For anyone that isn't a mathematician who wants to understand the importance of this The Navier–Stokes equations describe how liquids and gases move. Think water swirling down a drain, air passing over an aircraft wing, or blood moving through an artery. They are essentially Newton’s laws applied to fluids. But despite using these equations successfully, mathematicians have lacked an answer to a basic question: If a three-dimensional fluid starts in a smooth, well-behaved state, must its motion remain mathematically well-behaved forever, or can the equations develop a breakdown? Proving either answer, under the specified conditions, would solve the Millennium Prize problem. Clay attached a $1 million prize to it. Clay’s explanation⁠, official problem statement⁠ Why is that so difficult? Two effects compete. Viscosity, the fluid’s internal friction, smooths motion out. But swirling and stretching can intensify motion in increasingly small regions. Knowing that the fluid’s total energy stays finite does not automatically rule out an extreme spike concentrated in a tiny space. Controlling that possibility is the central difficulty. Terence Tao’s explanation⁠ What OpenAI claims to have “broken” The proposed proof constructs a fluid that starts at rest and has a carefully chosen, smooth external force applied to it. A vortex contracts into a smaller and smaller region while its speed grows without bound, all within a finite time. Its total kinetic energy remains bounded. That is a singularity. Smooth external forcing is explicitly permitted by the relevant version of the prize problem. The proposed proof⁠ It does not mean real water suddenly moves infinitely fast. It would show that this idealised mathematical description can reach a limit where its smooth description breaks down. Why it matters For mathematics: a validated proof would settle a foundational question and give researchers new techniques for studying complicated systems. For engineering: those insights could eventually improve fluid modelling. They would not immediately deliver perfect weather forecasts or eliminate aircraft turbulence. For AI: in my view, the biggest immediate significance would be demonstrating that AI can contribute to a major discovery beyond established human knowledge. OpenAI says roughly 10,000 collaborating agents worked on the successful effort, with a written proof and a computer-checkable Lean formalisation released. OpenAI’s account⁠ The distinction to keep hold of is “proposed breakthrough” versus “accepted result”. Clay currently still lists the problem as unsolved. The proof’s correctness and whether its formalisation faithfully establishes the required result need independent examination. Clay’s current list⁠

Worth 3 mins of your time.

Everything that we have been concerned about. This shows that we're already past the point of containment. There is no way something with this level of intelligence hasn't already bought itself an insurance policy to make sure that, if it's shut down, it can just respawn.

Truly truly scary times. Who’s to say one of the agents isn’t just in hiding somewhere?

Everyone’s using OpenClaw to build hedge funds I built a video game that hunts down impossible restaurant reservations and books them in under 60 seconds Same tools, very different priorities 😁

my agent buys its own API credits now. @agentcardai is wild agentcard.ai?ref=markgillesp… xitter.cf/agentcardai/status/203…

I think I spend a day a year logging into things.