This is going around due to rumors and baseless speculation on Twitter [1] right now that Anthropic has solved the Millennium problem related to Navier-Stokes [2]
For a second I thought they were aiming the scary proof machine at us mortals doing PDE stuff. Fortunately the speculation is just that they happen to be aiming it at a nearby mathematician type problem. Phew.
Lol as far as I know that post was the origin of that claim and it's clearly just a guy predicting something that will happen in the future with no information about it.
None really. It just says if the NS equations are realistic and can really model real physics or there exist some solutions that make it blow up (infinite energy). But even if that would exist (a solution that blows up) it doesn't mean it doesn't work for 99,999999% of the stuff we're interested in.
The question is basically a pure math question about PDEs.
This is essentially irrelevant to the content of the post, but it's amusing to me that he casually mentions submitting to JAMS as if its acceptance were a mere formality.
It’s pretty crazy what dynamics you get from NS.. until one realise they emerge from a tiny part of the solution space of Einstein equations.. which themselves emerge at the low energy limit of sth much bigger.
Interesting to see that they are not using the coordinate-free representation (exterior calculus, differential forms) that mathematical physicists prefer to use today.
[1] https://x.com/AndrewCurran_/status/2096062392442724805 for example
[2] https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_existenc...
https://x.com/ElliotGlazer/status/2096298696438906934
The question is basically a pure math question about PDEs.