I'm not sure what you mean by "mathematics as a system", but mathematics generally does not stem from the physical world, but rather from basic axioms. This is what separates from science, which is based on observation.
For instance, all of euclidean geometry can be derived from [wiki]Euclid's postulates[/wiki], of which there are only 5. This includes Pathogen's theorem, tessellations mentioned above, and more. By contrast, Newton's laws of motion, were accepted because they agree with experiment. In 1915, Albert Einstein Published the [wiki]Theory of General Relativity[/wiki], which describes a world that does not follow euclidean geometry or newton's laws of motion. Newton's laws are now considered incorrect (though very good approximations for most applications). However, euclidean geometry is still considered true, and not dispoven by Einstein. You can no longer expect the world to obey euclidean geometry, but the principles that are derived from Euclid's postulates still follow from Euclid's postulates.
Language is not build off axioms.