There’s a Reddit thread that provides useful context to this, what it is and the scope: https://www.reddit.com/r/math/s/OD0Jy9Rdns

A talk on it by one of the authors

https://www.simonsfoundation.org/video/yu-deng-the-hilbert-s...

I couldn't get an idea of what they did from TFA because it explains they derived a continuum model from a particle model by considering the particle number going to infinity and their size going to zero... which sounds a bit like a continuum

Nice, but uniting Newtonian physics with Navier-Stokes equations is „easy“.

It is much more difficult to do the same and unite relativistic mechanics with relativistic fluid mechanics. The fact that in relativity you have to deal with particle creation and annihilation makes the issue much much harder, because particle number is not conserved and it is difficult to define probability densities if the particle number is not constant. And in addition each particle has its own proper time, so a standard phase space does‘t exist. It might well be that the idea of point-particles and relativity are in some sense incompatible even at the classical level.

archive link https://web.archive.org/web/20250426022659/https://www.scien...

And arXiv link: https://arxiv.org/abs/2503.01800

The article does a wonderful job in providing context for the proof.

I really enjoyed the clear descriptions of the three scales.

It's interesting how so many important papers are always on arxiv first. it makes me wonder what purpose peer reviews serves. I think also, this is to help establish priority over the result. So getting it up on arxiv is like a timestamp to avoid someone else deriving it at the same time and getting credit by having it published first.

The purpose of the (pre-print) arChive is to allow for a wider circulation during review. That many today simply leave their stuff on Arxiv without publishing is arguably a bit of “cargoculting”, as it signals legitimacy without any quality control.

Peer review is important for checking the correctness of the results, among other things. It's not uncommon to find big errors; small mistakes are everywhere.

Peer review is of utmost importance. Any researcher can make mistakes. I can read papers and apply them, but I need expert opinion to trust the papers. I am not skilled enough in any but my specialties.

I do see papers with outlandish claims and very weak support. This kind of excessively bold statement I see in many papers is a red flag for me.

Its easier to tear down than build up. Resilient structures are tested structures and last the longest.