stingc

Math does use the experimental method in a particular sense. Imagine that you are learning some type of math, and have just been presented with a set of definitions. These will generally seem to be too abstract to grasp on any sort of intuitive level, so you generally want to construct some examples to get a feel for how things work. Say that you now have several different examples, but are surprised to notice that they all share one particular property. You might then guess that all possible examples share this propery. So your examples have now given you an idea for a possible theorem. Examples are even more powerful in showing that a particular property is not correct when intuition would imply the opposite.

A well-known example would be Fermat's Last Theorem. Whatever progress Fermat may have made in proving it (nobody knows), the rest of the world didn't have a proof until a few years ago. It was, however, thought to be true because it seemed to work for every example that was tried. People kept showing that more and more special cases of it were correct. This gave people enough motivation to continue to try finding a complete proof even after 300 years.

So "experimentation" with mathematical definitions is an important part of mathematical progress. Unlike in the natural sciences, however, it is not absolutely required. Also, unlike math, science can never provide absolute proofs of anything.

I spend my days doing mathematical physics, so I also have plenty of experience with math. Its not terribly relevant though. I overspoke by saying "everyone," and I apologize.