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.