> there is no proof that just because AI found counter example for a conjecture, it can break math behind cryptography

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".

When we're talking about things like AES and SHA2, a common answer among experts to (1) is "probably no".

(That's not a common answer to the same question about, say, ECDLP, even leaving quantum aside).