"We need to distinguish between two different ways of viewing the external physical reality: the outside view or bird perspective of a mathematician studying the mathematical structure and the inside view or frog perspective of an observer living in it. ...a mathematical structure is an abstract, immutable entity existing outside of space and time. If history were a movie, the structure would therefore correspond not to a single frame of it but to the entire videotape. ... If a future physics textbook contains the TOE, then its equations are the complete description of the mathematical structure that is the external physical reality. ...is rather than corresponds to...If our external physical reality is isomorphic to a mathematical structure, it therefore fits the definition of being a mathematical structure."