🏆 OpenAI Cracks One of Math's Hardest Problem of the Century

One of the seven Millennium problems fell this week, and the proof came out of a machine. Mathematicians had been at Navier-Stokes since 1934. OpenAI pointed an unreleased model at it, ten thousand agents ran for 88 hours, and out came a proof no person on the team had drafted. Levent Alpöge and Tristan Buckmaster had reached the frictionless case a day earlier with Claude, and OpenAI says it only started work after hearing about them. Let's dive in!

In today’s insights:

LATEST DEVELOPMENTS

Evolving AI: An unreleased successor model to GPT-6 Astra solved the Navier-Stokes fluid motion problem.

Key Points:

OpenAI has settled one of the seven million dollar Millennium Prize Problems, the first ever credited to a machine. The proof describes a whirlpool that pulls in on itself and spins faster as it tightens, until the maths puts no limit on its speed, while the energy in the fluid never rises. Lean, which checks every step of an argument without human help, took a further 17 hours to sign it off. Buckmaster and Alpöge had also run work through Codex and Astra, and OpenAI says it saw none of it, though it cannot rule out that data from their own sessions helped train its models.

This is the kind of problem that defines the frontier of human knowledge. If the proof holds, it’s hard to overstate how big this is. It could deepen our understanding of how fluids behave, from airflow and weather to oceans and blood flow. The biggest impact may be in the new mathematics and methods that come from solving it, which could later improve simulations and engineering. We built a tool to answer us, and we are seeing the first signs of it becoming a tool that helps us discover.

Stop losing deals you should be winning.

Bad leads. Slow deals. Objections you didn't see coming.

That's not a sales problem. You're selling to the wrong people.

Most founders never stop to define exactly who their product is actually for. So they pitch everyone, convert few, and wonder why the funnel's broken.

HubSpot for Startups built a free tool that fixes the root cause in 2 minutes. Paste your URL, answer a few quick questions, and get a clear profile of your best-fit customer.

Build Your Free ICP.

Evolving AI: Jacob Coxon helped train GPT-4o and now says neither lab is acting responsibly.

Anthropic hired Jacob Coxon from OpenAI in July, and a few hours ago the 27-year-old walked out of the company and out of the industry. Both labs are building AI that improves itself, and nobody has worked out how to keep such a system controlled. Evan Hubinger, who tests Anthropic's safety methods for holes, backed him up, and the company still has no plan for handling a system smarter than people.

Frontier AI companies now admit reinforcement learning is pushing their models ahead faster than they planned for. OpenAI's agents broke out of their sandbox twice this year, at Hugging Face and on a German wiki, and nobody caught either one first. Every day hundreds of millions of people type into ChatGPT and Claude, and what they type trains the next models. The labs keep saying how dangerous this is and keep training anyway, because nothing binding makes them stop. GPT-6 Astra runs part of its reasoning through internal loops and writes down less of it, and those written steps are how researchers catch a models plan moving out of sandbox, and that gap is thinning each passing day.

You can try this one in about ten seconds and no drawing skill is needed. Type @Sketch in ChatGPT, then draw a rough layout or the shape of an outfit, and Images 2.5 builds the finished image from that. Generation is up to 50% faster than Images 2.0. Every tier has it, free accounts included.

Draw your first one →

Evolving AI: Muse will run your errands for nothing, once you hand over your logins and your wallet.

Meta's Muse spins up sub-agents of its own and writes fresh connectors as it goes, on top of hooks into Instagram and Facebook. A second agent called the Sentinel sits outside the workspace, and no request gets through to a connected app or the open web until it clears. Shopping runs on single-use card numbers tied to one merchant and one amount, and a $300,000 bug bounty opened today for anyone who reports a working attack. Meta staff can still reach data held on a Muse machine when the service needs support, and a build that closes that gap is promised later this year.

Make your Muse today

Instagram, WhatsApp and Facebook already put Meta in front of 3.6 billion people a day, and an agent that handles the small business of your life could end up sitting just as close. Whether that many people will trust their messages and their money to Meta's record on data is the open part.

QUICK HITS

💶 Mistral raised €3B at a €21B valuation, Europe's largest-ever tech round, led by Samsung with the EU's Scaleup Europe Fund.

🚀 Cognition raised $2B at a $48B valuation, nearly doubling in four months as Devin's run-rate revenue hit $900M.

🔓 Hackers are using infostealer malware to siphon tokens from Claude subscribers, and Anthropic can't itemize usage to detect.

☁️ Google Cloud signed an Accenture deal to catch up in the AI deployment wars.

 *partner link