Why do mathematicians insist on having proofs of all results? A case in point is Cleo on math stackexchange. Cleo regularly is able to come up with values of complicated integrals faster than any one else, but because she does not post a proof, people say that her results are useless or disrespectful. In fact all proofs depend on axioms, so if a result is known to be true, one should just work in an axiomatic system that accepts it as an axiom. I prefer this approach when I know the result. Therefore, Cleo in fact gave full proofs. It is like Bertrand Russell says about the First Cause argument:
" If everything must have a cause, then God must have a cause. If there can be anything without a cause, it may just as well be the world as God, so that there cannot be any validity in that argument. There is no reason why the world could not have come into being without a cause; nor, on the other hand, is there any reason why it should not have always existed. There is no reason to suppose that the world had a beginning at all. The idea that things must have a beginning is really due to the poverty of our imagination. Therefore, perhaps, I need not waste any more time upon the argument about the First Cause. "