493:"After completing his dissertation, Brouwer made a conscious decision to temporarily keep his contentious ideas under wraps and to concentrate on demonstrating his mathematical prowess" (Davis (2000), p. 95); by 1910 he had published a number of important papers, in particular the Fixed Point Theorem. Hilbert—the formalist with whom the intuitionist Brouwer would ultimately spend years in conflict—admired the young man and helped him receive a regular academic appointment (1912) at the University of Amsterdam (Davis, p. 96). It was then that "Brouwer felt free to return to his revolutionary project which he was now calling
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624:: "Comments on Hilbert's second lecture on the foundations of mathematics," 480-484. In 1920 Weyl, Hilbert's prize pupil, sided with Brouwer against Hilbert. But in this address Weyl "while defending Brouwer against some of Hilbert's criticisms...attempts to bring out the significance of Hilbert's approach to the problems of the foundations of mathematics."
1204:“Brouwer's debt to Schopenhauer is fully manifest. For both, Will is prior to Intellect." . (Mark van Atten and Robert Tragesser, “Mysticism and mathematics: Brouwer, Gödel, and the common core thesis,” Published in W. Deppert and M. Rahnfeld (eds.), Klarheit in Religionsdingen, Leipzig: Leipziger Universitätsverlag 2003, pp.145–160)
562:"...he felt more and more isolated, and spent his last years under the spell of 'totally unfounded financial worries and a paranoid fear of bankruptcy, persecution and illness.' He was killed in 1966 at the age of 85, struck by a vehicle while crossing the street in front of his house." (Davis, p. 100 quoting van Stigt. p. 110.)
489:"... Brouwer, in a paper entitled 'The untrustworthiness of the principles of logic', challenged the belief that the rules of the classical logic, which have come down to us essentially from Aristotle (384--322 B.C.) have an absolute validity, independent of the subject matter to which they are applied" (Kleene (1952), p. 46).
31:
388:. Among mathematicians generally, the best known is the first one, usually referred to now as the Brouwer fixed point theorem. It is a corollary to the second, concerning the topological invariance of degree, which is the best known among algebraic topologists. The third theorem is perhaps the hardest.
500:
He was combative as a young man. According to Mark van Atten, this pugnacity reflected his combination of independence, brilliance, high moral standards and extreme sensitivity to issues of justice. He was involved in a very public and eventually demeaning controversy with
Hilbert in the late 1920s
485:
thesis advisor refused to accept his
Chapter II "as it stands, ... all interwoven with some kind of pessimism and mystical attitude to life which is not mathematics, nor has anything to do with the foundations of mathematics" (Davis, p. 94 quoting van Stigt, p. 41). Nevertheless, in 1908:
484:
had a formative influence on
Brouwer, not least because he insisted that all concepts be fundamentally based on sense intuitions. Brouwer then "embarked on a self-righteous campaign to reconstruct mathematical practice from the ground up so as to satisfy his philosophical convictions"; indeed his
595:
1923. L. E. J. Brouwer: "On the significance of the principle of excluded middle in mathematics, especially in function theory." With two
Addenda and corrigenda, 334-45. Brouwer gives brief synopsis of his belief that the law of excluded middle cannot be "applied without reservation even in the
554:
attended lectures given by
Brouwer in later years, and commented: "Even though his most important research contributions were in topology, Brouwer never gave courses in topology, but always on — and only on — the foundations of his intuitionism. It seemed that he was no longer convinced of his
603:: "On the principle of excluded middle", pp. 414–437. Kolmogorov supports most of Brouwer's results but disputes a few; he discusses the ramifications of intuitionism with respect to "transfinite judgements", e.g. transfinite induction.
1110:
616:
1927. L. E. J. Brouwer: "Intuitionistic reflections on formalism," 490-92. Brouwer lists four topics on which intuitionism and formalism might "enter into a dialogue." Three of the topics involve the law of excluded
665:, vol. 37 (1996), pp. 389–429. Translated by W. P. van Stigt with an introduction by the translator, pp. 381–87. Davis quotes from this work, "a short book... drenched in romantic pessimism" (p. 94).
1391:
pbk. Cf. Chapter Five: "Hilbert to the Rescue" wherein Davis discusses
Brouwer and his relationship with Hilbert and Weyl with brief biographical information of Brouwer. Davis's references include:
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results in topology because they were not correct from the point of view of intuitionism, and he judged everything he had done before, his greatest output, false according to his philosophy."
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310:. Regarded as one of the greatest mathematicians of the 20th century, he is known as one of the founders of modern topology, particularly for establishing his
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1927. L. E. J. Brouwer: "On the domains of definition of functions". Brouwer's intuitionistic treatment of the continuum, with an extended commentary.
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in particular. The original meaning of his intuitionism probably cannot be completely disentangled from the intellectual milieu of that group.
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parents. Early in his career, Brouwer proved a number of theorems in the emerging field of topology. The most important were his
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In later years, he became relatively isolated; the development of intuitionism at its source was taken up by his student
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527:. Brouwer was accused of being a Nazi collaborator, for which there is no evidence. He retained his Jewish assistant
543:, as his assistant in 1948. However, Brouwer did encourage his students to sign a loyalty oath to the Nazis in 1943.
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as a general axiom in mathematical reasoning, although it may be proven as a theorem in some special cases.
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in the 30s, refused the request of a Nazi to remove Jewish mathematicians from the board of his journal
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Brouwer wrote that "the original interpretation of the continuum of Kant and
Schopenhauer as pure
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mathematics of infinite systems" and gives two examples of failures to illustrate his assertion.
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L. E. J. Brouwer: Topologist, Intuitionist, Philosopher. How
Mathematics is Rooted in Life.
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L.E.J. Brouwer – Topologist, Intuitionist, Philosopher: How
Mathematics is Rooted in Life
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L. E. J. Brouwer collected works, Volume I, Philosophy and foundations of mathematics
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In 1905, at the age of 24, Brouwer expressed his philosophy of life in a short tract
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1952. "Historical background, principles, and methods of intuitionism," 1197-1207.
1174:"...Brouwer and Schopenhauer are in many respects two of a kind." Teun Koetsier,
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Brouwer (right) at the
International Mathematical Congress, Zurich 1932
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From Kant to Hilbert: A Source Book in the Foundations of Mathematics
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in 1908 at Rome and in 1912 at Cambridge, UK. He was elected to the
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74:
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Brouwer’s Intuitionism: Mathematics in the Being Mode of Existence
422:, a philosophy of mathematics that challenged the then-prevailing
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Mystic, Geometer, and Intuitionist: The Life of L. E. J. Brouwer.
1274:"Interview with B L van der Waerden, reprinted in AMS March 1997"
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intuition can in essence be upheld." (Quoted in Vladimir Tasić's
592:
pbk. The original papers are prefaced with valuable commentary.
535:, and hid Jews in his home during the war. Likewise he took on
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as "drenched in romantic pessimism" (Davis (2002), p. 94).
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Handbook of the History and Philosophy of Mathematical Practice
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Stephen Kleene, 1952 with corrections 1971, 10th reprint 1991,
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Sur la notion de «Classe» de transformations d'une multiplicité
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Members of the Royal Netherlands Academy of Arts and Sciences
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356:. Brouwer's ideas were subsequently taken up by his student
1398:, North-Holland Publishing Company, Amsterdam Netherlands,
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and Hilbert removed him from the editorial board of
1417:, Amsterdam: Elsevier Science and Technology, 2004,
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L. E. J. Brouwer (trans. by Arnold Dresden) (1913).
1100:. Proc. 5th Intern. Math. Congr. Cambridge, 2, 9–10.
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Biographical Memoirs of Fellows of the Royal Society
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1928. "Mathematics, science, and language," 1170-85.
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Atti IV Congr. Intern. Mat. Roma 3 (1908): 569–571.
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550:. Dutch mathematician and historian of mathematics
1193:Mathematics and the roots of postmodernist thought
333:school of mathematics which argues that math is a
1408:Chapter III: A Critique of Mathematical Reasoning
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442:(cf. Kleene (1952), p. 46–59). A variety of
286:(27 February 1881 – 2 December 1966) was a Dutch
1497:
1065:. Royal Netherlands Academy of Arts and Sciences
639:1928. "The structure of the continuum," 1186-96.
476:, which has been described by the mathematician
384:, the topological invariance of degree, and the
661:Brouwer, L. E. J., "Life, Art, and Mysticism,"
1415:Mathematics and the Divine: A Historical Study
582:A Source Book in Mathematical Logic, 1879-1931
405:Royal Netherlands Academy of Arts and Sciences
1621:Members of the American Philosophical Society
1616:Academic staff of the University of Amsterdam
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523:after Brouwer objected to contributions from
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558:About his last years, Davis (2002) remarks:
1571:Members of the Prussian Academy of Sciences
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773:
613:: "The foundations of mathematics," 464-80
580:, 1967 3rd printing 1976 with corrections,
1371:London: Springer (based on previous work).
885:"Brouwer: The Genesis of his Intuitionism"
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861:
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584:. Harvard University Press, Cambridge MA,
321:Brouwer also became a major figure in the
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1410:, §13 "Intuitionism" and §14 "Formalism".
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461:. It formed part of the early history of
115:Brouwer–Heyting–Kolmogorov interpretation
820:"Luitzen Egbertus Jan Brouwer 1881–1966"
727:. The words in isolation are pronounced
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131:Tietze-Urysohn-Brouwer extension theorem
1596:Road incident deaths in the Netherlands
933:MacTutor History of Mathematics Archive
915:
856:
724:[ˈlœytsə(n)ɛɣˈbɛrtəˈɕɑmˈbrʌuər]
1521:20th-century Dutch non-fiction writers
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979:Philosophical Theories of Probability.
446:, intuitionism is a philosophy of the
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1551:Foreign members of the Royal Society
1432:, Published in: Sriraman, B. (ed)
1063:"Luitzen E.J. Brouwer (1881 - 1966)"
1005:Routledge Encyclopedia of Philosophy
430:and his collaborators, who included
348:, in which Brouwer sparred with his
1490:Stanford Encyclopedia of Philosophy
1024:Stanford Encyclopedia of Philosophy
964:Stanford Encyclopedia of Philosophy
407:. He was an Invited Speaker of the
386:topological invariance of dimension
316:topological invariance of dimension
189:Foreign Member of the Royal Society
13:
1466:Works by or about L. E. J. Brouwer
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663:Notre Dame Journal of Formal Logic
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1516:20th-century Dutch mathematicians
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952:
658:, Amsterdam: North-Holland, 1976.
651:, Amsterdam: North-Holland, 1975.
119:Jordan-Brouwer separation theorem
1460:L. E. J. Brouwer (mathematician)
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757:
672:, Amsterdam: North-Holland, 1990
393:simplicial approximation theorem
229:Over de grondslagen der wiskunde
135:Simplicial approximation theorem
16:Dutch mathematician and logician
1526:20th-century Dutch philosophers
1442:10.1007/978-3-030-19071-2_103-1
1396:Introduction to Metamathematics
1327:10.1090/S0002-9904-1977-14185-2
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1279:. American Mathematical Society
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1611:University of Amsterdam alumni
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955:"Luitzen Egbertus Jan Brouwer"
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633:, 2 vols. Oxford Univ. Press.
629:Ewald, William B., ed., 1996.
413:American Philosophical Society
143:Degree of a continuous mapping
1:
1085:"Die mögliche Mächtigkeiten."
1041:. Springer. 4 December 2012.
872:Mathematics Genealogy Project
798:
465:—the study of symbols—around
360:and Hilbert's former student
1484:Luitzen Egbertus Jan Brouwer
1136:"Intuitionism and Formalism"
1018:Luitzen Egbertus Jan Brouwer
751:, respectively. The surname
719:Luitzen Egbertus Jan Brouwer
457:Brouwer was a member of the
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42:Luitzen Egbertus Jan Brouwer
7:
1591:Philosophers of mathematics
717:The Dutch pronunciation of
700:Constructivist epistemology
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346:Brouwer–Hilbert controversy
344:. This position led to the
111:Brouwer fixed-point theorem
107:Brouwer–Hilbert controversy
10:
1637:
1428:Pambuccian, Victor, 2022,
1176:Mathematics and the Divine
1096:Brouwer, L. E. J. (1912).
448:foundations of mathematics
1581:Scientists from Rotterdam
1478:written by L.E.J. Brouwer
1237:Times Literary Supplement
507:, at that time a leading
501:over editorial policy at
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1413:Koetsier, Teun, Editor,
1383:, W. W. Norton, London,
1234:Letters: L.E.J. Brouwer,
999:Van Atten, Mark (2016),
981:Routledge. Milton Park.
977:Gillies, Donald. (2012)
938:University of St Andrews
883:van DALEN, Dirk (1978).
705:
656:Collected Works, Vol. II
444:constructive mathematics
391:Brouwer also proved the
366:Life, Art, and Mysticism
178:Hendrik Albertus Brouwer
151:Indecomposable continuum
127:Phragmen–Brouwer theorem
1476:Life, Art and Mysticism
668:W. P. van Stigt, 1990,
649:Collected Works, Vol. I
474:Life, Art and Mysticism
216:University of Amsterdam
97:University of Amsterdam
1566:Mathematical logicians
1531:20th-century essayists
1355:The Dawning Revolution
1250:"Dostoevsky's beliefs"
839:10.1098/rsbm.1969.0002
670:Brouwer's Intuitionism
572:In English translation
533:Compositio Mathematica
452:law of excluded middle
395:in the foundations of
340:rather than a type of
272:
1586:Philosophers of logic
1561:Mathematical analysts
1314:Bull. Amer. Math. Soc
1239:19 November 2021 p.6.
1140:Bull. Amer. Math. Soc
521:Mathematische Annalen
504:Mathematische Annalen
270:
1462:at Wikimedia Commons
1406:. Cf. in particular
1381:The Engines of Logic
1362:Hope and Disillusion
1350:Oxford Univ. Press.
1115:search.amphilsoc.org
1111:"APS Member History"
924:Robertson, Edmund F.
730:[ˈlœytsə(n)]
515:, Brouwer espoused
467:Victoria, Lady Welby
401:simplicial complexes
376:Brouwer was born to
276:Luitzen Egbertus Jan
155:Invariance of domain
123:Kleene–Brouwer order
1214:Abraham A. Fraenkel
922:O'Connor, John J.;
736:[ɛɣˈbɛrtəs]
654:Brouwer, L. E. J.,
647:Brouwer, L. E. J.,
578:Jean van Heijenoort
539:, who had survived
482:Arthur Schopenhauer
382:fixed point theorem
312:fixed-point theorem
1546:Dutch male writers
1436:. Springer, Cham.
1307:ed. by A. Heyting"
1083:Brouwer, L. E. J.
928:"L. E. J. Brouwer"
690:George F. C. Griss
517:Germanic Aryanness
397:algebraic topology
273:
164:hairy ball theorem
1458:Media related to
1218:‘Hitler’s Math,’
1001:"Brouwer, L.E.J."
953:Atten, Mark van.
748:[ˈbrʌuər]
436:Wilhelm Ackermann
265:
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252:Doctoral students
246:Diederik Korteweg
196:Scientific career
147:Indecomposability
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1470:Internet Archive
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378:Dutch Protestant
308:complex analysis
241:Doctoral advisor
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52:27 February 1881
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77:, Netherlands
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1556:Intuitionism
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1395:
1380:
1377:Martin Davis
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1281:. Retrieved
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1257:. Retrieved
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622:Hermann Weyl
581:
567:Bibliography
557:
545:
502:
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495:intuitionism
494:
492:
478:Martin Davis
473:
471:
456:
432:Paul Bernays
420:intuitionism
417:
390:
375:
365:
362:Hermann Weyl
327:intuitionism
320:
283:
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212:Institutions
195:
168:Intuitionism
69:(1966-12-02)
1606:Topologists
1511:1966 deaths
1506:1881 births
1299:Kreisel, G.
1283:13 November
849:10077/30385
812:Kreisel, G.
792:in English.
292:philosopher
206:Mathematics
83:Nationality
1500:Categories
1259:2023-11-21
1120:2023-04-12
889:Dialectica
799:References
537:Daniel Kan
497:" (ibid).
352:colleague
323:philosophy
300:set theory
48:1881-02-27
1487:entry in
1320:: 86–93.
1303:"Review:
1021:entry in
901:0012-2017
832:: 39–68.
463:semiotics
424:formalism
415:in 1943.
372:Biography
350:formalist
338:construct
335:cognitive
180:(brother)
174:Relatives
56:Overschie
1379:, 2000.
1301:(1977).
1189:a priori
989:. p. 53.
909:42970321
818:(1969).
679:See also
525:Ostjuden
368:(1905).
314:and the
296:topology
162:Proving
75:Blaricum
1468:at the
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1069:21 July
961:(ed.).
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617:middle.
284:Brouwer
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185:Awards
159:Spread
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1277:(PDF)
957:. In
905:JSTOR
706:Notes
87:Dutch
1419:ISBN
1400:ISBN
1385:ISBN
1285:2015
1071:2015
1043:ISBN
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745:and
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