Luitzen Egbertus Jan Brouwer (February 27, 1881 - December 2, 1966), usually cited as "L.E.J. Brouwer", was a Dutch mathematician who worked in topology, set theory, and measure theory and complex analysis. The Brouwer fixed point theorem is named in his honor. He proved the simplicial approximation theorem in the foundations of algebraic topology, which justifies the reduction to combinatorial terms, after sufficient subdivision of simplicial complexes, the treatment of general continuous mappings.
Brouwer adhered to an intuitionist philosophy of mathematics, which is sometimes characterized by saying that its adherents refuse to use the law of excluded middle in mathematical reasoning, and wrote books on the subjects mentioned above in which he proceeded accordingly.
His ideas were initially exposed in Beweis des Jordanschen Satzes für N Dimensionen (1912) ("Proof of Jordan's theorem for N dimensions").
He was involved in an eventually demeaning controversy with David Hilbert.
He was member of the Significs group, containing others with a generally neo-Kantian philosophy. It formed part of the early history of semiotic study, around Victoria, Lady Welby.