Is there some theoretical reasoning behind the fact that the same numbers ($\pi$, $e$, $\gamma$, etc) appear again and again in every application in every field of Mathematics?
Most people just accept that fact and enjoy it, but I think this is a field of study in itself, and could be a focus of rigorous theoretical work, not only by the number theorists, but every mathematician.
There is an infinite amount of real numbers, most of them are uncomputable (we can't use these), but even among the computable numbers we regularly use no more than a hundred.
Or maybe there are many more equally important mathematical constants, but we have not invented the relevant areas of mathematics to apply them? Will we be able to do it? Maybe some alien civilization uses a completely different set of constants in their mathematics? What do you think?
There is a related question here, but this question is different, besides there was no satisfactory answer to that one.
Edit
And I do not include simple rational numbers here (but I do include the numbers that are not proven to be either way).