Spengler and Mathematics in a Mesopotamian Mirror

  • Jens Høyrup
Part of the Universal- und kulturhistorische Studien. Studies in Universal and Cultural History book series (UUKS)


Mathematics plays a major role in Der Untergang des Abendlandes – in outspoken contrast to two other grand and famous syntheses from the same epoch In total, H G Wells’ slightly more extensive Outline of History from 1920 thus offers no more than twelve references to the topic, all of them without any depth.


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  1. Ascher, Marcia and Robert Ascher. 1986. Ethnomathematics. History of Science 24: 125–144.Google Scholar
  2. Barnes, Barry. 1977. Interests and the Growth of Knowledge. London/ Boston: Routledge & Kegan Paul.Google Scholar
  3. Chemla, Karine and Guo Shuchun (ed., trans.). 2004. Les neuf chapitres. Le Classique mathématique de la Chine ancienne et ses commentaires. Paris: Dunod.Google Scholar
  4. Finkelstein, J. J. 1969. The Laws of Ur-Nammu. Journal of Cuneiform Studies 22: 66–82.Google Scholar
  5. Foucault, Michel. 1966. Les Mots et les choses. Une archéologie des sciences humaines. Paris: Gallimard.Google Scholar
  6. Foucault, Michel. 1971. The Order of Things: an Archaeology of the Human Sciences. New York: Pantheon Books.Google Scholar
  7. Glassner, Jean-Jacques. 2013. “AD.GI4: essai d’interprétation: la création d’un domaine institutionnel?” N.A.B.U. 2013 (N° 4 – décembre): 101–103.Google Scholar
  8. Høyrup, Jens. 1984. Review of Restivo, The Social Relations of Physics, Mysticism, and Mathematics. Dordrecht et al. 1983: D. Reidel. Annals of Science 41: 599–601.Google Scholar
  9. Høyrup, Jens. 2001. On a Collection of Geometrical Riddles and Their Role in the Shaping of Four to Six ‘Algebras’”. Science in Context 14: 85–131.Google Scholar
  10. Høyrup, Jens. 2002a. Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin. New York: Springer.Google Scholar
  11. Høyrup, Jens. 2002b. How to Educate a Kapo, or, Reflections on the Absence of a Culture of Mathematical Problems in Ur III. In Under One Sky: Astronomy and Mathematics in the Ancient Near East, ed. John M. Steele and Annette Imhausen, 121–145. Münster: Ugarit-Verlag.Google Scholar
  12. Høyrup, Jens. 2009. State, ‘Justice’, Scribal Culture and Mathematics in Ancient Mesopotamia. Sartoniana 22: 13–45.Google Scholar
  13. Høyrup, Jens. 2012. A Hypothetical History of Old Babylonian Mathematics: Places, Passages, Stages, Development. Ganita Bhāratī 34 (actually published 2014): 1–23.Google Scholar
  14. Høyrup, Jens. 2013. Algebra in Cuneiform. Introduction to an Old Babylonian Geometrical Technique (Max-Planck-Institut für Wissenschaftsgeschichte, Preprint 452). Berlin. To appear in Edition Open Access, Berlin, 2017. Accessed: 20 April 2017.
  15. Høyrup, Jens. 2014. Written Mathematical Traditions in Ancient Mesopotamia: Knowledge, ignorance, and reasonable guesses. In Traditions of Written Knowledge in Ancient Egypt and Mesopotamia. Proceedings of Two Workshops held at Goethe-University, Frankfurt/Main in December 2011 and May 2012, ed. Daliah Bawanypeck and Annette Imhausen, 189–214. Münster: Ugarit-Verlag.Google Scholar
  16. Lambert, W. G. and A. R. Millard. 1969. Atra-hasīs: The Babylonian Story of the Flood. Oxford: Oxford University Press.Google Scholar
  17. Luria, Aleksandr R. 1976. Cognitive Development. Its Cultural and Social Foundations. Cambridge, MA/London: Harvard University Press.Google Scholar
  18. Nappi, Carla. 2013. The Global and Beyond: Adventures in the Local Historiographies of Science. Isis 104: 102–110.Google Scholar
  19. Neugebauer, O. 1935. Mathematische Keilschrift-Texte. I–III. Berlin: Julius Springer (I–II: 1935, III: 1937).Google Scholar
  20. Nissen, Hans J., Peter Damerow, and Robert Englund. 1993. Archaic Bookkeeping: Writing and Techniques of Economic Administration in the Ancient Near East. Chicago: Chicago University Press.Google Scholar
  21. Peet, T. Eric (ed., trans.). 1923. The Rhind Mathematical Papyrus, British Museum 10057 and 10058. London: University Press of Liverpool.Google Scholar
  22. Restivo, Sal. 1983. The Social Relations of Physics, Mysticism, and Mathematics: Studies in Social Structure, Interests, and Ideas. Dordrecht/Boston: Reidel.Google Scholar
  23. Richardson, Seth F. 2010. On Seeing and Believing: Liver Divination and the Era of Warring States (II). In Divination and Interpretation of Signs in the Ancient World, ed. Amar Annus, 225–266. Chicago: The Oriental Institute of the University of Chicago.Google Scholar
  24. Spengler, Oswald. 1923. Der Untergang des Abendlandes: Umrisse einer Morphologie der Weltgeschichte. 2 vols. + Namen- und Sachverzeichnis. München: Beck.Google Scholar
  25. Spengler, Oswald. 1927. The Decline of the West: Form and Actuality. New York: Knopf.Google Scholar
  26. Spengler, Oswald. 1931. Der Mensch und die Technik. München: Beck.Google Scholar
  27. Spengler, Oswald. 1932. Man and Technics. New York: Knopf.Google Scholar
  28. Toynbee, Arnold. 1934. A Study of History. 12 vols. Oxford/New York: Oxford University Press (1934–1961).Google Scholar
  29. Tredennick, Hugh (ed., trans.). 1933. Aristotle, The Metaphysics. 2 vols. London: Heinemann/ New York: Putnam (vol. 1: 1933, vol. 2:1935).Google Scholar
  30. Wells, H. G. 1920. The Outline of History: Being a Plain History of Life and Mankind. Revised and corrected edition. London et al.: Cassell.Google Scholar

Copyright information

© Springer Fachmedien Wiesbaden GmbH, ein Teil von Springer Nature 2018

Authors and Affiliations

  1. 1.Frederiksberg CDenmark

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