Cuneiform Mathematics

When, in the early 20^th century, the assyriologist François Thureau-Dangin and, after him, the mathematician Otto Neugebauer undertook the systematic publication of cuneiform mathematical texts preserved in European and American museums, the scientific community discovered that highly sophisticated mathematical methods were developed in Mesopotamia more than one millennium before Euclid and Pythagoras.

The pages on mathematics of the cdli:wiki offers a brief general overview of the known mathematical cuneiform sources and a selected bibliography. Several more focused articles develop further some of the most important aspects of the mathematical traditions that have emerged in the Ancient Near East from the mi-third millennium to the end of the first millennium BC.

• General overview

Transversal articles

• The Sexagesimal Place Value Notation
• Historiography of Cuneiform Mathematics
• Reasoning
• Transmissions

3^rd millennium

• Early Dynastic mathematical texts
• Mathematics in the Ur III period

2^nd millennium

• Learning mathematics in Old Babylonian scribal schools
• Old Babylonian mathematical traditions

1^st millennium

• Mathematical texts of the Achaemenid and Hellenistic periods

A tentative complete bibliography by Duncan Melville is available here.

A basic tool indispensable for any people interested by the subject is Friberg's commented bibliography, alas unpublished, A Survey of Publications on Sumero-Akkadian Mathematics, Metrology and Related Matters (1854-1982), Göteborg 1982.

• Bruins, Evert M. and Marguerite Rutten. 1961. Textes mathématiques de Suse. Paris: Geuthner.
• Damerow, Peter (2001) "Kannten die Babylonier den Satz des Pythagoras? Epistemologische Anmerkungen zur Natur der babylonischen Mathematik" in Changing Views on Ancient Near Eastern Mathematics (Jens Høyrup and Peter Damerow, eds.), Berlin: 219-310.
• Englund, Robert K. (1988) "Administrative timekeeping in Ancient Mesopotamia" JESHO 31: 121-185.
• Englund, Robert K. and Jean-Pierre Grégoire (1991) The Proto-Cuneiform Texts from Jemdet Nasr (MSVO 1), Berlin.
• Friberg, Jöran (1978) "Early Roots of Babylonian Mathematics 1. A method for the decipherment … of proto- Sumerian and proto-Elamite semi-pictographic inscriptions" Department of Mathematics CTH-GU 1978- 9, Gothenburg.
• Friberg, Jöran (1990) "Mathematik" (in English) in RlA 7 (Dietz Otto Edzard, ed.), Berlin, New York: 531-585.
• Friberg, Jöran. 2000. Mathematics at Ur in the Old Babylonian period. Revue d'Assyriologie 94:98-188.
• Friberg, Jöran. 2005. Unexpected Links Between Egyptian and Babylonian Mathematics. Singapour: World Scientific.
• Friberg, Jöran. 2007. Amazing Traces of Babylonian Origin in Greek Mathematics. Singapour: World Scientific.
• Friberg, Jöran. 2007. A Remarkable Collection of Babylonian Mathematical Texts, vol. I. New York: Springer.
• Friberg, Jöran. 2005. On the Alleged Counting with Sexagesimal Place Value Numbers in Mathematical Cuneiform Texts from the Third Millennium B. C. CDLJ 2005:2.
• Friberg, Jöran. 2009. A Geometric Algorithm with Solutions to Quadratic Equations in a Sumerian Juridical Document from Ur III Umma. CDLJ 2009-3.
• Høyrup, Jens. 2002. Lengths, Widths, Surfaces. A Portrait of Old Babylonian Algebra and its Kin. Berlin & Londres: Springer.
• Middeke-Conlin, Robert, and Christine Proust. 2014. Interest, price, and profit: an overview of mathematical economics in YBC 4698. Cuneiform Digital Library Journal 2014-3.
• Neugebauer, Otto. 1935-1937. Mathematische Keilschrifttexte I-III. Berlin: Springer.
• Neugebauer, Otto and Abraham J. Sachs. 1945. Mathematical Cuneiform Texts. New Haven: American Oriental Series & American Schools of Oriental Research
• Neugebauer, Otto. 1957. The exact sciences in antiquity. Providence: Brown University Press.
• Nissen, Hans J., Peter Damerow, and Robert K. Englund (1993) Archaic Bookkeeping, Early Writing and Techniques of Economic Administration in the Ancient Near East, Chicago, London Nougayrol, Jean, et al. (1968) Ugaritica V, Paris.
• Powell, M. A., Jr. (1976) "The antecedents of Old Babylonian place notation and the early history of Babylonian mathematics" HM 3: 417-439.
• Powell, Marvin A. 1987-1990. Masse und Gewichte. In Reallexikon der Assyriologie.
• Proust, Christine (with the collaboration of A. Cavigneaux). 2007. Tablettes mathématiques de Nippur. Istanbul: Institut Français d'Etudes Anatoliennes, De Boccard.
• Proust, Christine (with the collaboration of M. Krebernik and J. Oelsner). 2008. Tablettes mathématiques de la collection Hilprecht. Leipzig: Harrassowitz.
• Proust, Christine. 2009. Numerical and metrological graphemes: from cuneiform to transliteration. Cuneiform Digital Library Journal 2009:1.
• Robson, Eleanor. 1999. Mesopotamian Mathematics, 2100-1600 BC. Technical Constants in Bureaucracy and Education, vol. XIV. Oxford: Clarendon Press.
• Robson, Eleanor. 2008. Mathematics in Ancient Iraq: A Social History. Princeton: Princeton University Press.
• Thureau-Dangin, François. 1938. Textes Mathématiques Babyloniens. Leiden: Ex Oriente Lux.

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