Theoretical Computer Science was one of the great intellectual developments of the 20th Century and only very recently have its ideas been integrated into basic science. I argue that these ideas and tools could be vital to understanding the relationship between mathematics and physics. In particular, if we are to ask if the utility of mathematics is a trick or otherwise, then we can use methods from the theory of cryptography and computation to pitch theory and experiment up against each other. Given this perspective we can ask if an experimenter can convince us to accept the theorist's version of events. I will outline that this contest is not as simple as it initially seems. There could be a stalemate between theory and experiment and it comes in the form of undecidability: a theorist can neither confirm or deny if Nature is behaving according to our most-trusted physical theories. Surprisingly, undecidability is a very real prospect in our current theories as I will discuss, and it forces us to question the relationship between mathematics and physics.
Matthew Joseph Hoban