Reductio ad absurdum … is one of a mathematician’s finest weapons.

Reductio ad absurdum, which Euclid loved so much, is one of a mathematician’s finest weapons. It is a far finer gambit than any chess play: a chess player may offer the sacrifice of a pawn or even a piece, but a mathematician offers the game.

— Godfrey H Hardy (English mathematician, 1877 – 1947)