Third Millennium Mathematics

    Many people are aware of the earliest mathematical artifacts, the tokens of the Near East, and equally well-known is the flourishing of mathematics in the Old Babylonian period.  The intervening period is much less well-known, and yet this crucial third millennium witnessed the development of abstract numbers and the arrival of the famous sexagesimal place value system.  This section of the site gives a brief overview of third millennium mathematics.  From some places and times, we have a great abundance of tablets and are able to build up a detailed picture of mathematical practices; at others the archaeological record is sparse and we shall pass in silence over great passages of time about which we know nothing.

    Most of the sites in Mesopotamia yielding good third millennium tablets are found in the southern region, in Sumer, although one important site, Jemdet Nasr, is further north. It is believed that this southern region, containing such cities as Ur and Uruk, was the most developed area at the time, but how much this conclusion could be challenged by new archaeological evidence is unclear. Certainly the current excavations of Hamoukar in the far north could provide important new information and the standard view of the Uruk expansion in the fourth millennium seems to be undergoing some revisions which will doubtless affect our view of the subsequent periods (see, for example, Algaze (1993), Stein (1999) and Van de Mieroop (1997)). We restrict our attention here to core Mesopotamia and say nothing about the important sources from Ebla to the northwest (see Archi (1989), Friberg (1986)) and Elam in the southeast (Damerow and Englund (1989)).

  • Chronology: Summary chronology of the Third Millennium.
  • Archaic Mathematics: Emergence of mathematics in late Fourth Millennium.
  • Early Dynastic
  • Sargonic
  • Ur III 
  • Tablets
  • Bibliography

  • This section is largely based on a talk I gave at the Annual Meeting of the Canadian Society for History and Philosophy of Mathematics in June 2000, and the paper that appeared in the subsequent Proceedings.

    Go to Mesopotamian Mathematics

    Last modified: 30 August 2003
    Duncan J. Melville

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