On OpenAI's spinning top-counterexample to the existence of smooth solutions of the Navier-Stokes equations

So, the idea is to define a flow that has an anomaly, then use the fact that up to that anomaly such a flow has a pressure field at every moment that is supposed to determine its acceleration and then define a force field as the force that needs to be added so as to turn the supposed acceleration due to the pressure into the actual acceleration of the predefined flow.

It's been more than 20 years, since I've concerned myself with this seriously, but I do remember the following theorem: For a force field to be the gradient of an energy field it is necessary and sufficient that the curl of the force field, i.e. rot(v)=dvⁱ/dx_j-dv^j/dx_i, vanishes. Actually, I'm still capable of proving that.

So, the curl of the gradient of the pressure field is 0. And for the defined force field to be a physical force field derived from an energy field instead of a mathematical fiction that would allow you to build a perpetuum mobile, the curl of the predefined motion has to be 0 as well. However, the curl of the acceleration of an accelerating spinning top isn't 0, trivially, really.

So, this wasn't really the Deep Blue moment of mathematics. More like children drilling a hole into a bucket, thinking that they've just built a bathtub with plumbing and all.

If you have a bachelor in mathematics or physics you should understand all this. Yet... if people are pointing this out, and everybody with a bachelor in mathematics or physics could, they don't get a lot of publicity.