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After Neugebauer: Recent Developments in Mesopotamian Mathematics

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A Mathematician's Journeys

Part of the book series: Archimedes ((ARIM,volume 45))

Abstract

When Otto Neugebauer began writing on Old Babylonian mathematics in the late 1920s, despite a certain amount of pre-history and heroic efforts by early pioneers, it was still a little-studied and poorly understood area. Once he engaged with the subject, a torrent of papers followed, leading up to the publication of the monumental Mathematische Keilschrift-Texte (MKT) in three volumes in 1935 and 1937. The appearance in 1945 of Mathematical Cuneiform Texts (MCT (Neugebauer and Sachs 1945)), mostly concerned with publishing tablets from Yale that had not been available to him earlier in Europe, as well as the infamous Plimpton 322, essentially completed his project. Neugebauer had read, translated, understood and described in precise mathematical detail the known corpus of Old Babylonian problem texts, as well as giving a categorization of the various types of table texts. Neugebauer himself moved on and, while his work on astronomy continued for the rest of his life, he rarely published on mathematics again. What was there left to do?

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References

  • Bruins, E.M., and M. Rutten. 1961. Textes mathématiques de Suse, MDP, vol. 34. Paris: Geuthner.

    Google Scholar 

  • Chrisomalis, S. 2010. Numerical notation: A comparative history. New York: Cambridge University Press.

    Book  Google Scholar 

  • Civil, M. 1979. Ea A = nâqu, Aa A = nâqu, with their forerunners and related texts, Materials for the Sumerian Lexicon, vol. 14. Rome: Pontifical Biblical Institute.

    Google Scholar 

  • Davis, P.J. 1994. Otto Neugebauer: Reminiscences and appreciation. American Mathematical Monthly 101: 129–131.

    Article  Google Scholar 

  • Deimel, A. 1923. Die Inschriften von Fara, II: Schultexte aus Fara. Leipzig: J.C. Hinrichs.

    Google Scholar 

  • Deimel, A. 1924. Die Inschriften von Fara, III: Wirtschaftstexte aus Fara. Leipzig: J.C. Hinrichs.

    Google Scholar 

  • Foster, B.R., and E. Robson. 2004. A new look at the Sargonic mathematical corpus. Zeitschrift für Assyriologie 94: 1–15.

    Article  Google Scholar 

  • Friberg, J. 1978. The third millennium roots of Babylonian mathematics. I. A method for the decipherment, through mathematical and metrological analysis, of proto-Sumerian and proto-Elamitesemipictographic inscriptions. Preprint 78-09, Chalmers University of Technology.

    Google Scholar 

  • Friberg, J. 1996. Pyramids and cones in cuneiform and other mathematical texts. New hints of a common tradition. Proceedings of the Cultural History of Mathematics 6: 80–95.

    Google Scholar 

  • Friberg, J. 2000. Mathematics at Ur in the Old Babylonian period. Revue d’Assyriologie et d’Archéologie Orientale 94: 97–188.

    Google Scholar 

  • 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.

    Google Scholar 

  • Friberg, J. 2007. A remarkable collection of Babylonian mathematical texts, Manuscripts in the Schøyen collection: Cuneiform texts I. New York: Springer.

    Book  Google Scholar 

  • Gandz, S. 1940. Studies in Babylonian mathematics II: Conflicting interpretations of Babylonian mathematics. Isis 31: 405–425.

    Article  Google Scholar 

  • George, A. 2005. In search of the é.dub.ba.a: The ancient Mesopotamian school in literature and reality. In An experienced scribe who neglects nothing: Ancient Near Eastern studies in honor of Jacob Klein, ed. Y. Sefati et al., 127–137. Bethesda: CDL Press.

    Google Scholar 

  • Guitel, G. 1963. Signification mathématique d’une tablette sumérienne. Revue d’Assyriologie et d’Archéologie Orientale 57: 145–150.

    Google Scholar 

  • Hilprecht, H.V. 1906. Mathematical, metrological and chronological tablets from the library at Nippur, BE 20,1. Philadelphia: Department of Archaeology: The University of Pennsylvania.

    Google Scholar 

  • Høyrup, J. 1982. Investigations of an early Sumerian division problem. Historia Mathematica 9: 19–36.

    Article  Google Scholar 

  • Høyrup, J. 1996. Changing trends in the historiography of Mesopotamian mathematics: An insider’s view. History of Science 34: 1–32.

    Article  Google Scholar 

  • Høyrup, J. 1998. The finer structure of the Old Babylonian mathematical corpus. Elements of classification, with some results. In Assyriologica et Semitica, Festschrift für Joachim Oelsneranläßlich seines 65. Geburtstages am 18. Februar 1997, ed. J. Marzahn and H. Neumann, 117–178. Kevelaer: Neukirchen-Vluyn.

    Google Scholar 

  • Høyrup, J. 2002. Lengths, widths, surfaces: A portrait of Old Babylonian algebra and its kin. New York: Springer.

    Book  Google Scholar 

  • Isma’el, K.S., and E. Robson. 2010. Arithmetical tablets from Iraqi excavations in the Diyala. In Your praise is sweet: A memorial volume for Jeremy Black from students, colleagues and friends, ed. H.D. Baker, E. Robson, and G.G. Zólyomi, 151–164. London: British Institute for the Study of Iraq.

    Google Scholar 

  • Jestin, R. 1937. Tablettes sumériennes de Shuruppak au Musée de Stamboul. Paris: E. de Boccard.

    Google Scholar 

  • Jestin, R. 1957. Nouvelles tablettes sumériennes de Shuruppak au Musée d’Istanbul. Paris: Maisonneuve.

    Google Scholar 

  • Knuth, D.E. 1972. Ancient Babylonian algorithms. Communications for the Association of Computing Machinery 15: 671–677.

    Article  Google Scholar 

  • Kramer, S.N. 1949. Schooldays: A Sumerian composition relating to the education of a scribe. Journal of the American Oriental Society 69(4): 199–215.

    Article  Google Scholar 

  • Limet, H. 1973. Etude de documents de la période d’Agade appartenant à l’Université de Liège. Paris: Société d’Éditions ‘Les Belles Lettres’.

    Google Scholar 

  • Martin, H. 1988. Fara: A reconstruction of the ancient Mesopotamian city of Å uruppak. Birmingham: Chris Martin & Associates.

    Google Scholar 

  • Martin, H., F. Pomponio, G. Visicato, and A. Westenholz. 2001. The Fara tablets in the University of Pennsylvania Museum of Archaeology and Anthropology. Bethesda: CDL Press.

    Google Scholar 

  • Melville, D.J. 2002a. Ration computations at Fara: Multiplication or repeated addition? In Under one sky: Atronomy and mathematics in the Ancient Near East (London, 2001), AOAT, vol. 297, ed. J.M. Steele and A. Imhausen, 237–252. Münster: Ugarit-Verlag.

    Google Scholar 

  • Melville, D.J. 2002b. Weighing stones in ancient Mesopotamia. Historia Mathematica 29: 1–12.

    Article  Google Scholar 

  • Melville, D.J. 2005. The area and the side I added: Some Old Babylonian geometry. Revue d’histoire des mathématiques 11: 7–21.

    Google Scholar 

  • Neugebauer, O. 1927. Zur Entstehung des Sexagesimalsystems. Abhandlungen der Gesellschaft der Wissenschaften in Göttingen, Mathematisch-Physikalische Klasse 13: 1–55.

    Google Scholar 

  • Neugebauer, O. 1935–1937. Mathematische Keilschrifttexte I-III (MKT). Berlin: Springer.

    Google Scholar 

  • Neugebauer, O., and A. Sachs. 1945. Mathematical cuneiform texts (MCT), American oriental series, vol. 29. New Haven: American Oriental Society.

    Google Scholar 

  • 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.

    Google Scholar 

  • Pomponio, F., and G. Visicato. 1994. Early dynastic administrative texts of Å uruppak. Napoli: Istituto universitario orientale di Napoli, Dipartimento di studi asiatici.

    Google Scholar 

  • Powell, M.A. 1971. Sumerian numeration and metrology, Unpublished Ph.D. dissertation. University of Minnesota, Minneapolis.

    Google Scholar 

  • Powell, M.A. 1972a. The origin of the sexagesimal system: The interaction of language and writing. Visible Language 6: 5–18.

    Google Scholar 

  • Powell, M.A. 1972b. Sumerian area measures and the alleged decimal substratum. Zeitschrift für Assyriologie und Vorderasiatische Archäologie 62: 165–221.

    Article  Google Scholar 

  • Powell, M.A. 1976. The antecedents of Old Babylonian place notation and the early history of Babylonian mathematics. Historia Mathematica 3: 414–439.

    Article  Google Scholar 

  • Powell, M.A. 1990. Masse und Gewichte. In Reallexikon der Assyriologie, vol. 7, ed. D.O. Edzard et al., 457–530. Berlin/New York: De Gruyter.

    Google Scholar 

  • Proust, C. 2007. Tablettes mathématiques de Nippur. Paris: Institut français d’études anatoliennes Georges-Dumezil.

    Google Scholar 

  • Proust, C. 2008. Tablettes mathématiques de la collection Hilprecht, Texte und Materialen der Frau Professor Hilprecht Collection, vol. 8. Leipzig: HarrassowitzVerlag.

    Google Scholar 

  • Proust, C. 2009. Deux nouvelles tablettes mathématiques du Louvre: AO 9071 et AO 9072. Zeitschrift für Assyriologie und Vorderasiatische Archäologie 99: 167–232.

    Article  Google Scholar 

  • Proust, C. 2012. Reading colophons from Mesopotamian clay tablets dealing with mathematics. NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 20: 123–156.

    Article  Google Scholar 

  • Proust, C. 2015. Mathematical and philological insights on cuneiform texts. Neugebauer’s correspondence with fellow Assyriologists, Dordrecht: Springer.

    Google Scholar 

  • Rashed, R., and L. Pyenson. 2012. Otto Neugebauer, Historian. History of Science 30, preprint.

    Google Scholar 

  • Ritter, J. 1995a. Babylon -1800. In A history of scientific thought, ed. M. Serres, 17–43. Oxford: Blackwell.

    Google Scholar 

  • Ritter, J. 1995b. Measure for measure: Mathematics in Egypt and Mesopotamia. In A history of scientific thought, ed. M. Serres, 44–72. Oxford: Blackwell.

    Google Scholar 

  • Ritter, J. 2004. Reading Strasbourg 368: A thrice-told tale. In History of science, history of text, ed. K. Chemla, 177–200. New York: Springer.

    Chapter  Google Scholar 

  • Robson, E. 1999. Mesopotamian mathematics, 2100-1600 BC. Technical constants in bureaucracy and education), OECT, vol. 14. Oxford: Clarendon.

    Google Scholar 

  • Robson, E. 2000. Mathematical cuneiform tablets in Philadelphia. I. Problems and calculations. SCIAMVS 1: 11–48.

    Google Scholar 

  • Robson, E. 2001. The Tablet House: A scribal school in Old Babylonian Nippur. Revue d’Assyriologie et d’Archéologie Orientale 95: 39–66.

    Article  Google Scholar 

  • Robson, E. 2002. More than metrology: Mathematics education in an Old Babylonian scribal school. In Under one sky: Astronomy and mathematics in the ancient Near East (London, 2001), AOAT, vol. 297, ed. J.M. Steele and A. Imhausen, 325–365. Münster: Ugarit-Verlag,

    Google Scholar 

  • Robson, E. 2004. Mathematical cuneiform tablets in the Ashmolean Museum, Oxford. SCIAMVS 5: 3–65.

    Google Scholar 

  • Robson, E. 2008. Mathematics in Ancient Iraq: A social history. Princeton: Princeton University Press.

    Google Scholar 

  • Sarton, G. 1940. Remarks on the study of Babylonian Mathematics. Isis 31: 398–404.

    Article  Google Scholar 

  • Schlimm, D., and T.R. Widom. 2012. Methodological reflections on typologies for numerical notations. Science in Context 25(2): 155–195.

    Article  Google Scholar 

  • Steinkeller, P. 1987. The administrative and economic organization of the Ur III state: The core and the periphery. In The organization of power: Aspects of bureaucracy in the Ancient Near East, Studies in ancient oriental civilization, vol. 46, ed. McG. Gibson and R.D. Biggs, 19–41. Chicago: Oriental Institute of the University of Chicago.

    Google Scholar 

  • Swerdlow, N. 1993. Otto E. Neugebauer (26 May 1899–19 February 1990). Proceedings of the American Philosophical Society 137: 138–165.

    Google Scholar 

  • Thureau-Dangin, F. 1928. L’Origine du système sexagésimal. Revue d’Assyriologie et d’Archéologie Orientale 25: 115–121.

    Google Scholar 

  • Thureau-Dangin, F. 1929. L’Origine du système sexagésimal. Un postscriptum. Revue d’Assyriologie et d’Archéologie Orientale 26: 43.

    Google Scholar 

  • Thureau-Dangin, F. 1932. Esquisse d’une histoire du système sexagésimal. Paris: Geuthner.

    Google Scholar 

  • Thureau-Dangin, F. 1936. L’Équation du deuxième degré dans la mathématique babylonienne d’après une tablette inédite du British Museum. Revue d’Assyriologie et d’Archéologie Orientale 33: 27–48.

    Google Scholar 

  • Thureau-Dangin, F. 1938. Textes mathématiques babyloniens (TMB). Leiden: Ex Oriente Lux 1.

    Google Scholar 

  • Thureau-Dangin, F. 1939. Sketch of a history of the sexagesimal system. Osiris 7: 95–141.

    Article  Google Scholar 

  • Tinney, S. 1998. Texts, tablets and teaching. Expedition 40(2): 40–50.

    Google Scholar 

  • Tinney, S. 1999. On the curricular setting of Sumerian literature. Iraq 61: 159–172.

    Article  Google Scholar 

  • Van De Mieroop, M. 2004. A history of the ancient Near East ca. 3000–232 bc. Oxford: Blackwell.

    Google Scholar 

  • Veldhuis, N. 1997. Elementary education at Nippur: The lists of trees and wooden objects. Unpublished doctoral thesis, University of Groningen.

    Google Scholar 

  • Veldhuis, N. 2004. Religion, literature, and scholarship: The Sumerian composition NanÅ¡e and the birds. With a catalogue of Sumerian bird names, Cuneiform monographs, vol. 22. Leiden: Brill Publications.

    Google Scholar 

  • Visicato, G. 1995. The Bureaucracy of Å uruppak. Münster: Ugarit-Verlag.

    Google Scholar 

  • Visicato, G. 2000. The power and the writing. Bethesda: CDL Press.

    Google Scholar 

  • Woods, C. (ed.). 2010. Visible language: Inventions of writing in the ancient Middle East and beyond. Chicago: The Oriental Institute.

    Google Scholar 

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Melville, D.J. (2016). After Neugebauer: Recent Developments in Mesopotamian Mathematics. In: Jones, A., Proust, C., Steele, J. (eds) A Mathematician's Journeys. Archimedes, vol 45. Springer, Cham. https://doi.org/10.1007/978-3-319-25865-2_8

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