Unbruteforceable Encryption

Are there any theoretical forms of encryption that cannot be cracked? With the advent of Quantum computers busting SHA-512 encryption in the blink of an eye (only partially exaggerated) are there theoretical algorithms or methods to encrypt data in a way that it cannot be cracked?

I'm assuming this would involve secret functions (it cannot be cracked if the function used is unknown to the attacker)?

Is computer science or mathematics the better educational path to take to enter a field involving cryptography?