# Luitzen Egbertus Jan Brouwer

# Luitzen Egbertus Jan Brouwer

**1881-1966**

**Dutch Mathematician**

Dutch mathematician L. E. J. Brouwer made two principal contributions to the study of mathematics, though one—his development of a topological principle known as Brouwer's theorem—received far more attention. In the realm of logic, he approached concepts of concern to philosophers as well as to mathematicians. His intuitionist school, though it never became highly influential, challenged the two prevailing schools of thought regarding the nature of mathematical knowledge.

The son of Egbert and Henderika Poutsma Brouwer, the future mathematician was born in Overschie, Holland, on February 27, 1881. He studied at the Haarlem Gymnasium, and in 1897 entered the University of Amsterdam, an institution with which he was to remain connected throughout his career. At the university, he first distinguished himself in 1904, when he was twenty-three years old, with his studies on the properties of four-dimensional space. Also in 1904, Brouwer married Reinharda de Holl. The couple had no children.

Showing the diversity of his interests, in 1905 Brouwer published *Leven, Kunst, en Mystiek,* in which he examined the role of individuals in society. He earned his doctorate in 1907 with a thesis "On the Foundations of Mathematics," in which he laid the groundwork for intuitionism. At that time, the philosophy of mathematics was dominated by two schools: logicism, which maintained that mathematical concepts had an existence independent of the human mind's conception of them; and formalism, which was concerned with the rules by which such concepts were to be interpreted. Brouwer's intuitionism offered a third viewpoint by maintaining that mathematical truths are a matter of common sense, apprehended *a priori *through intuition.

Though Brouwer remained committed to intuitionism, which he considered his principal achievement, the intuitionist school never gained many adherents, in his lifetime or thereafter. By contrast, his other significant contribution, in topology, was a highly influential one. Brouwer's fixed-point theorem, which he formulated in 1912, states that for any transformation affecting all points on a circle, at least one point must remain unchanged. He later extended the application of this theorem to three-dimensional objects.

Also in 1912, Brouwer became a professor of mathematics at the University of Amsterdam, after having served there for three years as an unsalaried tutor. He maintained that position until his retirement in 1951, and in the meantime earned a variety of awards and honors. The latter included election to the Royal Dutch Academy of Science (1912), the German Academy of Science (1919), the American Philosophical Society (1943), and the Royal Society of London (1948). He was also awarded a knighthood in the Order of the Dutch Lion in 1932. In 1959, Reinharda died, and Brouwer himself passed away in Blaricum, Holland, on December 2, 1966.

**JUDSON KNIGHT**

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**Luitzen Egbertus Jan Brouwer**