Earlier quoted context omitted.
This is more along the lines of "SHA256 has not been proven to be secure, therefore, it may be cracked." It would require novel discoveries in mathematics to do so.
Actually many cryptographic algorithms that got defeated, haven't been defeated with " new discoveries in mathematics ". Also, you can't really prove that such an algorithm is secure. You can only prove that it exhibits certain properties that make it more secure versus other algorithms. Judging by how cryptographic methods got defeated in the past, I think it's safe to assume that it's only a matter of time.
Proving cryptographic algorithms are secure involves proving statements over all turing machines. For example, one definition of a 'secure' pseudo random number generator is one such that no turing machine can distinguish its output from 'true' random (with 2/3 certainty) in polynomial time.
However, we do know a really-really-probably secure one way function. If there are any one way functions, then it is secure. It just isn't really practical. http://en.wikipedia.org/wiki/One-way_function#Universal_one-...