> Cryptography is a branch of mathematics, and cryptographic systems can be formally proved to have certain properties, such as being unable to derive the private key from the content of the encrypted message.

A small correction: All those proofs (if they exist) are relative to complexity-theoretical conjectures that are (ideally) widely believed to be true, but open. The only system that I am aware of where an "absolute" security proof exists is OTP, but this is hardly suitable to use in practice.