Skip to main content
SpringerLink
Log in

The Algorithm Concept – Tool for Historiographic Interpretation or Red Herring?

  • Conference paper
Logic and Theory of Algorithms (CiE 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5028))

Included in the following conference series:

  • 1054 Accesses

Abstract

With starting point in Donald Knuth’s paper “Ancient Babylonian Algorithms”, and using the algebraic reading of pre-Modern mathematical texts as a parallel, the paper discusses the relevance of the algorithm concept, on one hand as an analytical tool for the understanding and comparison of mathematical procedures, on the other as a possible key to how pre-Modern reckoners thought their mathematics and to how they thought about it.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aujac, G.: Le langage formulaire dans la géométrie grecque. Revue d’Histoire des Sciences 37(2), 97–109 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  2. Boncompagni, B. (ed.): Scritti di Leonardo Pisano matematico del secolo decimoterzo. I. Il Liber abbaci di Leonardo Pisano. Tipografia delle Scienze Matematiche e Fisiche, Roma (1857)

    Google Scholar 

  3. Cantor, M.: Vorlesungen über Geschichte der Mathematik. Erster Band, von den ältesten Zeiten bis zum Jahre 1200 n. Chr. 3Teubner, Leipzig (1907)

    Google Scholar 

  4. Folkerts, M.: The Development of Mathematics in Medieval Europe: The Arabs, Euclid, Regiomontanus. Variorum Collected Studies Series, vol. CS811. Ashgate, Aldershot (2006)

    Google Scholar 

  5. Freudenthal, H.: What Is Algebra and What Has It Been in History? Archive for History of Exact Sciences 16, 189–200 (1977)

    Article  MathSciNet  Google Scholar 

  6. Heiberg, J.L.: Euclidis Elementa. 5 vols. Euclidis Opera omnia, vol. I-V. Teubner, Leipzig (1883–1888)

    Google Scholar 

  7. Høyrup, J.: Changing Trends in the Historiography of Mesopotamian Mathematics: An Insider’s View. History of Science 34, 1–32 (1996)

    MathSciNet  Google Scholar 

  8. Høyrup, J.: Embedding: Multi-purpose Device for Understanding Mathematics and Its Development, or Empty Generalization? Filosofi og Videnskabsteori på Roskilde Universitetscenter. 3. Række: Preprints og Reprints, Nr. 8 (2000)

    Google Scholar 

  9. Høyrup, J.: Lengths, Widths, Surfaces: A Portrait of Old Babylonian Algebra and Its Kin. In: Studies and Sources in the History of Mathematics and Physical Sciences. Springer, New York (2002)

    Google Scholar 

  10. Høyrup, J.: Seleucid Innovations in the Babylonian ‘Algebraic’ Tradition and Their Kin Abroad. In: Dold-Samplonius, et al. (eds.) From China to Paris: 2000 Years Transmission of Mathematical Ideas. Boethius, vol. 46, pp. 9–29. Steiner, Stuttgart (2002)

    Google Scholar 

  11. Høyrup, J.: Leonardo Fibonacci and Abbaco Culture: a Proposal to Invert the Roles. Revue d’Histoire des Mathématiques 11, 23–56 (2005)

    Google Scholar 

  12. Høyrup, J.: Jacopo da Firenze’s Tractatus Algorismi and Early Italian Abbacus Culture. In: Science Networks. Historical Studies, Birkhäuser, Basel etc, vol. 34 (2007)

    Google Scholar 

  13. Imhausen, A.: The Algorithmic Structure of the Egyptian Mathematical Problem Texts. In: Steele, J.M., Imhausen, A. (eds.) Under One Sky. Astronomy and Mathematics in the Ancient Near East. Alter Orient und Altes Testament, vol. 297, pp. 147–166. Ugarit-Verlag (2002)

    Google Scholar 

  14. Imhausen, A.: Ägyptische Algorithmen. Eine Untersuchung zu den mittelägyptischen mathematischen Aufgabentexten. Ägyptologische Abhandlungen, vol. 65. Harrassowitz, Wiesbaden (2003)

    Google Scholar 

  15. Knuth, D.: Ancient Babylonian Algorithms. Communications of the Association of Computing Machinery 15, 671–677 (1972); A correction of an erratum in 19, 108 (1976) is of no importance here

    MathSciNet  MATH  Google Scholar 

  16. Libri, G.: Histoire des mathématiques en Italie. 4 vols. Jules Renouard. Paris (1838–1841)

    Google Scholar 

  17. Mahoney, M.S.: Babylonian Algebra: Form vs. Content. Studies in History and Philosophy of Science 1, 369–380 (1972)

    Google Scholar 

  18. Netz, R.: The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History. Ideas in Context, vol. 51. Cambridge University Press, Cambridge (1999)

    Google Scholar 

  19. Neugebauer, O. (ed.) Mathematische Keilschrift-Texte. 3 vols. Quellen und Studien zur Geschichte der Mathematik, Astronomie und Physik. Abteilung A: Quellen. 3. Band, erster-dritter Teil. Julius. Springer, Berlin (1935, 1935, 1937)

    Google Scholar 

  20. Peet, T.E. (ed.): The Rhind Mathematical Papyrus, British Museum 10057 and 10058. Introduction, Transcription, Translation and Commentar. University Press of Liverpool, London (1923)

    Google Scholar 

  21. Rebstock, U. (ed.): Die Reichtümer der Rechner (Ġunyat al-Ḥussāb) von Aḥmad b.Ṯabāt (gest. 631/1234). Die Araber – Vorläufer der Rechenkunst. Beiträge zur Sprach- und Kulturgeschichte des Orients, vol. 32. Verlag für Orientkunde Dr. H. Vorndran, Walldorf-Hessen (1993)

    Google Scholar 

  22. Ritter, J.: Reading Strasbourg 368: A Thrice-Told Tale. Max-Planck-Institut für Wissenschaftsgeschichte. Preprint 103 (1998)

    Google Scholar 

  23. Ritter, J.: Reading Strasbourg 368: A Thrice-Told Tale. In: Chemla, K. (ed.) History of Science, History of Text. Boston Studies in the Philosophy of Science, vol. 238, pp. 177–200. Kluwer, Dordrecht (2004); (I used an electronic manuscript version kindly put at my disposition by Jim Ritter and therefore have to omit page references)

    Google Scholar 

  24. Rodet, L.: Les prétendus problèmes d’algèbre du manuel du calculateur égyptien (Papyrus Rhind). Journal asiatique. septième série 18, 184–232, 390–559 (1881)

    Google Scholar 

  25. Spiesser, M. (ed.) Une arithmétique commerciale du XVe siècle. Le Compendy de la praticque des nombres de Barthélemy de Romans. De Diversis artibus, Brepols, Turnhout, vol. 70 (2003)

    Google Scholar 

  26. Unguru, S.: On the Need to Rewrite the History of Greek Mathematics. Archive for History of Exact Sciences 15, 67–114 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  27. van der Waerden, B.L.: Defence of a “Shocking” Point of View. Archive for History of Exact Sciences 15, 199–210 (1976)

    Article  MATH  Google Scholar 

  28. Weil, A.: Who Betrayed Euclid? Archive for History of Exact Sciences 19, 91–93 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  29. Zeuthen, H.G.: Die Lehre von den Kegelschnitten im Altertum. Höst & Sohn, København (1886)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. No Affiliations,  

    Jens Høyrup

Authors
  1. Jens Høyrup
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Arnold Beckmann Costas Dimitracopoulos Benedikt Löwe

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Høyrup, J. (2008). The Algorithm Concept – Tool for Historiographic Interpretation or Red Herring?. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds) Logic and Theory of Algorithms. CiE 2008. Lecture Notes in Computer Science, vol 5028. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69407-6_30

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-69407-6_30

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69405-2

  • Online ISBN: 978-3-540-69407-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation