Notably, it is not uncommon for math and physics researchers to bypass journals as a gatekeeper and directly publish to arXiv. This still allows for other researchers to see the claims presented in a rigorous format and rebut them.

It's pretty uncommon (read: I've literally never heard of this outside of one obvious famous exception) for math researchers to put something important on arxiv and never submit it to a journal.

As someone totally unfamiliar with all of this, what's the exception you're referring to?

Perelman's proof of the poincare conjecture.

He said recently in a conversation with Lex Friedman that he intends to release a complete paper April 1st.

Which would be great if he follows through. Unfortunately he has made promises in the past and not followed through, so I can't take his word on that.

I'm surprised Weinstein doesn't consider it important to put technical details out there, especially when it's not like anyone is going to steal this research. All it takes is a submission to arXiv to not only popularize his ideas but to submit them to the peer review of everyone, since he holds a quarrel with institutional review.

He points out that most of our foundational science was published outside of peer review. For example: Watson & Crick's double-helix hypothesis.

That’s a pretty bold claim. The 1953 Nature paper laid out both the double helix and the Central Dogma (which is arguably the more important result). https://en.wikipedia.org/wiki/Molecular_Structure_of_Nucleic...