Hmmm I think even in something very nominally nearby like theoretical physics, there's very little that's similar to theorem proving. I don't see how AlphaProof could be a stepping stone to anything like what you're describing.

Generally, I think many people who haven't studied mathematics don't realize how huge the gulf is between "being logical/reasonable" and applying mathematical logic as in a complicated proof. Neither is really of any help for the other. I think this is actually the orthodox position among mathematicians; it's mostly people who might have taken an undergraduate math class or two who might think of one as a gateway to the other. (However there are certainly some basic commonalities between the two. For example, the converse error is important to understand in both.)