Historians think that out of this way of arguing the first proofs and especially the theory of odd and even numbers were developed. Due to the fact that odd- and evenness are contradictions in a logical sense, they allow for indirect proofs. These are very powerful instruments and one of the most famous proofs that we still learn at school is done in this way: the proof that the square root of two is irrational. The Greeks would say: diagonal and side of the square are incommensurable: you will never find a common measure for both of them.