No, there's no proof that most crypto "calculations" are impossible to reverse. That's why algorithms got weakened by researchers regularly. As of now, it's totally possible someone finds an algorithm to break a next one tomorrow. They just haven't found it yet.
Of course there isn't, nothing like that could be formally proven. But that is neither here nor there.
The important issues remain:
1. Whether some as yet unknown technique exists for efficiently breaking a code.
2. If the answer to (1) is yes, whether LLMs can find it at a reasonable cost.
TTBOMK we still don't know anything about (1). I think the answer to (2) is "probably yes".
(That's not a common answer to the same question about, say, ECDLP, even leaving quantum aside).
Most of the breakthroughs so far have been finding counter examples. They can just search tirelessly to find one. Finding a good algorithm (maybe even one faster than people assume is possible) seems the obvious next step for them (as opposed to more conceptual proofs e.g. existance or non-existence where they still aren't quite terrifyingly good).
The phrase "for all we know some undergrad might find a counter example" is the new "it works for n<100 so I don't see why it won't continue indefinitely".
That's the 3rd point. correctness of the algorithms.
A few basic things are known - for example, you can't make a symmetric cipher with just bitshifts and XOR, because then linear algebra techniques can trivially reverse it.
Two cases: 1) you have to find a route to the middle 2) someone gives you a route to the middle and you have to validate it
It’s not proven that case 2 is necessarily easier than case 1. But logic and every case in the history of computing suggest that it is.
I don’t see how LLMs could possibly change that fact