One of the most peculiar characteristics of mathematics is its seemingly limitless ability to accurately account for real world phenomena. The success of the discipline in providing a rigorous structure on which principles of physics and chemistry can be scaffolded is perhaps most strongly demonstrated by the justification frequently given for studying theoretical math: although some given piece of research may have no connection to the real world, there is a high probability that one will be found at a future time. The confidence that researchers have in the usefulness of mathematics, even before an actual use has been found, speaks volumes about the strong parallels between mathematical principles and the underlying architecture of reality.
This is a concept we are accustomed to. Few and unfortunate are the students who walk into a physics course not expecting a heavily mathematical treatment of the subject matter. And virtually no one believes that the much sought after physical "theory of everything" will be properly elucidated
