Indirect proofs, also known as reductiones ad absurdum (``reductions to the absurd'') are quite common in mathematics. In fact, students of mathematics tend to use them too often---providing an indirect proof where a direct one would do just as well.

Intuitionist mathematics (which is much more well-grounded than the name would seem to indicate; it is related to constructivism) does not allow the indirect method of mathematical proof.