Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-23T04:04:17.506Z Has data issue: false hasContentIssue false
  • English
  • Français

Facets of the cultural history of mathematics

Published online by Cambridge University Press:  13 July 2009

Hansjörg Geiges
Get access Rights & Permissions [Opens in a new window]

Abstract

This article highlights the position of mathematics within general culture at various stages of the development of Western civilization. Special emphasis is given to the role of mathematics in Greek philosophy, the influence of mathematics on Gothic architecture and the place of mathematics in 17th and 18th century society. Literary quotations illustrate the shifts in the view of mathematics in society.

Type
Research Article
Information
European Review , Volume 8 , Issue 4 , October 2000 , pp. 487 - 497
Copyright
Copyright © Academia Europaea 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Vitruvius, (1999) Ten Books on Architecture, Rowland, I. D. and Howe, T. N. (eds), (Cambridge: Cambridge University Press), p. 75. I first learned Vitruvius' story about Aristippus from the beautiful book by J. L. Heilbron (1998) Geometry Civilized: History, Culture, and Technique (Oxford: Clarendon Press).Google Scholar
2.Levitt, N. (1996) Mathematics as the stepchild of contemporary culture. In Gross, P. R., Levitt, N., and Lewis, M. W. (eds), The Flight from Science and Reason (New York: The New York Academy of Sciences), pp. 39–53. This article and the book by Heilbron (op. cit.) have been a main source and inspiration for my inaugural lecture at Leiden University of 12 November 1999, on which the present essay is based.Google Scholar
3. One of the standard English editions, containing a useful commentary, is Euclid (1956) The Elements (with Introduction and Commentary by SirHeath, Thomas L.), 3 volumes (New York: Dover Publications).Google Scholar
4. ‘Tripos’ is a name derived from the three-legged stool on which medieval undergraduates used to sit. In Cambridge it has come to denote a course of study.Google Scholar
5.Tacquet, A. (1654) Elementa geometriae planae et solidae (Antwerp: Mersius); quoted after Heilbron, op. cit., p. 14.Google Scholar
6.Goethe, J. W. (1999) Schöne, Faust A. (ed), Goethe-Ausgabe Band 7/1, (Frankfurt am Main: Deutscher Klassiker Verlag), p. 547: ‘With pathetic self-conceit/Squares the circle/Bisects the angle/And where even the most sagacious set to work clumsily/Here it becomes a task for pupils’. (‘Bissecirt den Winckel’ stands probably erroneously for ‘trisects the angle’, another famous geometric problem that is unsolvable with ruler and compass.)Google Scholar
7.Mann, T. (1924) Der Zauberberg (Berlin: S. Fischer Verlag). The relevant passages in the 1997 edition are on pp. 571, 865–867.Google Scholar
8.Proclus, (1992) A Commentary on the First Book of Euclid's Elements (Princeton: Princeton University Press), pp. 24, 38.Google Scholar
9.op. cit., pp. 71–72.Google Scholar
10. Stained-glass windows, mosaics and other works of art by my great-grandfather Fritz Geiges can be found, for instance, in the Gothic cathedrals of Cologne and Freiburg im Breisgau.Google Scholar
11. A recent expanded edition is von Simson, O. (1988) The Gothic Cathedral: Origins of Architecture and the Medieval Concept of Order (Bollingen Series, 48) (Princeton: Princeton University Press).CrossRefGoogle Scholar
12.von Simson, O. (1992) op. cit., p. 26 of the German edition (Darmstadt: Wissenschaftliche Buchgesellschaft).Google Scholar
13.Aubrey, J. (1996) Aubrey's Brief Lives, Dick, O. L. (ed) (Jaffrey, New Hampshire: Nonpareil Books), p. xxxii.Google Scholar
14.Aubrey, J. (1996) Aubrey's Brief Lives, Dick, O. L. (ed) (Jaffrey, New Hampshire: Nonpareil Books), p. xxxii., p. 150.Google Scholar
15. Concerning the wider philosophical significance of the controversy between Hobbes and the mathematician Wallis over the matter of circle squaring, see Bird, A. (1996) Squaring the circle: Hobbes on philosophy and geometry. Journal of the History of Ideas, 57(2), 217–231, and D. M. Jesseph (1999) Squaring the Circle: The War Between Hobbes and Wallis (Chicago: University of Chicago Press).CrossRefGoogle Scholar
16. See Gross, P. R. and Levitt, N. (1994) Higher Superstition– The Academic Left and its Quarrels with Science (Baltimore: The Johns Hopkins University Press), pp. 63–69, for a discussion of this dispute in the context of recent postmodern attacks on science.Google Scholar
17.Knopp, K. (1928) Mathematik und Kultur. Preussische Jahrbücher, 211, 283–300, and A. Pringsheim (1904) Über Wert und angeblichen Unwert der Mathematik. Jahresbericht der Deutschen Mathematiker-Vereinigung, 13, 357–382.Google Scholar
18.Herschbach, D. R., Imagining gardens with real toads. In: P. R. Gross, N. Levitt, and M.W. Lewis, op. cit., pp. 11–30.CrossRefGoogle Scholar
19. The original form of this epigram, due to Turgot, A. R. (1727–1781), seems to have been ‘Eripuit coelo fulmen, mox sceptra tyrannis’, cf. K. Bayer (1999) Nota bene–Das lateinische Zitatenlexikon (Zürich: Artemis und Winkler).Google Scholar
20. Quoted after Heilbron, op. cit., p. 17.Google Scholar
21. For this issue and the relevance of evolutionary psychology cf. the discussion in Pinker, S. (1998) How the Mind Works (London: Penguin Books) pp. 338–342.Google Scholar
22. This information is taken from the article ‘Throwing away a part of our universe’ by C. Willis, Financial Times, 11 09 1999.Google Scholar