Differential Eqns @diff_eq

Everyone's talking about finite-time blow-up for Navier–Stokes. Here's a very simple example of what that means for an ODE: y' = y² y(0) = y₀ > 0 y(t) = y₀/(1 − y₀t) It grows to infinity in finite time T* = 1/y₀. Inspired by @MarastiMattia #builtWithmarimo notebook 👇👇👇

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Differential Eqns @diff_eq

2 weeks ago

Chebyshev polynomials T_n(x) satisfy (1 - x²) y'' - x y' + n² y = 0.

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Differential Eqns @diff_eq

2 weeks ago

'The boundary condition of the universe is that it has no boundary.' -- Stephen Hawking

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Josh @yFactr

2 weeks ago

watch out odysseus, despite smooth boundary conditions it is generating a singularity

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Differential Eqns @diff_eq

2 weeks ago

Bowie integrator and the nonlinear pendulum johndcook.com/blog/2025/12/2…

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Konsti Wohlwend @konstiwohlwend

2 weeks ago

drama summary for those confused: - Aug 15th: Tristan Buckmaster & Levent Alpöge make progress on a few important math problems - they do NOT have a proof for the $1,000,000 Millenium Prize problem. BUT, they do claim to have a proof for a similar (non-Millenium) Navier Stokes problem that could help lead the way there - Levent works at Anthropic, but this research was independent of his work there, with a mix of GPT and Claude models. Tristan is not related to Anthropic. - Early Sep: Rumor spreads to OpenAI that Anthropic has solved a major problem. Tristan emails OpenAI to clarify. without revealing the problem they solved or how they did it. - After hearing of the rumor, OpenAI started researching Navier Stokes with a new internal model. - Sep 6th: OpenAI's Sebastien Bubeck tells Tristan that they solved the $1,000,000 Millenium Prize Navier Stokes problem. The approach is very similar to Tristan & Levent's approach to the non-Millenium problem. - Tristan is suspicious of the timing, as only few others were trying this approach. OpenAI says the model didn't access his user data directly, but leaves unanswered whether Tristan's chat conversations were part of the training. - OpenAI says they would partially credit Tristan for the $1,000,000 discovery (even though Tristan did not solve the $1,000,000 problem) — but only if they remove Levent as an author, as he works for Anthropic. - Sep 8th: Tristan refuses to remove Levent, and rushes to publish their results independently. Currently unclear is whether Anthropic had a separate solution for the $1,000,000 problem, or whether the rumor was about Tristan & Levent's independent research.

Hensen Juang @basedjensen

2 weeks ago

Wow Navier-Stokes thing is getting really ugly. But from the sounds of things it looks like both labs have actually solved Navier-Stokes independently and drama aside is massive

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John D. Cook @JohnDCook

2 weeks ago

Navier-Stokes in the news johndcook.com/blog/2026/09/0…

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Differential Eqns @diff_eq

2 weeks ago

Finite time blowup with smooth forcing term for the incompressible porous medium, Boussinesq, and incompressible Euler equations terrytao.wordpress.com/2026/09/07/fin…

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Differential Eqns @diff_eq

2 weeks ago

Burgers' equation: u_t + u u_x = v u_xx

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ℏεsam @Hesamation

2 weeks ago

this rumor that Anthropic has solved a Millennium Prize Problem is getting very interesting. Terence Tao a few hours ago:

Andrew Curran @AndrewCurran_

2 weeks ago

It's fun to make predictions. Here's a new one: Anthropic has solved a Millennium Prize Problem. And I'll be even more specific. Claude has solved Navier–Stokes. It is out for expert review. And to give myself a hard deadline, they will announce it before the IPO.