Abstract
“Brouwer – that is the revolution!” – with these words from his manifesto “On the New Foundations Crisis in Mathematics” (Weyl 1921) Hermann Weyl jumped headlong into ongoing debates concerning the foundations of set theory and analysis. His decision to do so was not taken lightly, knowing that this dramatic gesture was bound to have immense repercussions not only for him, but for many others within the fragile and politically fragmented European mathematical community. Weyl felt sure that modern mathematics was going to undergo massive changes in the near future. By proclaiming a “new” foundations crisis, he implicitly acknowledged that revolutions had transformed mathematics in the past, even uprooting the entire edifice of mathematical knowledge. At the same time he drew a parallel with the “ancient” foundations crisis commonly believed to have been occasioned by the discovery of incommensurable magnitudes, a finding that overturned the Pythagorean worldview that was based on the doctrine “all is Number.” In the wake of the Great War that changed European life forever, the Zeitgeist appeared ripe for something similar, but even deeper and more pervasive.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In an interview with B.L. van der Waerden from 1984, I asked him why he thought Weyl had retreated from intuitionism by the mid 1920s. His reply, no doubt based on logic rather than personal knowledge of Weyl’s motives, offered a simple explanation. Weyl was essentially an analyst, he said, and if one accepts intuitionism then one cannot even prove the intermediate value theorem.
References
Alexanderson, G.L. 1987. George Pólya: A Biographical Sketch. In The Pólya Picture Album: Encounters of a Mathematician. Boston: Birkhäuser.
Brouwer, L.E.J. 1928. Intuitionistische Betrachtungen über den Formalismus. Sitzungsberichte der Preußischen Akademie der Wissenschaften: 48–52.
Corry, Leo. 1997. David Hilbert and the Axiomatization of Physics (1894–1905). Archive for History of Exact Sciences 51: 83–198.
———. 1999. David Hilbert between Mechanical and Electromagnetic Reductionism (1910–1915). Archive for History of Exact Sciences 53: 489–527.
Einstein. 1998a. Collected Papers of Albert Einstein (CPAE), Vol. 8A: The Berlin Years: Correspondence, 1914–1917, Robert Schulmann, et al., eds. Princeton: Princeton University Press.
———. 1998b Collected Papers of Albert Einstein (CPAE), vol. 8B: The Berlin Years: Correspondence, 1918, Robert Schulmann, et al., eds. Princeton: Princeton University Press.
Feferman, Solomon. 2000. The Significance of Weyl’s Das Kontinuum, in [Hendricks, Pederson, Jørgensen 2000], 179–193
Frei, Günther, and Urs Stammbach. 1992. Hermann Weyl und die Mathematik an der ETH Zürich, 1913–1930. Birkhäuser: Basel.
Hendricks, V.F., S.A. Pedersen, and K.F. Jørgensen, eds. 2000. Proof Theory. History and Philosophical Significance. Dordrecht: Kluwer.
Hilbert, David. 1904. Über die Grundlagen der Logik und der Arithmetik, Verhandlungen des III. Internationalen Mathematiker-Kongresses in Heidelberg 1904, 174–185.
———. 1915. Die Grundlagen der Physik. (Erste Mitteilung), Königliche Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-physikalische Klasse. Nachrichten: 395–407.
———. 1918 Axiomatisches Denken, Mathematische Annalen, 79: 405–415. (Reprinted in [Hilbert 1932–35], vol. 3, 146–156.)
———. 1922. Neubegründung der Mathematik. Erste Mitteilung, Abhandlungen aus dem Mathematischen Seminar der Hamburgischen Universität, 1: 157–177. (Reprinted in [Hilbert 1932–35], vol. 3, 157–177.)
———. 1932–35. Gesammelte Abhandlungen. Vol. 3. Berlin: Julius Springer.
Moore, Gregory H. 1982. Zermelo’s Axiom of Choice: Its Origins, Development and Influence. New York: Springer.
Peckhaus, Volker. 1990. Hilbertprogramm und Kritische Philosophie, Studien zur Wissenschafts-, Sozial- und Bildungsgeschichte der Mathematik, vol. 7, Göttingen; Vandenhoeck & Ruprecht.
Pólya, Georg. 1972. Eine Erinnerung an Hermann Weyl. Mathematische Zeitschrift 126: 296–298.
Rowe, David E. 2000. The Calm before the Storm: Hilbert’s Early Views on Foundations, in [Hendricks, Pederson, Jørgensen 2000], 55–94.
———. 2001. Felix Klein as Wissenschaftspolitiker. In Changing Images in Mathematics. From the French Revolution to the New Millennium, ed. Umberto Bottazzini and Amy Dahan, 69–92. London: Routledge.
Sauer, Tilman. 2002. Hopes and Disappointments in Hilbert’s Axiomatic ‘Foundations of Physics. In History of Philosophy of Science, ed. M. Heidelberger and F. Stadler, 225–237. Dordrecht: Kluwer.
Scholz, Erhard. 2000. Hermann Weyl on the Concept of Continuum, in [Hendricks, Pederson, Jørgensen 2000], 195–220.
———. 2001a. Hermann Weyl’s Raum-Zeit-Materie and a General Introduction to his Scientific Work, (DMV Seminar, 30.) Basel/Boston: Birkhäuser Verlag.
———. 2001b. Weyls Infinitesimalgeometrie, 1917–1925, in [Scholz 2001a], 48–104.
Sieg, Wilfried. 2000. Toward Finitist Proof Theory, in [Hendricks, Pederson, Jørgensen 2000], 95–115.
Sigurdsson, Skúli. 2001. Journeys in Spacetime, in [Scholz 2001a], 15–47.
van Dalen, Dirk. 1995. Hermann Weyl’s Intuitionistic Mathematics. The Bulletin of Symbolic Logic 1: 145–169.
———. 1999. Mystic, Geometer, and Intuitionist. The Life of L. E. J. Brouwer, vol. 1: The Dawning Revolution. Oxford: Oxford Clarendon Press.
———. 2000. The Development of Brouwer’s Intuitionism, in [Hendricks, Pederson, Jørgensen 2000], 117–152.
———. 2013. L.E.J. Brouwer: Topologist, Intuitionist, Philosopher, 419. Heidelberg: Springer-Verlag.
Weyl, Hermann. 1910. Über die Definitionen der mathematischen Grundbegriffe. Mathematisch-naturwissenschaftliche Blätter 7 (1910): 93–95, 109–113. (Reprinted in [Weyl 1968], vol. 1, 298–304.)
———. 1913. Die Idee der Riemannschen Fläche. Leipzig: Teubner.
———. 1918a. Das Kontinuum. Leipzig: Veit & Co., 1918. The Continuum. Trans. S. Pollard and T. Bole. New York: Dover.
———. 1918b. Raum, Zeit, Materie. 1st ed. Berlin: Springer.
———. 1919. Der circulus vitiosus in der heutigen Begründung der Analysis. Jahresbericht der Deutschen Mathematiker-Vereinigung 28: 85–92.
———. 1921. Über die neue Grundlagenkrise der Mathematik, Mathematische Zeitschrift, 10: 39–79. (Reprinted in [Weyl 1968], vol. 2, 143–180.)
———. 1944. Obituary: David Hilbert, 1862–1943, Obituary Notices of Fellows of the Royal Society 4: 547–553. Reprinted in [Weyl 1968], vol. 4, 120–129.
———. 2009. In Mind and Nature: Selected Writings in Philosophy, Mathematics, and Physics, ed. Peter Pesic. Princeton: Princeton University Press.
Zermelo, Ernst. 1908. Neuer Beweis für die Möglichkeit einer Wohlordnung. Mathematische Annalen 65: 107–128.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG
About this chapter
Cite this chapter
Rowe, D.E. (2018). Hermann Weyl, The Reluctant Revolutionary. In: A Richer Picture of Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-67819-1_27
Download citation
DOI: https://doi.org/10.1007/978-3-319-67819-1_27
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-67818-4
Online ISBN: 978-3-319-67819-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)