High Quality Content by WIKIPEDIA articles! In a foundational controversy in twentieth century mathematics, L. E. J. Brouwer, a supporter of intuitionism, opposed David Hilbert, the founder of formalism. Brouwer in effect founded the mathematical philosophy of intuitionism as a challenge to the then-prevailing formalism of David Hilbert and his collaborators Paul Bernays, Wilhelm Ackermann, John von Neumann and others. As a variety of constructive mathematics, intuitionism is essentially a philosophy of the foundations of mathematics. It is sometimes and rather simplistically characterized by saying that its adherents refuse to use the law of excluded middle in mathematical reasoning. In the later 1920s, Brouwer became involved in a public and demeaning controversy with Hilbert over editorial policy at Mathematische Annalen, at that time a leading learned journal. He became relatively isolated; the development of intuitionism at its source was taken up by his student Arend Heyting.

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