Talk with AI like you’d talk with a friend. About your day, a random idea, or something that’s been on your mind.
I built this for a lively back-and-forth: it can ask questions, make connections, and jump in with a thought while you’re still talking—without waiting for another prompt.
Set the tone. Adjust excitement for a calmer or more animated exchange.
Keep your space. Use “Let me finish” when you want the floor.
Keep the thread. Save the conversation to revisit later.
Experimental local app, tested on Mac. Requires Node.js 22+, signed-in Codex, a microphone, and internet access. Uses your Codex allowance. Audio and conversation text are processed by OpenAI—not offline.
Timing and relevance can vary. This is not an official OpenAI app; its experimental Codex voice integration can change or stop working. Windows has not been tested on a Windows machine.
THE CONTEXT BEHIND THE CONVERSATION
Checked
A serious step forward. Not “Navier–Stokes solved.”
In the hours before this update, mathematicians released AI-assisted work on how fluid equations can develop singularities. It is an exciting research development—and a good example of why the exact claim matters.
01 / ANNOUNCED
Three related results
At 03:58 UTC, Tristan Buckmaster announced work with Levent Alpöge on finite-time blowup with smooth forcing for incompressible porous media, Boussinesq, and three-dimensional incompressible Euler equations. Read the announcement ↗
02 / EXPERT RESPONSE
Promising, with work ahead
At 04:27–04:28 UTC, Terence Tao praised the advance. He described substantial AI input and Lean formalization, while emphasizing that extending the approach to Navier–Stokes would face enormous technical difficulties. Tao’s assessment ↗
03 / STILL OPEN
The full prize problem
The Clay Mathematics Institute still lists Navier–Stokes as unsolved. Results for related equations do not establish a solution to that precise problem. Official problem status ↗
What does “blowup with smooth forcing” mean?
Think of a fluid that starts in a well-behaved state. A blowup means the mathematical solution loses a required kind of regularity in finite time—for example, a quantity needed to describe the flow becomes unbounded. It is not a claim that an actual liquid literally explodes.
Forcing is an external push included in the equations. “Smooth” means that push has no abrupt mathematical irregularities. The importance of this work is that the breakdown is not simply being put into the model through a rough forcing term.
Euler is not Navier–Stokes. Euler models flow without viscosity; Navier–Stokes includes viscosity, which changes the problem. The precise equation, initial conditions, forcing, and notion of solution must match before one result can settle another question.
Where does AI fit—and what has actually been checked?
Tao says the arguments contain significant AI input, with the authors working to make them understandable. The authors also released a Lean repository. Formal proof checking can provide strong evidence about the statements encoded in it, but this page has not independently compiled or audited that code, its assumptions, or its correspondence with the papers.
Tao sees a possible route toward Navier–Stokes, potentially with extensive computation and AI assistance. That is an expert view about what might be achievable, not a completed proof or a timetable. His priority is understanding the ideas, not merely obtaining an answer. Read his continuation ↗
This is evidence of a human-led, AI-assisted research process. It does not establish that an AI independently solved the Millennium Prize problem. This update does not treat circulating claims about unreleased proofs as verified results.
How to watch the conversation: treat it as an exploration of a fast-moving idea, not a proof review. The dated source notes here—not every spontaneous remark in the recording—set out what this page can substantiate.