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Progress, Recognition, and Frictions

  • Dirk van Dalen

Abstract

Brouwer was extremely critical of Hilbert’s formalism, which was completely opposed to the intuitionistic philosophy of mathematics. Brouwer trod softly in his publications in order to avoid conflict. However, when Hermann Weyl joined Brouwer’s intuitionism, his ‘New crisis-paper’ the tone changed. Hilbert told Brouwer and Weyl in unmistakable terms how wrong they were. The Grundlagenstreit was born. The conflict dragged on for years.

From time to time the scientific discussion was replaced by external causes. One such was the planned publication of the Riemann memorial volume by the Mathematische Annalen. A conflict arose when the participation of French mathematicians could in this project of their arch enemy was questioned. One section of the editorial board objected to the French participation, which was advocated by Hilbert. The conflict left bad feelings.

Inspired by the contributions of Alexandrov, Menger, and Urysohn, Brouwer collected in 1925 a small group of topologists in Amsterdam, including Vietoris and Wilson. The brief concentration of topologists was later called the Dutch topological school.

Keywords

Dimension Theory Proof Theory Mathematical Community German Scientist Choice Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Alexandrov, P.S.: Die Topologie in und um Holland in den Jahren 1920–1930. Nieuw Arch. Wiskd. 17, 109–127 (1969) Google Scholar
  2. Alexandrov, P.S.: Pages from an autobiography. Russ. Math. Surv. 35, 315–358 (1980) CrossRefGoogle Scholar
  3. Belinfante, M.J.: Over oneindige reeksen. Ph.D. thesis, Amsterdam (1923) Google Scholar
  4. Bernays, P.: Über Hilbert’s Gedanken zur Grundlegung der Arithmetik. Jahresber. Dtsch. Math.-Ver. 31, 10–19 (1922) MATHGoogle Scholar
  5. Bernstein, F.: Die Mengenlehre George Cantors und der Finitismus. Jahresber. Dtsch. Math.-Ver. 28, 63–78 (1919) MATHGoogle Scholar
  6. Borwein, J.M.: Brouwer–Heyting sequences converge. Math. Intell. 20, 14–15 (1998) MATHCrossRefGoogle Scholar
  7. Brouwer, L.E.J.: Over de grondslagen der wiskunde. Ph.D. thesis, Amsterdam (1907) Google Scholar
  8. Brouwer, L.E.J.: Begründung der Mengenlehre unabhängig vom logischen Satz vom ausgeschlossenen Dritten. Zweiter Teil, Theorie der Punktmengen. Verh. K. Akad. Wet. Amst. 7, 1–33 (1919a) Google Scholar
  9. Brouwer, L.E.J.: Intuitionistische Mengenlehre. Jahresber. Dtsch. Math.-Ver. 28, 203–208 (1919h). Appeared in 1920 MATHGoogle Scholar
  10. Brouwer, L.E.J.: Intuitionistische Mengenlehre. K. Ned. Akad. Wet. Proc. Sect. Sci. 23, 949–954 (1922a) Google Scholar
  11. Brouwer, L.E.J.: Over de rol van het principium tertiï exclusi in the wiskunde, in het bijzonder in de functietheorie. Wis- Natuurkd. Tijdschr. 2, 1–7 (1923b) Google Scholar
  12. Brouwer, L.E.J.: Über die Bedeutung des Satzes vom ausgeschlossenen Dritten in der Mathematik insbesondere in der Funktionentheorie. J. Reine Angew. Math. 154, 1–8 (1923f) Google Scholar
  13. Brouwer, L.E.J.: Beweis dass jede volle Funktion gleichmässig stetig ist. K. Ned. Akad. Wet. Proc. Sect. Sci. 27, 189–193 (1924a) Google Scholar
  14. Brouwer, L.E.J.: Intuitionistische Ergänzung des Fundamentalsatzes der Algebra. K. Ned. Akad. Wet. Proc. Sect. Sci. 27, 631–634 (1924b) Google Scholar
  15. Brouwer, L.E.J.: Bewijs van de onafhankelijkheid van de onttrekkingsrelatie van de versmeltingsrelatie. K. Ned. Akad. Wet. Versl. Gewone Vergad. Afd. Natuurkd. 33, 479–480 (1924c) MATHGoogle Scholar
  16. Brouwer, L.E.J.: Bemerkungen zum Beweise der gleichmässigen Stetigkeit voller Funktionen. K. Ned. Akad. Wet. Proc. Sect. Sci. 27, 644–646 (1924d) Google Scholar
  17. Brouwer, L.E.J.: Zur Begründung der intuitionistischen Mathematik I. Math. Ann. 93, 244–257 (1925a). Corr. in Brouwer (1926a) MathSciNetMATHCrossRefGoogle Scholar
  18. Brouwer, L.E.J.: Intuitionistische Betrachtungen über den Formalismus. K. Ned. Akad. Wet. Proc. Sect. Sci. 31, 374–379 (1928b) Google Scholar
  19. Brouwer, L.E.J.: Zur Geschichtsschreibung der Dimensionstheorie. K. Ned. Akad. Wet. Proc. Sect. Sci. 31, 953–957 (1928f). Corr. in KNAW Proc. 32, p. 1022 MATHGoogle Scholar
  20. Brouwer, L.E.J.: Herinnering aan C.S. Aama van Scheltema door L.E.J. Brouwer, p. 69. Querido, Amsterdam (1929b) Google Scholar
  21. Brouwer, L.E.J.: Zum freien Werden von Mengen und Funktionen. Indag. Math. 4, 107–108 (1942a) Google Scholar
  22. Brouwer, L.E.J.: Sur la possibilité d’ordonner le continu. C. R. Math. Acad. Sci. Paris 230, 349–350 (1950) MathSciNetMATHGoogle Scholar
  23. Brouwer, L.E.J.: Historical background, principles and methods of intuitionism. South Afr. J. Sci. 49, 139–146 (1952b) MathSciNetGoogle Scholar
  24. Brouwer, L.E.J.: Point and spaces. Can. J. Math. 6, 1–17 (1954a) MathSciNetMATHCrossRefGoogle Scholar
  25. Brouwer, L.E.J.: Collected Works 2. Geometry, Analysis Topology and Mechanics. Freudenthal, H. (ed.). North-Holland, Amsterdam (1976) Google Scholar
  26. Brouwer, L.E.J.: Brouwer’s Cambridge Lectures on Intuitionism. van Dalen, D. (ed.). Cambridge University Press, Cambridge (1981) MATHGoogle Scholar
  27. Brouwer, L.E.J.: Intuitionismus. van Dalen, D. (ed.). Bibliographisches Institut Wissenschaftsverlag, Mannheim (1992) MATHGoogle Scholar
  28. Brouwer, L.E.J., de Loor, B.: Intuitionistischer Beweis des Fundamentalsatzes der Algebra. K. Ned. Akad. Wet. Proc. Sect. Sci. 27, 186–188 (1924) Google Scholar
  29. de Vries, Hk.: Inleiding tot de studie der meetkunde van het aantal. Noordhoff, Groningen (1936) MATHGoogle Scholar
  30. Drost, F.: Carel Steven Adama van Scheltema. Ph.D. thesis, Rijksuniversiteit Groningen (1952) Google Scholar
  31. Feigl, G.: Geschichtliche Entwicklung der Topologie. Jahresber. Dtsch. Math.-Ver. 37, 273–286 (1928) MATHGoogle Scholar
  32. Fraenkel, A.: Einleitung in die Mengenlehre. Springer, Berlin (1919) MATHGoogle Scholar
  33. Fraenkel, A.: Einleitung in die Mengenlehre, 2nd edn. Springer, Berlin, (1923) MATHGoogle Scholar
  34. Gray, J.J.: The Hilbert Challenge. Oxford University Press, Oxford (2000) MATHGoogle Scholar
  35. Hesseling, D.E.: Gnomes in the fog. The reception of Brouwer’s intuitionism in the 1920s. Ph.D. thesis, Utrecht (1999) Google Scholar
  36. Hesseling, D.E.: Gnomes in the Fog. The Reception of Brouwer’s Intuitionism in the 1920s. Birkhäuser, Basel (2002) Google Scholar
  37. Heyting, A.: Philosphische Grundlegung der Mathematik. Blätter für Deutsche Philosophie (4), 1930 (review). Jahresber. Dtsch. Math.-Ver. 40, 50–52 (1931b) Google Scholar
  38. Hilbert, D.: Neubegründung der Mathematik (Erste Mitteilung). Abh. Math. Semin. Univ. Hamb. 1, 157–177 (1922) CrossRefGoogle Scholar
  39. Hilbert, D.: Die Logischen Grundlagen der Mathematik. Math. Ann. 88, 151–165 (1923) MathSciNetCrossRefGoogle Scholar
  40. Hilbert, D.: Über das Unendliche. Math. Ann. 95, 161–190 (1926) MathSciNetCrossRefGoogle Scholar
  41. Hilbert, D., Bernays, P.: Grundlagen der Mathematik I. Springer, Berlin (1934) MATHGoogle Scholar
  42. Hilbert, D., Bernays, P.: Grundlagen der Mathematik II. Springer, Berlin (1939) MATHGoogle Scholar
  43. Johnson, D.M.: The problem of the invariance of dimension in the growth of modern topology, part II. Arch. Hist. Exact Sci. 25, 85–267 (1981) MathSciNetMATHCrossRefGoogle Scholar
  44. Karo, G.: Der geistige Krieg gegen Deutschland. Z. Völkerpsychol. Soziol. 2 (1926), 22 pp. Google Scholar
  45. Kneser, A.: Leopold Kronecker. Jahresber. Dtsch. Math.-Ver. 33, 210–228 (1925) MATHGoogle Scholar
  46. Kreisel, G.: Lawless sequences of natural numbers. Compos. Math. 20, 222–248 (1968) MathSciNetMATHGoogle Scholar
  47. MacLane, S.: Mathematics at the University of Göttingen, 1931–1933. In: Brewer, J., Smith, M. (eds.) Emmy Noether: A Tribute to Her Life and Work, pp. 65–78. Marcel Dekker, New York (1981) Google Scholar
  48. Mancosu, P.: From Brouwer to Hilbert. The Debate on the Foundations of Mathematics in the 1920s. Oxford University Press, Oxford (1998). Collection of papers MATHGoogle Scholar
  49. Menger, K.: Über die Dimensionalität von Punktmengen. I. Monatshefte Math. Phys. 33, 148–160 (1923) MathSciNetMATHCrossRefGoogle Scholar
  50. Menger, K.: Zur Entstehung meiner Arbeiten über Dimensions- und Kurventheorie. Proc. K. Ned. Akad. Wet. 29, 1122–1124 (1926). Subm. 29.5.1926 MATHGoogle Scholar
  51. Menger, K.: Bemerkungen zu Grundlagenfragen. Jahresber. Dtsch. Math.-Ver. 37, 213–226 (1928a). On the analogy Spreads-Analytic sets MATHGoogle Scholar
  52. Menger, K.: Selected Papers in Logic and Foundations, Didactics, Economics. Reidel, Dordrecht (1979) MATHCrossRefGoogle Scholar
  53. Menger, K.: Reminiscences of the Vienna Circle and the Mathematical Colloquium. Golland, L., McGuinness, B., Sklar, A. (eds.). Kluwer, Dordrecht (1994) MATHCrossRefGoogle Scholar
  54. Menger, K.: Selecta Mathematica. Schweizer, B., Sklar, A., Sigmund, K., Gruber, P., Hlawka, E., Reich, L., Schmetterer, L. (eds.). Springer, Vienna (2003) MATHGoogle Scholar
  55. Poincaré, H.: Science et Méthode. Flammarion, Paris (1905) Google Scholar
  56. Poincaré, H.: L’Avenir des mathématiques. In: Castelnuovo, G. (ed.) Atti IV Congr. Intern. Mat. Roma, vol. 1, pp. 167–182. Accad. Naz. Lincei, Roma (1908) Google Scholar
  57. Reid, C.: Hilbert. Springer, Berlin (1970) MATHGoogle Scholar
  58. Rowe, D.E.: Interview with Dirk Jan Struik. Math. Intell. 11, 14–26 (1989) MathSciNetMATHCrossRefGoogle Scholar
  59. Schmidt-Ott, F.: Erlebtes und Erstrebtes. 1860–1950. Franz Steiner Verlag, Wiesbaden (1952) Google Scholar
  60. Schroeder-Gudehus, B.: Deutsche Wissenschaft und internationale Zusammenarbeit, 1914–1928. Ein Beitrag zum Studium kultureller Beziehungen in politischen Krisenzeiten. Imprimerie Dumaret & Golay, Geneve (1966) Google Scholar
  61. Schroeder-Gudehus, B.: Les Scientifiques et la Paix. La communauté scientifique internationale au cours des années 20. Les Presses de l’Université de Montréal, Montréal (1978) Google Scholar
  62. Sieg, W.: Hilbert’s programs: 1917–1922. Bull. Symb. Log. 5, 1–44 (1999) MathSciNetMATHCrossRefGoogle Scholar
  63. Sieg, W.: Towards finitist proof theory. In: Jørgensen, K.F., Hendricks, V., Pedersen, S.A. (eds.) Proof Theory. History and Philosophical Significance. Synthese Library, vol. 292, pp. 95–116. Kluwer, Dordrecht (2000) Google Scholar
  64. Springer, T.A.: B.L. van der Waerden. Levensber. Herdenk. 999, 45–50 (1997) Google Scholar
  65. Troelstra, A.S.: On the origin and development of Brouwer’s concept of choice sequence. In: Troelstra, A.S., van Dalen, D. (eds.) The L.E.J. Brouwer Centenary Symposium, vol. 999, pp. 465–486. North-Holland, Amsterdam (1982) CrossRefGoogle Scholar
  66. Tumarkin, L.: Nouvelle démonstration d’un théorème de Paul Urysohn. Fundam. Math. 8, 360–361 (1926) MATHGoogle Scholar
  67. van Atten, M., van Dalen, D.: Arguments for the continuity principle. Bull. Symb. Log. 8, 329–347 (2002) MATHCrossRefGoogle Scholar
  68. van Dalen, D.: From Brouwerian counter examples to the creating subject. Stud. Log. 62, 305–314 (1999a) MATHCrossRefGoogle Scholar
  69. van Dalen, D.: Brouwer and Fraenkel on intuitionism. Bull. Symb. Log. 6, 284–310 (2000) MATHCrossRefGoogle Scholar
  70. van der Waerden, B.L.: De algebraiese grondslagen der meetkunde van het aantal. Ph.D. thesis, University of Amsterdam (1926) Google Scholar
  71. van Heijenoort, J.: From Frege to Gödel. A Source Book in Mathematical Logic, 1879–1931. Harvard University Press, Cambridge (1967) MATHGoogle Scholar

Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  • Dirk van Dalen
    • 1
  1. 1.Department of PhilosophyUtrecht UniversityUtrechtNetherlands

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