> 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).