Tweets on ordinary and partial differential equations from @JohnDCook

Joined March 2013
Differential Eqns retweeted
Having friends come up to me wanting to discuss the Navier-Stokes equations was not on my bingo card for 2026.
5
1
45
2,686
Differential Eqns retweeted
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 👇👇👇
8
45
2
284
25,915
Differential Eqns retweeted
watch out odysseus, despite smooth boundary conditions it is generating a singularity
🤖 Made with AI
30
409
17
6,907
132,798
Differential Eqns retweeted
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.
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
100
1,102
305
9,967
1,610,107
Differential Eqns retweeted
Navier-Stokes in the news johndcook.com/blog/2026/09/0…
3
40
244
12,336
Differential Eqns retweeted
this rumor that Anthropic has solved a Millennium Prize Problem is getting very interesting. Terence Tao a few hours ago:
Andrew Curran
@AndrewCurran_Sep 5
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.
141
634
137
7,573
1,532,337
Differential Eqns retweeted
How large initial displacement affects a pendulum johndcook.com/blog/2026/04/2…
1
3
24
3,981
Differential Eqns retweeted
The moment you realize... #professor
43
823
13,740
Differential Eqns retweeted
📉
4
13
2
439
37,821
Differential Eqns retweeted
An infinite degree ordinary differential equation to brighten your weekend. 🙂 Happy #Einstein's Birthday and a Happy weekend! #math #calculus #DifferentialEquations
1
12
125
12,258
Differential Eqns retweeted
“The key to understanding the Dirac delta function is that it’s not a function on real numbers but a continuous linear functional on the space of smooth functions with compact support.”
22
79
7
873
38,152
Differential Eqns retweeted
New post: Weak derivatives johndcook.com/blog/2025/12/1…
3
3
31
5,634
Differential Eqns retweeted
10
18
3
415
17,340
Differential Eqns retweeted
Stabilizing the Spherical Pendulum from Scratch community.wolfram.com/groups…
1
22
3,440
Differential Eqns retweeted
19
76
15
1,163
32,887
Differential Eqns retweeted
if you're taking/teaching applied dynamical systems this term & want to peek at a book-in-progress, i've updated the draft on my website... see below
9
37
2
334
26,337
Differential Eqns retweeted
Bad frodo.
33
173
14
1,898
61,475
Differential Eqns retweeted
16
108
4
1,881
45,978