6 months ago
Last edited at 8:34AM on 10/21/2013
Math is the logical development of all true statements that follow from a set of axioms, whether they have anything to do with this universe or not. Physics is the study of the universe at the most fundamental level. While the language of physics is math, it uses math only in as much as it describes the universe. There are branches of math that physicists don't use because they don't see how they apply to this universe. This of course does not mean that in the future such a connection would not be found though. A good historical example is non-Euclidean geometry. Until Einstein no one suspected that it's important for physics, and physicists normally did not study it. After Einstein showed that it describes gravity, it became a standard branch of math for physicists to study. Now it is in use also in other fields of physics. One other difference is that physics at the end of the day is an experimental science, and we decide on theories based on experiments. Mathematics does not depend on experiment, but on proofs. That is, you can develop math at your desk without ever getting input from natural phenomena. Physics evolves in tandem with input from natural phenomena.