Non Constructive Proofs

Intuitionists have held that non-constructive proofs are invalid. However, most mathematics rests on non-constructive theorems. Quoting an example from Stage I mathematics: Euclid's proof of the irrationality of "root two." Root two is assumed to be rational and it is shown that this leads to a contradiction and is therefore wrong. Intuitionists say that something does not exist unless it can be constructed.