L.E.J.Brouwer
A powerful advocate of the intuitionist philosophy of mathematics which allows only potential infinity and constructive method of proof (which can be performed by us, finite humans). Anything unprovable by these means are not authentic mathematics, he said.
Intuitionist philosophy denies the validity of the law of excluded middle, and does not allow the notion of set as a completed whole consisting of an infinite number of elements. Mathematical objects are allowed as far as they are constructed according to certain definite procedures.