Brouwer, Luitzen Egbertus Jan

▪ Dutch mathematicianborn February 27, 1881, Overschie, Netherlandsdied December 2, 1966, BlaricumDutch mathematician who founded mathematical intuitionism (a doctrine that views the nature of mathematics as mental constructions governed by selfevident laws) and whose work completely transformed topology, the study of the most basic properties of geometric surfaces and configurations.Brouwer studied mathematics at the University of Amsterdam from 1897 to 1904. Even then he was interested in philosophical matters, as evidenced by his Leven, Kunst, en Mystiek (1905; “Life, Art, and Mysticism”). In his doctoral thesis, “Over de grondslagen der wiskunde” (1907; “On the Foundations of Mathematics”), Brouwer attacked the logical foundations of mathematics (mathematics, foundations of), as represented by the efforts of the German mathematician David Hilbert (Hilbert, David) and the English philosopher Bertrand Russell (Russell, Bertrand), and shaped the beginnings of the intuitionist school. The following year, in “Over de onbetrouwbaarheid der logische principes” (“On the Untrustworthiness of the Logical Principles”), he rejected as invalid the use in mathematical proofs of the principle of the excluded middle (or excluded third). According to this principle, every mathematical statement is either true or false; no other possibility is allowed. Brouwer denied that this dichotomy applied to infinite sets.Brouwer taught at the University of Amsterdam from 1909 to 1951. He did most of his important work in topology between 1909 and 1913. In connection with his studies of the work of Hilbert, he discovered the plane translation theorem, which characterizes topological mappings of the Cartesian plane, and the first of his fixedpoint theorems, which later became important in the establishment of some fundamental theorems in branches of mathematics such as differential equations (differential equation) and game theory. In 1911 he established his theorems on the invariance of the dimension of a manifold under continuous invertible transformations. In addition, he merged the methods developed by the German mathematician Georg Cantor (Cantor, Georg) with the methods of analysis situs, an early stage of topology. In view of his remarkable contributions, many mathematicians consider Brouwer the founder of topology.In 1918 he published a set theory, the following year a theory of measure, and by 1923 a theory of functions, all developed without using the principle of the excluded middle. He continued his studies until 1954, and, although he did not gain widespread acceptance for his precepts, intuitionism enjoyed a resurgence of interest after World War II, primarily because of contributions by the American mathematician Stephen Cole Kleene (Kleene, Stephen Cole).His Collected Works, in two volumes, was published in 1975–76.Additional ReadingDirk van Dalen, Mystic, Geometer, and Intuitionist: The Life of L.E.J. Brouwer (1999), discusses Brouwer's life and work.
* * *
Universalium. 2010.
Look at other dictionaries:
Brouwer , Luitzen Egbertus Jan — (1881–1966) Dutch mathematician and philosopher of mathematics Born in Overschie in the Netherlands, Brouwer took his first degree and doctorate at the University of Amsterdam, where he became successively Privatdozent and professor in the… … Scientists
Brouwer, Luitzen Egbertus Jan — ► (1881 1966) Matemático holandés. Fue uno de los fundadores de la moderna topología … Enciclopedia Universal
Luitzen Egbertus Jan Brouwer — Pour les articles homonymes, voir Brouwer. Luitzen Egbertus Jan Brouwer (1881 1966) était un mathématicien néerlandais. Biographie Il est né le 27 février 1881 à Overschie (Rotterdam), et est mort le 2 décembre 1966 à Blaricum. Il soutient son… … Wikipédia en Français
Luitzen Egbertus Jan Brouwer — Luitzen E. J. Brouwer (* 27. Februar 1881 in Overschie; † 2. Dezember 1966 in Blaricum) war ein niederländischer Mathematiker. Er schuf grundlegende topologische Methoden und Begriffe und bewies bedeutende topologische Sätze. Nach ihm ist der… … Deutsch Wikipedia
Luitzen Egbertus Jan Brouwer — [ˈlœyt.sən ɛx.ˈbɛʁ.təs jɑn ˈbʁʌu.əʁ] (February 27 1881, Overschie – December 2 1966, Blaricum), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, a graduate of the University of… … Wikipedia
Luitzen Egbertus Jan Brouwer — Este artículo o sección necesita referencias que aparezcan en una publicación acreditada, como revistas especializadas, monografías, prensa diaria o páginas de Internet fidedignas. Puedes añadirlas así o avisar … Wikipedia Español
BROUWER, Bertus (Luitzen Egbertus Jan) — (1881–1966) Mathematician and philosopher. Brouwer is considered the founder of mathematical intuitionism, which led to the rejection of parts of classical mathematics. He studied mathematics and physics at the University of Amsterdam and… … Historical Dictionary of the Netherlands
Luitzen Egbertus Jan Brouwer — Matemático holandés (1881 1966), graduado en la Universidad de Amsterdam. Sus trabajos ocuparon temas como Topología, Teoría de la Medida y Análisis Complejo. Formula el Teorema de Brouwer. Demostró la importancia de los espacios cartesianos y… … Enciclopedia Universal
Brouwer — Luitzen Egbertus Jan … Scientists
Brouwer's — Brouwer , Luitzen Egbertus Jan … Scientists