Abstract
The history of Mesopotamian mathematics begins around 3300 BCE with the development of written systems for recording the control and flow of goods and other economic resources such as land. Numeration was bound up with measurement and was a collection of concrete systems. One of the key developments over the subsequent thousand years or so was the gradual rationalization of these complex concrete systems and the consequent emergence of an abstract conception of number and techniques of computation that applied regardless of metrological category. Throughout their history Mesopotamian scribes organized knowledge in the form of lists. In mathematics there were also lists, but along with lists came metrological and mathematical tables, two-dimensional arrays of data that organized information both vertically and horizontally. A key example is tables giving lists of lengths of sides of square or rectangular fields, along with their areas; the problem of computation of areas remained a constant concern throughout the period covered here. In this chapter, we cover the development of Mesopotamian computation from the archaic period up to the edge of the emergence of the fully abstract sexagesimal computational system for which they are renowned, tracing, as far as can be seen with currently available sources, the long developmental process.
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
References
Adams, R. Mc. C. 1981. Heartland of cities. Surveys of ancient settlement and land use of the central floodplain of the Euphrates. Chicago: University of Chicago Press.
Deimel, A. 1923. Die Inschriften von Fara II: Schultexte aus Fara. Leipzig: J. C. Hinrichs’sche Buchhandlung.
Englund, R.K. 1993. Review of the origins of script. Science 260 (5114): 1670–1671.
Englund, R.K., and J.-P. Grégoire. 1991. The Proto-Cuneiform texts from Jemdet Nasr (Materialien zu den Frühen Schriftzeugnissen des Vorderen Orients, vol. 1). Berlin: Gebrüder Mann Verlag.
Feliu, L. 2012. A new Early Dynastic IIIb metro-mathematical table tablet of area measures from Zabalam. Altorientalische Forschungen 39: 218–225.
Foster, B.R. 2005. Shuruppak and the Sumerian city state. In Memoriae Igor M. Diakonoff, ed. L. Kogan, et al. Winona Lake: Eisenbrauns.
Foster, B.R., and E. Robson. 2004. A new look at the Sargonic mathematical corpus. Zeitschrift für Assyriologie 94: 1–15.
Friberg, J. 1986. The early roots of Babylonian Mathematics, III. Three remarkable texts from ancient Ebla. Vicino Oriente 6: 3–25.
Friberg, J. 1990. Mathematik. In Reallexikon der Assyriologie VII, ed. D.O. Edzard, 531–585. Berlin and New York: De Gruyter.
Friberg, J. 1994. Preliterate counting and accounting in the Middle East. Orientalistische Literaturzeitung 89: 477–502.
Friberg, J. 1997. Round and almost round numbers in protoliterate metro-mathematical field texts. Archiv für Orientforschung 44 (45): 1–58.
Friberg, J. 2005. On the alleged counting with sexagesimal place value numbers in mathematical cuneiform texts from the Third Millennium BC. Cuneiform Digital Library Journal 2005:2 (http://cdli.ucla.edu/pubs/cdlj/2005/cdlj2005_002.html).
Friberg, J. 2007. A remarkable collection of Babylonian mathematical texts. Manuscripts in the Schøyen collection: Cuneiform texts I. New York: Springer.
Friberg, J. 2014. Geometric division problems, quadratic equations, and recursive geometric algorithms in Mesopotamian mathematics. Archive for History of Exact Sciences 68 (1): 1–34.
Høyrup, J. 1996. Changing trends in the historiography of Mesopotamian mathematics: An insider’s view. History of Science 34: 1–32.
Høyrup, J. 2002a. A note on Old Babylonian computational techniques. Historia Mathematica 29: 193–198.
Høyrup, J. 2002b. Lengths, widths, surfaces: A portrait of Old Babylonian algebra and its kin. New York: Springer.
Jestin, R. 1937. Tablettes sumériennes de Shuruppak au Musée de Stamboul. Paris: E. de Boccard.
Lieberman, S.J. 1980. Of clay pebbles, hollow clay balls, and writing: A Sumerian view. American Journal of Archaeology 84: 339–358.
Limet, H. 1973. Étude de documents de la période d’Agadé appartenant à l’Université de Liège. Paris: Les Belles Lettres.
Liverani, M. 1990. The shape of Neo-Sumerian fields. Bulletin on Sumerian Agriculture 5: 147–186.
Luckenbill, D. 1930. Inscriptions from Adab. Chicago: The University of Chicago Press.
Melville, D. 2002. Ration computations at Fara: Multiplication or repeated addition? In Under one sky: Astronomy and mathematics in the Ancient Near East (London, 2001) (AOAT 297), ed. J.M. Steele, and A. Imhausen, 237–252. Münster: Ugarit-Verlag.
Melville, D. 2016. After Neugebauer: Recent developments in Mesopotamian mathematics. In A mathematician’s journeys: Otto Neugebauer and modern transformations of ancient science, ed. A. Jones, C. Proust, and J. Steele, 237–263. Cham: Springer.
Nissen, H.J., P. Damerow, and R. Englund. 1993. Archaic bookkeeping: Early writing and techniques of economic administration in the ancient Near East. Chicago: University of Chicago Press.
Pomponio, F., and G. Visicato. 1994. Early Dynastic administrative texts of Šuruppak. Napoli, Istituto universitario orientale di Napoli, Dipartimento di studi asiatici.
Powell, M.A. 1990. Masse und Gewichte. In Reallexikon der Assyriologie VII, ed. D.O. Edzard, 457–530. Berlin and New York: De Gruyter.
Proust, C. 2000. La multiplication babylonienne: la part non écrite du calcul. Revue d’histoire des mathématiques 6: 293–303.
Proust, C. 2007. Tablettes mathématiques de Nippur. Paris: Institut Français d’Études Anatoliennes-Georges Dumézil.
Proust, C. (forthcoming). Early-Dynastic tables from Southern Mesopotamia, or the multiple facets of the quantification of surfaces. In Mathematics and administration in the ancient world, ed. K. Chemla, and C. Michel.
Robson, E. 2007. Mesopotamian mathematics. In The mathematics of Egypt, Mesopotamia, China, India, and Islam, ed. V. Katz, 57–186. Princeton, NJ: Princeton University Press.
Robson, E. 2008. Mathematics in Ancient Iraq: A social history. Princeton, NJ: Princeton University Press.
Schmandt-Besserat, D. 1992. Before writing I–II. Austin: University of Texas Press.
Visicato, G. 1995. The Bureaucracy of Šuruppak. Münster: Ugarit-Verlag.
Visicato, G. 2000. The power and the writing. Bethesda, MD: CDL Press.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Appendix: Periodization
Appendix: Periodization
The absolute chronology of Mesopotamia is an area of current vigorous scholarly debate, especially before the first millennium. The further back in time one goes, the larger the uncertainties. For convenience here we follow the middle chronology periodization adopted by the Cuneiform Digital Library Initiative (CDLI), as follows:
Period | Date |
|---|---|
Uruk IV | ~3350 to 3200 |
Uruk III | ~3200 to 3000 |
Early Dynastic I–II | ~2900 to 2700 |
Early Dynastic IIIa | ~2600 to 2500 |
Early Dynastic IIIb | ~2500 to 2340 |
Sargonic | ~2340 to 2200 |
Ur III | ~2100 to 2000 |
Old Babylonian | ~2000 to 1600 |
Rights and permissions
Copyright information
© 2018 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Melville, D.J. (2018). Computation in Early Mesopotamia. In: Volkov, A., Freiman, V. (eds) Computations and Computing Devices in Mathematics Education Before the Advent of Electronic Calculators. Mathematics Education in the Digital Era, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-319-73396-8_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-73396-8_2
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-73394-4
Online ISBN: 978-3-319-73396-8
eBook Packages: EducationEducation (R0)