504:"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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635:: "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."
1215:“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)
573:"...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.)
500:"... 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).
42:
399:. 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.
511:
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
496:
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:
495:
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
606:
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
565:
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
614:: "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.
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627:
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
676:, 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).
1402:
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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321:. 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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538:. Brouwer was accused of being a Nazi collaborator, for which there is no evidence. He retained his Jewish assistant
554:, 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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461:. It is sometimes (simplistically) characterized by saying that its adherents do not admit the
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375:. In addition to his mathematical work, Brouwer also published the short philosophical tract
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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.
1185:"...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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85:
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Brouwer’s Intuitionism: Mathematics in the Being Mode of Existence
433:, a philosophy of mathematics that challenged the then-prevailing
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Mystic, Geometer, and Intuitionist: The Life of L. E. J. Brouwer.
1285:"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
603:
pbk. The original papers are prefaced with valuable commentary.
546:, 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
233:
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Members of the Royal Netherlands Academy of Arts and Sciences
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367:. Brouwer's ideas were subsequently taken up by his student
1409:, North-Holland Publishing Company, Amsterdam Netherlands,
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and Hilbert removed him from the editorial board of
1428:, Amsterdam: Elsevier Science and Technology, 2004,
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L. E. J. Brouwer (trans. by Arnold Dresden) (1913).
1111:. 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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561:. Dutch mathematician and historian of mathematics
1204:Mathematics and the roots of postmodernist thought
344:school of mathematics which argues that math is a
1419:Chapter III: A Critique of Mathematical Reasoning
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453:(cf. Kleene (1952), p. 46–59). A variety of
297:(27 February 1881 – 2 December 1966) was a Dutch
1508:
1076:. Royal Netherlands Academy of Arts and Sciences
650:1928. "The structure of the continuum," 1186-96.
487:, which has been described by the mathematician
395:, the topological invariance of degree, and the
672:Brouwer, L. E. J., "Life, Art, and Mysticism,"
1426:Mathematics and the Divine: A Historical Study
593:A Source Book in Mathematical Logic, 1879-1931
416:Royal Netherlands Academy of Arts and Sciences
1632:Members of the American Philosophical Society
1627:Academic staff of the University of Amsterdam
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534:after Brouwer objected to contributions from
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569:About his last years, Davis (2002) remarks:
1582:Members of the Prussian Academy of Sciences
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624:: "The foundations of mathematics," 464-80
591:, 1967 3rd printing 1976 with corrections,
1382:London: Springer (based on previous work).
896:"Brouwer: The Genesis of his Intuitionism"
874:
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595:. Harvard University Press, Cambridge MA,
332:Brouwer also became a major figure in the
40:
1421:, §13 "Intuitionism" and §14 "Formalism".
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472:. It formed part of the early history of
126:Brouwer–Heyting–Kolmogorov interpretation
831:"Luitzen Egbertus Jan Brouwer 1881–1966"
738:. The words in isolation are pronounced
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142:Tietze-Urysohn-Brouwer extension theorem
1607:Road incident deaths in the Netherlands
944:MacTutor History of Mathematics Archive
926:
867:
735:[ˈlœytsə(n)ɛɣˈbɛrtəˈɕɑmˈbrʌuər]
14:
1532:20th-century Dutch non-fiction writers
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990:Philosophical Theories of Probability.
457:, intuitionism is a philosophy of the
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1562:Foreign members of the Royal Society
1443:, Published in: Sriraman, B. (ed)
1074:"Luitzen E.J. Brouwer (1881 - 1966)"
1016:Routledge Encyclopedia of Philosophy
441:and his collaborators, who included
359:, in which Brouwer sparred with his
1501:Stanford Encyclopedia of Philosophy
1035:Stanford Encyclopedia of Philosophy
975:Stanford Encyclopedia of Philosophy
418:. He was an Invited Speaker of the
397:topological invariance of dimension
327:topological invariance of dimension
200:Foreign Member of the Royal Society
24:
1477:Works by or about L. E. J. Brouwer
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954:
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674:Notre Dame Journal of Formal Logic
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1527:20th-century Dutch mathematicians
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963:
669:, Amsterdam: North-Holland, 1976.
662:, Amsterdam: North-Holland, 1975.
130:Jordan-Brouwer separation theorem
1471:L. E. J. Brouwer (mathematician)
1464:
768:
683:, Amsterdam: North-Holland, 1990
404:simplicial approximation theorem
240:Over de grondslagen der wiskunde
146:Simplicial approximation theorem
27:Dutch mathematician and logician
1537:20th-century Dutch philosophers
1453:10.1007/978-3-030-19071-2_103-1
1407:Introduction to Metamathematics
1338:10.1090/S0002-9904-1977-14185-2
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1290:. American Mathematical Society
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563:Bartel Leendert van der Waerden
1622:University of Amsterdam alumni
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966:"Luitzen Egbertus Jan Brouwer"
887:
644:, 2 vols. Oxford Univ. Press.
640:Ewald, William B., ed., 1996.
424:American Philosophical Society
154:Degree of a continuous mapping
13:
1:
1096:"Die mögliche Mächtigkeiten."
1052:. Springer. 4 December 2012.
883:Mathematics Genealogy Project
809:
476:—the study of symbols—around
371:and Hilbert's former student
1495:Luitzen Egbertus Jan Brouwer
1147:"Intuitionism and Formalism"
1029:Luitzen Egbertus Jan Brouwer
762:, respectively. The surname
730:Luitzen Egbertus Jan Brouwer
468:Brouwer was a member of the
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53:Luitzen Egbertus Jan Brouwer
18:Luitzen Egbertus Jan Brouwer
7:
1602:Philosophers of mathematics
728:The Dutch pronunciation of
711:Constructivist epistemology
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357:Brouwer–Hilbert controversy
355:. This position led to the
122:Brouwer fixed-point theorem
118:Brouwer–Hilbert controversy
10:
1648:
1439:Pambuccian, Victor, 2022,
1187:Mathematics and the Divine
1107:Brouwer, L. E. J. (1912).
459:foundations of mathematics
1592:Scientists from Rotterdam
1489:written by L.E.J. Brouwer
1248:Times Literary Supplement
518:, at that time a leading
512:over editorial policy at
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1424:Koetsier, Teun, Editor,
1394:, W. W. Norton, London,
1245:Letters: L.E.J. Brouwer,
1010:Van Atten, Mark (2016),
992:Routledge. Milton Park.
988:Gillies, Donald. (2012)
949:University of St Andrews
894:van DALEN, Dirk (1978).
716:
667:Collected Works, Vol. II
455:constructive mathematics
402:Brouwer also proved the
377:Life, Art, and Mysticism
189:Hendrik Albertus Brouwer
162:Indecomposable continuum
138:Phragmen–Brouwer theorem
1487:Life, Art and Mysticism
679:W. P. van Stigt, 1990,
660:Collected Works, Vol. I
485:Life, Art and Mysticism
227:University of Amsterdam
108:University of Amsterdam
1577:Mathematical logicians
1542:20th-century essayists
1366:The Dawning Revolution
1261:"Dostoevsky's beliefs"
850:10.1098/rsbm.1969.0002
681:Brouwer's Intuitionism
583:In English translation
544:Compositio Mathematica
463:law of excluded middle
406:in the foundations of
351:rather than a type of
283:
1597:Philosophers of logic
1572:Mathematical analysts
1325:Bull. Amer. Math. Soc
1250:19 November 2021 p.6.
1151:Bull. Amer. Math. Soc
532:Mathematische Annalen
515:Mathematische Annalen
281:
1473:at Wikimedia Commons
1417:. Cf. in particular
1392:The Engines of Logic
1373:Hope and Disillusion
1361:Oxford Univ. Press.
1126:search.amphilsoc.org
1122:"APS Member History"
935:Robertson, Edmund F.
741:[ˈlœytsə(n)]
526:, Brouwer espoused
478:Victoria, Lady Welby
412:simplicial complexes
387:Brouwer was born to
287:Luitzen Egbertus Jan
166:Invariance of domain
134:Kleene–Brouwer order
1225:Abraham A. Fraenkel
933:O'Connor, John J.;
747:[ɛɣˈbɛrtəs]
665:Brouwer, L. E. J.,
658:Brouwer, L. E. J.,
589:Jean van Heijenoort
550:, who had survived
493:Arthur Schopenhauer
393:fixed point theorem
323:fixed-point theorem
1557:Dutch male writers
1447:. Springer, Cham.
1318:ed. by A. Heyting"
1094:Brouwer, L. E. J.
939:"L. E. J. Brouwer"
701:George F. C. Griss
528:Germanic Aryanness
408:algebraic topology
284:
175:hairy ball theorem
1469:Media related to
1229:‘Hitler’s Math,’
1012:"Brouwer, L.E.J."
964:Atten, Mark van.
759:[ˈbrʌuər]
447:Wilhelm Ackermann
276:
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263:Doctoral students
257:Diederik Korteweg
207:Scientific career
158:Indecomposability
16:(Redirected from
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1481:Internet Archive
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1371:2005. Volume 2:
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389:Dutch Protestant
319:complex analysis
252:Doctoral advisor
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1567:Intuitionism
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1388:Martin Davis
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489:Martin Davis
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443:Paul Bernays
431:intuitionism
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373:Hermann Weyl
338:intuitionism
331:
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223:Institutions
206:
179:Intuitionism
80:(1966-12-02)
1617:Topologists
1522:1966 deaths
1517:1881 births
1310:Kreisel, G.
1294:13 November
860:10077/30385
823:Kreisel, G.
803:in English.
303:philosopher
217:Mathematics
94:Nationality
1511:Categories
1270:2023-11-21
1131:2023-04-12
900:Dialectica
810:References
548:Daniel Kan
508:" (ibid).
363:colleague
334:philosophy
311:set theory
59:1881-02-27
1498:entry in
1331:: 86–93.
1314:"Review:
1032:entry in
912:0012-2017
843:: 39–68.
474:semiotics
435:formalism
426:in 1943.
383:Biography
361:formalist
349:construct
346:cognitive
191:(brother)
185:Relatives
67:Overschie
1390:, 2000.
1312:(1977).
1200:a priori
1000:. p. 53.
920:42970321
829:(1969).
690:See also
536:Ostjuden
379:(1905).
325:and the
307:topology
173:Proving
86:Blaricum
1479:at the
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1080:21 July
972:(ed.).
881:at the
764:Brouwer
628:middle.
295:Brouwer
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245:(1907)
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234:Thesis
213:Fields
196:Awards
170:Spread
1321:(PDF)
1288:(PDF)
968:. In
916:JSTOR
717:Notes
98:Dutch
1430:ISBN
1411:ISBN
1396:ISBN
1296:2015
1082:2015
1054:ISBN
994:ISBN
908:ISSN
798:BROW
756:and
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340:, a
317:and
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75:Died
49:Born
1449:doi
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