alt Hacker NewsNS is a question for natural science. Q: can we model these bodies of discrete particles with a continuous approximation? A: if you do, you can get aphysical singularities.
"If in other sciences we should arrive at certainty without doubt and truth without error, it behooves us to place the foundations of knowledge in mathematics."
This is a wrong interpretation. Physicists have a shit-ton of models that produce "aphysical singularities", they just work around those to get meaningful answers anyway. This is a whole trope and stereotype. Some of the most successfull and accurate predictions in all of physics come out after you discard a bunch of singularities.
See e.g. https://en.wikipedia.org/wiki/Renormalization
Nobody who actually works in fluid dynamics on any sort of application gives a hoot about the N-S millenium problem. Many do not even know what it is. There is no practical effect of this proof on how we do fluid mechanics.