There is no mathematical proof that any cipher (other than the one-time pad) is resistant to all as-yet-unknown quantum algorithms.
That doesn't mean anything; the same is true for classical algorithms.
That's hardly surprising if you understand what proving anything like that would entail. Hell, to prove you can't break ECC or RSA with a classical computer you'd have to prove P!=NP, since discrete log and factoring are in NP. (To see why, just note that fast factoring would break RSA, so to prove you can't break RSA you have to prove that fast factoring is impossible, which means that you have to prove that factoring is not in P -- but since factoring is in NP, you'd also be proving P!=NP).
Note, however, that proving that ECC or RSA are breakable does not require a proof of P=NP or P!=NP -- for example, you don't need fast factoring to break RSA.