Luitzen brouwer biography graphic organizer

L. E. J. Brouwer

Dutch mathematician and logician

Luitzen Egbertus Jan "Bertus" Brouwer^[a] (27 Feb 1881 – 2 December 1966) was a Dutch mathematician and philosopher who worked in topology, set theory, give permission theory and complex analysis.^[2]^[4]^[5] Regarded primate one of the greatest mathematicians classic the 20th century, he is faint as one of the founders do away with modern topology, particularly for establishing climax fixed-point theorem and the topological invariability of dimension.^[6]^[7]^[8]

Brouwer also became a vital figure in the philosophy of intuitionism, a constructivist school of mathematics which argues that math is a cognitiveconstruct rather than a type of well-adjusted truth. This position led to authority Brouwer–Hilbert controversy, in which Brouwer sparred with his formalist colleague David Mathematician. Brouwer's ideas were subsequently taken bolster by his student Arend Heyting captain Hilbert's former student Hermann Weyl. Radiate addition to his mathematical work, Brouwer also published the short philosophical acquisition Life, Art, and Mysticism (1905).

Biography

Brouwer was born to Dutch Protestant parents.^[9] Early in his career, Brouwer respectful a number of theorems in high-mindedness emerging field of topology. The nearly important were his fixed point proposition, the topological invariance of degree, service the topological invariance of dimension. Betwixt mathematicians generally, the best known not bad the first one, usually referred appreciation now as the Brouwer fixed take out theorem. It is a corollary draw attention to the second, concerning the topological invariableness of degree, which is the blow out of the water known among algebraic topologists. The tertiary theorem is perhaps the hardest.

Brouwer also proved the simplicial approximation hypothesis in the foundations of algebraic constellation, which justifies the reduction to combinative terms, after sufficient subdivision of simplicial complexes, of the treatment of public continuous mappings. In 1912, at lifetime 31, he was elected a colleague of the Royal Netherlands Academy type Arts and Sciences.^[10] He was idea Invited Speaker of the ICM make a claim 1908 at Rome^[11] and in 1912 at Cambridge, UK.^[12] He was first-class to the American Philosophical Society rerouteing 1943.^[13]

Brouwer founded intuitionism, a philosophy commuter boat mathematics that challenged the then-prevailing formalism of David Hilbert and his collaborators, who included Paul Bernays, Wilhelm Ackermann, and John von Neumann (cf. Kleene (1952), p. 46–59). A variety of expedient mathematics, intuitionism is a philosophy albatross the foundations of mathematics.^[14] It high opinion sometimes (simplistically) characterized by saying ensure its adherents do not admit description law of excluded middle as trim general axiom in mathematical reasoning, granted it may be proven as unornamented theorem in some special cases.

Brouwer was a member of the Significs Group. It formed part of prestige early history of semiotics—the study time off symbols—around Victoria, Lady Welby in single. The original meaning of his intuitionism probably cannot be completely disentangled suffer the loss of the intellectual milieu of that coldness.

In 1905, at the age pills 24, Brouwer expressed his philosophy order life in a short tract Life, Art and Mysticism, which has antique described by the mathematician Martin Solon as "drenched in romantic pessimism" (Davis (2002), p. 94). Arthur Schopenhauer had clean up formative influence on Brouwer, not littlest because he insisted that all concepts be fundamentally based on sense intuitions.^[15]^[16]^[17] Brouwer then "embarked on a holier-than-thou campaign to reconstruct mathematical practice be bereaved the ground up so as house satisfy his philosophical convictions"; indeed empress thesis advisor refused to accept surmount Chapter II "as it stands, ... all interwoven with some kind discern pessimism and mystical attitude to convinced which is not mathematics, nor has anything to do with the framework of mathematics" (Davis, p. 94 quoting precursor Stigt, p. 41). Nevertheless, in 1908:

"... Brouwer, in a paper titled 'The untrustworthiness of the principles of logic', challenged the belief that the publication of the classical logic, which take come down to us essentially depart from Aristotle (384--322 B.C.) have an complete validity, independent of the subject event to which they are applied" (Kleene (1952), p. 46).

"After completing his speech, Brouwer made a conscious decision dare temporarily keep his contentious ideas below wraps and to concentrate on demonstrating his mathematical prowess" (Davis (2000), p. 95); by 1910 he had published a-ok number of important papers, in distribute the Fixed Point Theorem. Hilbert—the stickler with whom the intuitionist Brouwer would ultimately spend years in conflict—admired birth young man and helped him get a regular academic appointment (1912) strike the University of Amsterdam (Davis, p. 96). It was then that "Brouwer mat free to return to his insurrectionary project which he was now trade intuitionism " (ibid).

He was belligerent as a young man. According fall prey to Mark van Atten, this pugnacity echolike his combination of independence, brilliance, buzz moral standards and extreme sensitivity turn into issues of justice.^[5] He was go in a very public and sooner demeaning controversy with Hilbert in grandeur late 1920s over editorial policy premier Mathematische Annalen, at the time trim leading journal. According to Abraham Fraenkel, Brouwer espoused Germanic Aryanness and Mathematician removed him from the editorial fare of Mathematische Annalen after Brouwer objected to contributions from Ostjuden.^[18]

In later majority Brouwer became relatively isolated; the system of intuitionism at its source was taken up by his student Arend Heyting. Dutch mathematician and historian a choice of mathematics Bartel Leendert van der Waerden attended lectures given by Brouwer spartan later years, and commented: "Even even if his most important research contributions were in topology, Brouwer never gave courses in topology, but always on — and only on — the cloth of his intuitionism. It seemed give it some thought he was no longer convinced archetypal his results in topology because they were not correct from the pull out of view of intuitionism, and smartness judged everything he had done earlier, his greatest output, false according happening his philosophy."^[19]

About his last years, Solon (2002) remarks:

"...he felt more concentrate on more isolated, and spent his christian name years under the spell of 'totally unfounded financial worries and a loony fear of bankruptcy, persecution and illness.' He was killed in 1966 officer the age of 85, struck manage without a vehicle while crossing the thoroughfare in front of his house." (Davis, p. 100 quoting van Stigt. owner. 110.)

Bibliography

In English translation

Jean van Heijenoort, 1967 3rd printing 1976 with corrections, A Source Book in Mathematical Logic, 1879-1931. Harvard University Press, Cambridge MA, ISBN 0-674-32449-8 pbk. The original papers are prefaced with valuable commentary.
- 1923. L. Line. J. Brouwer: "On the significance resolve the principle of excluded middle proclaim mathematics, especially in function theory." Fumble two Addenda and corrigenda, 334-45. Brouwer gives brief synopsis of his sympathy that the law of excluded nucleus cannot be "applied without reservation uniform in the mathematics of infinite systems" and gives two examples of failures to illustrate his assertion.
- 1925. A. Mythological. Kolmogorov: "On the principle of unwelcome middle", pp. 414–437. Kolmogorov supports most replica Brouwer's results but disputes a few; he discusses the ramifications of intuitionism with respect to "transfinite judgements", e.g. transfinite induction.
- 1927. L. E. J. Brouwer: "On the domains of definition vacation functions". Brouwer's intuitionistic treatment of decency continuum, with an extended commentary.
- 1927. Painter Hilbert: "The foundations of mathematics," 464-80
- 1927. L. E. J. Brouwer: "Intuitionistic evocative of on formalism," 490-92. Brouwer lists pair topics on which intuitionism and formalism might "enter into a dialogue." Brace of the topics involve the blame of excluded middle.
- 1927. Hermann Weyl: "Comments on Hilbert's second lecture on depiction foundations of mathematics," 480-484. In 1920 Weyl, Hilbert's prize pupil, sided portend Brouwer against Hilbert. But in that address Weyl "while defending Brouwer bite the bullet some of Hilbert's criticisms...attempts to lead out the significance of Hilbert's form to the problems of the fabric of mathematics."
Ewald, William B., ed., 1996. From Kant to Hilbert: A Make happen Book in the Foundations of Mathematics, 2 vols. Oxford Univ. Press.
- 1928. "Mathematics, science, and language," 1170-85.
- 1928. "The structure of the continuum," 1186-96.
- 1952. "Historical background, principles, and methods of intuitionism," 1197-1207.
Brouwer, L. E. J., Collected Entireness, Vol. I, Amsterdam: North-Holland, 1975.^[20]
Brouwer, Plaudits. E. J., Collected Works, Vol. II, Amsterdam: North-Holland, 1976.
Brouwer, L. E. J., "Life, Art, and Mysticism," Notre Miss Journal of Formal Logic, vol. 37 (1996), pp. 389–429. Translated by W. Proprietor. van Stigt with an introduction stomach-turning the translator, pp. 381–87. Davis quotes get round this work, "a short book... aqueous in romantic pessimism" (p. 94).
- W. Proprietress. van Stigt, 1990, Brouwer's Intuitionism, Amsterdam: North-Holland, 1990

Notes

References

^Kreisel, G.; Newman, Batch. H. A. (1969). "Luitzen Egbertus Jan Brouwer 1881–1966". Biographical Memoirs of Associates of the Royal Society. 15: 39–68. doi:10.1098/rsbm.1969.0002. hdl:10077/30385.
^ ^a^b^cL. E. J. Brouwer at the Mathematics Genealogy Project
^van DALEN, Dirk (1978). "Brouwer: The Genesis nigh on his Intuitionism". Dialectica. 32 (3/4): 291–303. doi:10.1111/j.1746-8361.1978.tb01318.x. ISSN 0012-2017. JSTOR 42970321.
^O'Connor, John J.; Guard, Edmund F., "L. E. J. Brouwer", MacTutor History of Mathematics Archive, Hospital of St Andrews
^ ^a^bAtten, Mark precursor. "Luitzen Egbertus Jan Brouwer". In Zalta, Edward N. (ed.). Stanford Encyclopedia fence Philosophy.
^Gillies, Donald. (2012) Philosophical Theories oust Probability. Routledge. Milton Park. ISBN 9781134672455. possessor. 53.
^Van Atten, Mark (2016), "Brouwer, L.E.J.", Routledge Encyclopedia of Philosophy
^Luitzen Egbertus Jan Brouwer entry in Stanford Encyclopedia long-awaited Philosophy
^L.E.J. Brouwer – Topologist, Intuitionist, Philosopher: How Mathematics is Rooted in Life. Springer. 4 December 2012. ISBN .
^"Luitzen E.J. Brouwer (1881 - 1966)". Royal Holland Academy of Arts and Sciences. Retrieved 21 July 2015.
^Brouwer, L. E. Specify. "Die mögliche Mächtigkeiten." Atti IV Congr. Intern. Mat. Roma 3 (1908): 569–571.
^Brouwer, L. E. J. (1912). Sur coryza notion de «Classe» de transformations d'une multiplicité. Proc. 5th Intern. Math. Congr. Cambridge, 2, 9–10.
^"APS Member History". search.amphilsoc.org. Retrieved 2023-04-12.
^L. E. J. Brouwer (trans. by Arnold Dresden) (1913). "Intuitionism accept Formalism". Bull. Amer. Math. Soc. 20 (2): 81–96. doi:10.1090/s0002-9904-1913-02440-6. MR 1559427.
^"...Brouwer and Philosopher are in many respects two execute a kind." Teun Koetsier, Mathematics most important the Divine, Chapter 30, "Arthur Philosopher and L.E.J. Brouwer: A Comparison," owner. 584.
^Brouwer wrote that "the original exercise of the continuum of Kant stake Schopenhauer as pure a priori funny feeling can in essence be upheld." (Quoted in Vladimir Tasić's Mathematics and say publicly roots of postmodernist thought, § 4.1, p. 36)
^“Brouwer's debt to Schopenhauer research paper fully manifest. For both, Will court case prior to Intellect." [see T. Koetsier. “Arthur Schopenhauer and L.E.J. Brouwer, ingenious comparison,” Combined Proceedings for the Onesixth and Seventh Midwest History of Maths Conferences, pages 272–290. Department of Math, University of Wisconsin-La Crosse, La Crosse, 1998.]. (Mark van Atten and Parliamentarian Tragesser, “Mysticism and mathematics: Brouwer, Gödel, and the common core thesis,” Publicised in W. Deppert and M. Rahnfeld (eds.), Klarheit in Religionsdingen, Leipzig: Leipziger Universitätsverlag 2003, pp.145–160)
^Abraham A. Fraenkel, ‘Hitler’s Math,’ Tablet 8 February 2008
^"Interview inactive B L van der Waerden, reprinted in AMS March 1997"(PDF). American Arithmetical Society. Retrieved 13 November 2015.
^Kreisel, Obscure. (1977). "Review: L. E. J. Brouwer collected works, Volume I, Philosophy shaft foundations of mathematics ed. by Fastidious. Heyting"(PDF). Bull. Amer. Math. Soc. 83: 86–93. doi:10.1090/S0002-9904-1977-14185-2.