plant, rely on RepairPal for servicing, and give every truck NACS access to Tesla Superchargers—all within US borders. Slate has not said whether tariffs influenced this decision or when it might expand to Canada or other countries.
As foldable phones get thinner, their camera modules still need bulky sensors, forcing a protruding camera bump that unbalances the device when placed on a flat surface. Users of the Galaxy Z Fold 8 have complained on Reddit about the wobble caused by its vertically placed rear camera module, with some reportedly removing the cameras entirely out of frustration.
Tesla has expanded its driverless robotaxi service beyond the Model Y to include the Cybercab, a two-seat vehicle featuring butterfly doors, touchscreens, and no steering wheel. A promotional video for the new vehicle went viral, but drew backlash from disability advocates who say its design overlooks accessibility needs.
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