Luitzen E.J. Brouwer,
one of the great mathematicians of the early 20th century; he almost singlehandedly founded topology
Brouwer was involved in a great debate concerning the foundations of mathematics.
Formalism, proposed by David Hilbert and others, regards mathematics as a system of formal rules.
Intuitionism, proposed by Brouwer, considers it the product of human intuition.
Intuitionism rejects a certain class of mathematical proofs.