[vbrandl]

Hashing is a separate problem from encryption. There is no proof that one way functions (the idea behind hashing) even exist (by proving this, you would actually prove P!=NP, IIRC). Encryption has a slightly better track record of being broken. AES still holds its promise and is also secure against quantum computing (you might want longer keys, but that's it).

And if you want really, provably unbreakable encryption, there is still OTP. But then you'd need a key, that is as long as the data you want to encrypt.

[blattimwind]

The best known attack against AES reduces attack complexity by about two bits over brute force. Given the history of block ciphers, the idea that AES might not be broken in this life time is not uncommon.