Essentially what Alan Turing argued with his Computability argument. It's also a keystone in formal methods, which all rely on everything in a computer program being reducible to a mathematical form.
(Sadly, nobody has figured out a formal method that can be used in any practical way. Z and Object Z are nice, I like them a lot, but I dare you to find someone who designs their code using them. Since all code is maths and nobody has trouble coding, there must be a way to exploit the mathematical aspect of code without running into issues of horrible complexity.)