A Short History of Computing Devices from Schickard to de Colmar: Emergence and Evolution of Ingenious Ideas and Technologies as Precursors of Modern Computer Technology

  • Viktor FreimanEmail author
  • Xavier Robichaud
Part of the Mathematics Education in the Digital Era book series (MEDE, volume 11)


Even the brief analysis of the history of the invention of mechanical computing devices from the 17th to early 20th centuries that we provide in this chapter demonstrates the rich potential available to mathematics educators today. The first devices designed by Schickard and Pascal showed a technological complexity when dealing with the issue of representing even simple arithmetic operations, such as addition, by means of gears and wheels. The knowledge they developed, along with the ideas they did not succeed to put in practice, inspired further generations of inventors who not only pursued the search for better aids for calculation practices but also envisioned novel mathematical structures allowing for a more universal approach to computing which, along with technological know-how, eventually led to the modern era of electronic computers, the Internet, and other digital tools and technology-rich environments. At the end of the chapter, we explore the educational potential of this historical development.


History of computing devices Mechanical calculators Arithmometers Educational implications 


  1. Ageron, P. 2016. L’arithmomètre de Thomas: sa réception dans les pays méditerranéens (1850–1915), son intérêt dans nos salles de classe. In Proceedings of the 2016 ICME Satellite Meeting of the International Study Group on the Relations Between the History and Pedagogy of Mathematics, ed. L. Radford, F. Furinghetti, and T. Hausberger, 655–670. Montpellier, France: IREM de Montpellier.Google Scholar
  2. Anon. 1820. Note sur la publication proposée par le gouvernement anglais des grandes tables logarithmiques et trigonométriques de M. de Prony. Paris: Didot.Google Scholar
  3. Babbage, C. 1832. On the economy of machinery and manufactures. London: Knight.Google Scholar
  4. Babbage, C. 1961. On the division of mental labour. In On the principles of and development of calculator, ed. P. Morison and E. Morrison, 315–321. New York: Dover Publications Inc.Google Scholar
  5. Bacon, F. 1623. De dignitate & augmentis scientiarum. London: J. Haviland.Google Scholar
  6. Bacon, F. 1640. Of the advancement and proficience of learning. Oxford: L. Lichfield. [The first English translation of Bacon 1623.].Google Scholar
  7. Baker, C. 1839. Infant schools. In Central society of education, vol. 3, 1–48. London: Taylor and Walton.Google Scholar
  8. Beeson, M. J. 2004. The mechanization of mathematics. In Alan Turing: Life and legacy of a great thinker, ed. C. Teuscher, 77–134. Berlin-Heidelberg-New York: Springer.CrossRefGoogle Scholar
  9. Belanger, J., and D. Stein. 2005. Shadowy vision: Spanners in the mechanization of mathematics. Historia Mathematica 32 (1): 76–93.CrossRefGoogle Scholar
  10. Bloch, L. 2016. Informatics in the light of some Leibniz’s works. Paper presented at XB2 Xenobiology Conference, Berlin.Google Scholar
  11. Blikstein, P. 2013. Digital fabrication and “making” in education: The democratization of invention. In FabLabs: Of machines, makers and inventors, ed. J. Walter-Herrmann and C. Buching, 1–21. Bielefeld: Transcript Publishers.Google Scholar
  12. Bradis, V.M. [Бpaдиc B. M.]. 1929. Пpиближeнныe вычиcлeния [Priblizhennye vychisleniya] (Approximative calculations). In Ha пyтяx к пeдaгoгичecкoмy caмooбpaзoвaнию: Ha пyтяx мaтeмaтики [Na putyakh k pedagogicheskomu samoobrazovaniyu: Na putyakh matematiki] (Various approaches to the self-directed pedagogical studies: Ways to mathematics), ed. M.M. Rubinschtein [M.M. Pyбинштeйн], 87–116. Moscow: Mir.Google Scholar
  13. Cajory, F. 1909. A history of the logarithmic slide rule and allied instruments. New York: The Engineering News Publishing Company & London: Archibald Constable & Co.Google Scholar
  14. Campbell-Kelly, M., W. Aspray, N.L. Ensmenger, and J.R. Yost. 2013. Computer: A history of the information machine. Boulder: Westview Press.Google Scholar
  15. Chazal, G. 2002. Les réseaux du sens: De l’informatique aux neurosciences. Revue Philosophique de Louvain 100 (1): 321–324.Google Scholar
  16. Cole, J.R. 1995. Pascal: The man and his two loves. New York: New York University Press.Google Scholar
  17. Cortada, J.W. 1993. Before the computer: IBM, NCR, Burroughs, and Remington Rand and the industry they created, 1865–1956. Princeton, NJ: Princeton University Press.Google Scholar
  18. Cragon, H.G. 2000. Computer architecture and implementation. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  19. Davis, M. 2000. Engines of logic: Mathematicians and the origin of the Computer. New York: W. W. Norton & Company.Google Scholar
  20. Diderot, D., and J.-B. le Rond d’Alembert (Eds.). 1751[-1772]. Encyclopédie, ou dictionnaire raisonné des sciences, des arts et des métiers. Paris: Briasson et al.Google Scholar
  21. Durand-Richard, M.-J. 2010. Le regard français de Charles Babbage (1791–1871) sur le “déclin de la science en Angleterre.” Documents pour l’histoire des techniques 19 (2): 287–304.Google Scholar
  22. Freeth, T. 2002. The Antikythera Mechanism: 2. Is it Posidonius’ Orrery? Mediterranean Archaeology and Archaeometry 2 (2): 45–58.Google Scholar
  23. Freeth, T. 2014. Eclipse prediction on the ancient Greek astronomical calculating machine known as the Antikythera mechanism. PLoS ONE 9 (7): e103275.CrossRefGoogle Scholar
  24. Freeth, T., A. Jones, J.M. Steele, and Y. Bitsakis. 2008. Calendars with Olympiad display and eclipse prediction on the Antikythera mechanism. Nature 454 (7204): 614–617.CrossRefGoogle Scholar
  25. Glaser, A. 1981. History of binary and other nondecimal numeration. Los Angeles: Tomash Publishers.Google Scholar
  26. Graf, K.-D. 1995. Promoting interdisciplinary and intercultural intentions through the history of informatics. In Integrating information technology into education, ed. D. Watson and D. Tinsley, 139–150. Dordrecht: Springer Science + Business Media. Scholar
  27. Green, C.D. 2005. Was Babbage’s analytical engine intended to be a mechanical model of the mind? History of Psychology 8 (1): 35–45.CrossRefGoogle Scholar
  28. Halliwell, J.O. 1838. A brief account of the life, writings, and inventions of Sir Samuel Morland, Master of Mechanics to Charles The Second. Cambridge: Metcalfe & Palmer.Google Scholar
  29. Horsburgh, E.M. 1914. Modern instruments and methods of calculation: A handbook of the Napier tercentenary exhibition. London: G. Bell & Sons.Google Scholar
  30. Jackson, L.L. 1906. The educational significance of sixteenth century arithmetic from the point of view of the present time. New York: Teachers College, Columbia University.Google Scholar
  31. Johnston, S. 1996. The identity of the mathematical practitioner in 16th-century England. In Der ‘mathematicus’: Zur Entwicklung und Bedeutung einer neuen Berufsgruppe in der Zeit Gerhard Mercators (Duisburger Mercator-Studien), ed. I. Hantsche, 93–120. Bochum: Brockmeyer.Google Scholar
  32. Johnston-Wilder, S., and D. Pimm. 2004. Teaching secondary mathematics with ICT. Maidenhead: Open University Press.Google Scholar
  33. Jones, M. 2016. Reckoning with matter: Calculating machines, innovation and thinking about thinking from Pascal to Babbage. Chicago: Chicago University Press.CrossRefGoogle Scholar
  34. Kidwell, P.A., A. Ackerberg-Hastings, and D.L. Roberts. 2008. Tools of American Mathematics Teaching, 1800–2000. Baltimore: Johns Hopkins University Press.Google Scholar
  35. Lardner, D. 1834. Babbage’s calculating engine. Edinburgh Review 59: 264–327.Google Scholar
  36. Leibniz, G.W. 1685/1929. Leibniz on his calculating machine (Translated from Latin by Mark Kormes). In A Source Book in Mathematics, ed. D.E. Smith, 173–181. New York: McGraw-Hill.Google Scholar
  37. Leibniz [= Leibniz, G.W.] 1703 [1720]. Explication de l’arithmétique binaire qui se sert des seuls caractères 0 & 1; avec des remarques sur son utilité, & sur ce qu’elle donne le sens des anciennes figures Chinoises de Fohy. Histoire de l'Académie royale, des sciences, avec les mémoires de mathématique & de physique, [section “Mémoires”,] 85–89.Google Scholar
  38. Lenz, K. 1924. Die Rechenmaschinen und das Maschinenrechnen. Wiesbaden: Springer.CrossRefGoogle Scholar
  39. Lions, J.-L. 1991. De la machine à calculer de Pascal aux ordinateurs. La Vie des sciences 3: 221–240.Google Scholar
  40. Lister, M., J. Dovey, S. Giddings, I. Grant, and K. Kelly. 2009. New media: A critical introduction. London and New York: Routledge.Google Scholar
  41. Marguin, J. 1997. L’arithmomètre de Thomas n° 1398. Bulletin de la Sabix 18: 31–42.Google Scholar
  42. Markushevich, A.I., A.Y. Hinchin, and P.S. Alexandrov [Mapкyшeвич, A. И., A. Я. Xинчин, П. C. Aлeкcaндpoв]. 1951. Энциклoпeдия элeмeнтapнoй мaтeмaтики [Entsiklopediya elementarnoĭ matematiki] (Encyclopedia of elementary mathematics). Moscow & Leningrad: GTTL.Google Scholar
  43. Maschietto, M. 2013. Systems of instruments for place value and arithmetical operations: An exploratory study with the Pascaline. Education 3 (4): 221–230.Google Scholar
  44. Mayo, E., and C. Mayo. 1837. Practical remarks on infant education, for the use of schools and private families. London: Seeley and Co.Google Scholar
  45. Menabrea, L.F. 1842. Notions sur la machine analytique de M. Charles Babbage. Bibliothèque universelle de Genève 41: 352–376.Google Scholar
  46. Morar, F.-S. 2015. Reinventing machines: The transmission history of the Leibniz calculator. British Society for the History of Science 48 (1): 123–146.CrossRefGoogle Scholar
  47. Mosconi, J. 1983. Charles Babbage: vers une théorie du calcul mécanique. Revue d’histoire des sciences 36 (1): 69–107.CrossRefGoogle Scholar
  48. Myers, G.W. 1903. The laboratory method in the secondary school. The School Review 11 (9): 727–741.CrossRefGoogle Scholar
  49. Nepero, I. (Napier, J.). 1614. Mirifici logarithmorum canonis descriptio. Edinburgum: A. Hart.Google Scholar
  50. Nepero, I. (Napier, J.). 1617. Rabdologiae seu numerationis per virgulas libri duo: cum appendice de expeditissimo multiplicationis promptuario. Edinburgum: A. Hart.Google Scholar
  51. Nordhaus, W.D. 2007. Two centuries of productivity growth in computing. The Journal of Economic History 67 (1): 128–159.CrossRefGoogle Scholar
  52. Pascal, B. 1645/1998. Lettre dedicatoire a Monseigneur le Chancelier sure le sujet de la Machine nouvellement inventée par le Sieur B.P. pour faire toutes sortes d’operations d’Arithmetique, par un mouvement reglé, sans plume ny jettons, avec un advis necessaire à ceux qui auront la curiosité de voir ladite Machine, et de s’en servir. [n.p.] (Reprinted in B. Pascal, Œuvres complètes. Tome 1. Paris: Édition de Michel Le Guern.).Google Scholar
  53. Poisard, C. 2006. The notion of carried-number, between the history of calculating instruments and arithmetic. Proceedings of the Annual Conference of Mathematics Education Research Group of Australasia (MERGA), 2, pp. 416–423.Google Scholar
  54. Project 2061. 1989. Science for all Americans: A Project 2061 report on literacy goals in science, mathematics, and technology. Washington, D.C.: American Association for the Advancement of Science.Google Scholar
  55. Rabardel, P. 1995. Les hommes et les technologies, une approche cognitive des instruments contemporains. Paris: Armand Colin.Google Scholar
  56. Raloff, J. 1982. On Beyond Babbage: The Rise of Automatic Digital Computers. Science News 121: 170–172.CrossRefGoogle Scholar
  57. Ratcliff, J.R. 2007. Samuel Morland and his calculating machines c.1666: The early career of a courtier–inventor in Restoration London. British Society for the History of Science 40 (2): 159–179.CrossRefGoogle Scholar
  58. Reuleaux, F. 1861. Der Constructeur: Ein Handbuch zum Gebrauch beim Maschinen-Entwerfen. Braunschweig: Friedrich Vieweg und Sohn.Google Scholar
  59. Ryan, J.A. 1996. Leibniz’ binary system and Shao Yong’s “Yijing”. Philosophy East and West 46 (1): 59–90.CrossRefGoogle Scholar
  60. Sawday, J. 2007. Engines of the imagination: Renaissance culture and the rise of the machine. Abingdon: Routledge.CrossRefGoogle Scholar
  61. Schlauch, W.S. 1940. The use of calculating machines in teaching arithmetic. The Mathematics Teacher 33 (1): 35–38.Google Scholar
  62. Sonnenschein, W.S. 1879. Description of Sonnenschein’s number-pictures, arithmometer and blackboard: their construction and use. London: W. Swan Sonnenschein.Google Scholar
  63. Taton, R. 1963. Sur l’invention de la machine arithmétique. Revue d’histoire des sciences et de leurs applications 16 (2): 139–160.CrossRefGoogle Scholar
  64. Temam, D. 2009. La pascaline, la “machine qui relève du défaut de la mémoire.” Bibnum. Retrieved from:
  65. Tent, M.B.W. 2012. Gottfried Wilhelm Leibniz: The polymath who brought us calculus. Boca Raton, FL: CRC Press.Google Scholar
  66. Trouche, L. 2005. Des artefacts aux instruments, une approche pour guider et intégrer les usages des outils de calcul dans l’enseignement des mathématiques. Actes de l’université d’été de Saint-Flour, pp. 265–290.Google Scholar
  67. Vygotsky, L.S. 1978. Mind in society: The development of higher psychological processes. Cambridge, MA: Harvard University Press.Google Scholar
  68. Walford, C. 1871. The insurance cyclopaedia. London: Layton.Google Scholar
  69. Wiener, N. 1988/1950. The human use of human beings: Cybernetics and society. New York: Da Capo Press.Google Scholar

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Authors and Affiliations

  1. 1.Université de MonctonMonctonCanada
  2. 2.Université de MonctonShippaganCanada

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