BIBLIOGRAPHY OF MESOPOTAMIAN MATHEMATICS

This bibliography is by no means exhaustive -- I've tried to give the most reliable and/or up-to-date references wherever possible, and I may well have missed out a work or two through my own inefficiency. For a more complete bibliography up to the early 1980s, see Friberg's contribution to Dauben 1985 cited below. Thereafter, one can chase relevant works and authors through the regular bibliographies in Historia Mathematica (annotated) and the Assyriological journal Orientalia (unannotated but well cross-referenced).

 I've assumed knowledge of English, French and German only -- which means omitting works in Russian and Italian in particular.

If you would like further information or advice on anything in particular, do e-mail me. I'll try my very best to help but I'm afraid I can't always respond immediately, particularly in term-time.

 Dr. Eleanor Robson
eleanor.robson@wolfson.ox.ac.uk
Oriental Institute
University of Oxford
Pusey Lane
Oxford OX1 2LE
UK
 

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HISTORIES OF MATHS WHICH INCLUDE A SECTION ON ANCIENT MESOPOTAMIA

Most histories of maths have a section on 'Babylonian' maths, which minimally consist of a discussion of the sexagesimal place value system and Plimpton 322. Most seem heavily reliant on Neugebauer 1954/69 below. Some of the more interesting ones are:

 Fauvel, J. and Gray, J. (1987), The history of mathematics: a reader, Macmillan/Open University. Extracts of text translations and other works cited below.

 Joseph, G. G. (1991). The crest of the peacock: non-European roots of mathematics, Harmondsworth: Penguin. Some errors, but particularly valuable for the introductory chapter, which looks at transmission from the Middle East to Europe.

 Neugebauer, O. (1954, 1969). The exact sciences in antiquity, New York: Dover.

 Vogel, K. (1958-59). Vorgriechische Mathematik, Würzburg.
 

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OVERVIEWS OF MESOPOTAMIAN MATHS, AND THE MAIN TEXT EDITIONS

Bruins, E. M., and Rutten, M. (1961). Textes mathématiques de Suse (MDP 34), Paris. Around 30 mathematical tablets from late OB Susa, in SW Iran, with unsatisfactory and idiosycratic translation and commentary. See W. von Soden's review in Bibliotheca Orientalis 21 (1964), 44-50.

 Friberg, J. (1985). 'Babylonian mathematics', in The history of mathematics from antiquity to the present: a selective bibliography (ed. J. W. Dauben), New York: Garland, 37-51. Friberg, J. (1987-90). 'Mathematik', in Reallexikon der Assyriologie VII (ed. D. O. Edzard et al.), Berlin and New York: De Gruyter, 531-585. In English. comprehensive but rather reader-unfriendly. See W. Hallo's review in Bibliotheca Orientalis 50 (1993), 162-166.

 Høyrup, J. (1992). 'Mathematics, algebra, and geometry', in The Anchor Bible Dictionary IV (ed. D. N. Freedman), New York, 601-612.

 Høyrup, J. (1994). 'Babylonian mathematics', in Companion encyclopædia for the history and philosophy of the mathematical sciences I, (ed. I. Grattan-Guinness), London: Routledge, 21-29.

 *Høyrup, J. (1996). 'Changing trends in the historiography of Mesopotamian mathematics: an insider's view', History of Science 34, 1-32.

 Nemet-Nejat, K. R. (1993). Cuneiform mathematical texts as a reflection of everyday life in Mesopotamia (American Oriental Series 75), New Haven: American Oriental Society. Naive survey of 'practical' mathematics, with long (but inaccurate) bibliography. To be handled with care, and in conjuction with my review in Bibliotheca Orientalis 52 (1995), 424-432.

 Neugebauer, O. (1935-37). Mathematische Keilschrifttexte I-III, Berlin. Reprinted in 1973.

Neugebauer, O. and Sachs, A. (1945). Mathematical cuneiform texts (American Oriental Series 29), New Haven: American Oriental Society. Reprinted in 1986 and available from Harrassowitz.

Powell, M. A. (1987-90). 'Masse und Gewichte, in Reallexikon der Assyriologie VII (ed. D. O. Edzard et al.), Berlin and New York: De Gruyter, 457-530. In English.

Powell, M. A. (1995). 'Metrology and mathematics in ancient Mesopotamia', in Civilizations of the ancient Near East III (ed. J. M. Sasson), New York: Scribners, 1941-1958.

 Ritter, J. (1989). 'Chacun sa verité; les mathématiques en Egypte et en Mesopotamie', in Elements d'histoire des sciences (ed. M. Serres), Paris, 39-61.

 *Robson, E. (1996). 'From Uruk to Babylon: 4500 years of Mesopotamian mathematics', in História e Educação Matemática -- proceedings I (ed. J. M. Lagarto et al.), Porto, 35-44.

 Thureau-Dangin, F. (1938). Textes mathématiques babyloniens (Ex Oriente Lux 1), Leiden. Same content as Neugebauer 1935-37, but in a different format - just transcriptions, translations and little discussion.

 Vaiman, A. A. (1960). Über die sumerisch-babylonische angewandte Mathematik. (XXV Internationaler Orientalisten Kongress, Vorträge der Delegation des UdSSR), Moscow.
 

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PRE-OB MATHS AND NUMERATION

Archi, A. (1989). 'Tables de comptes eblaites', Revue d'Assyriologie 83, 2-6. Mid III mill. Syria.

 Damerow, P., and Englund, R. (1987). 'Die Zahlzeichensystem der Archaischen Texten aus Uruk'. in Archaischen Texte aus Uruk, (eds. M. Green and H. J. Nissen), 117-166. Earliest tablets, c. 3000 BC.

 Edzard, D. O. (1969). 'Eine altsumerische Rechentafel (OIP 14, 70)'. in lishan mithurti, Festschrift von Soden, (ed. W. Röllig), Neukirchen-Vluyn, 101-104.

 Friberg, J. (1986). 'Three remarkable texts from ancient Ebla'. Vicino Oriente 6, 3-25.

 Høyrup, J. (1982). 'Investigations of an early Sumerian division problem'. Historia Mathematica 9, 19-32.

Nissen, H. J., Damerow, P. and Englund, R. (1990). Frühe Schrift und Techniken der Wirtschaftsverwaltung im Alten Orient, Berlin. Now translated into English as Archaic bookkeeping : early writing and techniques of the economic administration in the ancient Near East, University of Chicago Press 1993. Beautifully produced and written, and right up-to-the-minute. A must-read!

 Powell, M. A. (1971). Sumerian numeration and metrology (University Microfilms 72-14 445), Minneapolis.

 Powell, M. A. (1972). 'The origin of the sexagesimal system: the interaction of language and writing', Visible Language 6, 5-18.

 Powell, M. A. (1976). 'The antecedents of Old Babylonian place notation and the early history of Babylonian mathematics', Historia Mathematica 3, 414-439.

 Powell, M. A. (1976). 'Two notes on metrological mathematics in the Sargonic period'. Revue d'Assyriologie 70, 97-102.

 Schmandt-Besserat, D. (1992). Before writing I-II, Dallas. On preliterate accounting. Essentially right, though rather over-enthusiastic. Must be read in conjunction with one or more of the following reviews:
 
 

Whiting, R. M. (1984). 'More evidence for sexagesimal calculations in the third millennium'. Zeitschrift für Assyriologie 74, 59-66.
 

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OB (OLD BABYLONIAN = EARLY SECOND MILLENNIUM) MATHS

Al-Rawi, F. and Roaf, M. (1984). 'Ten Old Babylonian mathematical problems from Tell Haddad'. Sumer 43, 175-218. From the volume of a truncated cone to the labour involved in manufacturing bricks.

 Baqir, T. (1950a). 'An important mathematical problem text from Tell Harmal'. Sumer 6, 39-54. On 'Pythagorean' triangles.

 Baqir, T. (1950b). 'Another important mathematical text from Tell Harmal'. Sumer 6, 130-148. Three problems and a little coefficient list.

 Baqir, T. (1951). 'Some more mathematical texts'. Sumer 7, 28-45. Ten problem texts on various subjects.

 Baqir, T. (1962). 'Tell Dhiba'i: new mathematical texts'. Sumer 18, 11-14. Geometrical tablet.

 Brack-Bernsen, L. and Schmidt, O. (1990). 'Bisectable trapezia in Babylonian mathematics'. Centaurus 33, 1-38.

Caveing, M. (1985). 'La tablette babylonienne AO 17264 du Musee du Louvre et la probleme des six fr&egraveres', Historia Mathematica 12, 6-24. On division of trapezia.

 Friberg, J. (1981). 'Methods and traditions of Babylonian mathematics: Plimpton 322, Pythagorean triples and the Babylonian triangle parameter equation', Historia Mathematica 8, 277-318.

 Friberg, J. (1981). 'Methods and traditions of Babylonian mathematics 2: an Old Babylonian catalogue text with equations for squares and circles'. Journal of Cuneiform Studies 33, 57-64.

 Goetze, A. (1951). 'A mathematical compendium from Tell Harmal'. Sumer 7, 126-155. Coefficient list and teacher's list combined.

 Harper, P. O., Aruz, J. and Tallon, F. (1992). The royal city of Susa. Ancient Near Eastern treasures in the Louvre, New York. Contains photos and a brief discussion of two tablets published by Bruins and Rutten (1961).

 Høyrup, J. (1990). 'Algebra and naive geometry: an investigation of some basic aspects of Old Babylonian mathematical thought'. Altorientalische Forschungen 17, 27-69; 262-354. Difficult, but absolutely central to understanding OB maths.

 Høyrup, J. (1993). 'On subtractive operations, subtractive numbers and purportedly negative numbers in Old Babylonian mathematics'. Zeitschrift für Assyriologie 83, 42-60.

 Høyrup, J. (1993). ' "Remarkable numbers" in Old Babylonian mathematical texts: a note on the psychology of numbers'. Journal of Near Eastern Studies 52, 281-286.

 Høyrup, J. (1993). 'Mathematical Susa texts VII and VIII. A reinterpretation', Altorientalische Forschungen 20, 245-260.

Kilmer, A. D. (1960). 'Two new lists of key numbers for mathematical operations'. Orientalia 29, 273-308. Now superseded by my (as yet unpublished) D.Phil. thesis 'Old Babylonian coefficient lists', Oxford 1995.

 Kilmer, A. D. (1990). 'Sumerian and Akkadian names for designs and geometrical shapes'. in Investigating artistic environments in the ancient Near East, (ed. A. Gunter), New York, 83-91. Mainly useful for its summaries of Vaiman's work in Russian.

 Knuth, D. (1972). 'Ancient Babylonian algorithms'. Communications for the Association of Computing Machinery 15, 671-677, with corrections in vol. 19 (1976), 108.

 Leemans, W. F. and Bruins, E. M. (1951). 'Un texte vieux-babylonien concernant des cercles concentriques'. Comptes Rendus de la Rencontre Assriologique Internationale 2, 31-35.

 Neugebauer, O. and Sachs, A. (1984). 'Mathematical and metrological texts'. Journal of Cuneiform Studies 36, 243-251. OB tables and rough work from Nippur.

 Powell, M. A. (1982a). 'Metrological notes on the Esagila tablet and related matters. Appendix II: bricks as evidence for metrology'. Zeitschrift für Assyriologie 72, 116-123. On the OB maths of bricks.

Powell, M. A. (1982b). 'Merodach-Baladan at Dur-Jakin: a note on the defense of Babylonian cities'. Journal of Cuneiform Studies 34, 59-61. On a mathematical problem from the tablet BM 85194.

 Powell, M. A. (1984). 'Late Babylonian surface mensuration: a contribution to the history of Babylonian agriculture and arithmetic'. Archiv für Orientforschungen 31, 32-66. With sections on OB maths and capacity metrology.

 Powell, M. A. (1988). 'Evidence for agriculture and waterworks in Babylonian mathematical texts'. Bulletin on Sumerian Agriculture 4, 161-177.

 Price, D. J. de Solla (1964). 'The Babylonian "Pythagorean triangle" tablet.' Centaurus 10, 219-231. - i.e. Plimpton 322.

 Ritter, J. (1987). 'Les practiques de la raison en Mesopotamie', in La naissance de la raison en Gr&egravece (Actes du Congr&egraves de Nice, mai 1987), Paris, 99-110. On logical structure of OB problem texts, and their relation to other contemporary 'scientific' texts.

 Ritter, J. (1989). 'Babylone -- 1800', in Elements d'histoire des sciences (ed. M. Serres), Paris, 17-37.

 Robson, E. (1995). 'More on "Pythagoras' Theorem" in ancient Mesopotamia'. British Society for the History of Mathematics Newsletter 28 (Spring 1995), 34-38. Note and illustration about new tablet.

 Robson, E. (in press). 'Building with bricks and mortar: quantity surveying in the Ur III and Old Babylonian periods'. in Houses and households in ancient Mesopotamia: papers read at the 40e Rencontre Assyriologique Internationale, (ed. K. R. Veenhof), Istanbul. On Ur III and OB problems about building walls, and a new tablet. *Should* be out this year...

 Sachs, A. J. (1946). 'Notes on fractional expressions in Old Babylonian mathematical texts', Journal of Near Eastern Studies 5, 203-214.

Sachs, A. J. (1947). 'Babylonian mathematical texts I: reciprocals of regular sexagesimal numbers'. Journal of Cuneiform Studies 1, 219-240.

 Sachs, A. (1952). 'Babylonian mathematical texts II: approximations of reciprocals of irregular numbers in an Old Babylonian text. III: the problem of finding the cube root of a number'. Journal of Cuneiform Studies 6, 151-156.

 Saggs, H. W. F. (1960). 'A Babylonian geometrical text'. Revue d'Assyriologie 54, 131-145. That lovely big tablet with lots of geometrical pictures on, often illustrated in the secondary literature - it's on display at the British Museum too.

 Schmidt, O. (1980). 'On Plimpton 322: Pythagorean numbers in Babylonian mathematics', Centaurus 24, 4-13.

 Soubeyran, D. (1984). 'Textes mathematiques de Mari'. Revue d'Assyriologie 78, 19-48.
 

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POST-OB MATHS

Britton, J. P. (1991-93). 'A table of 4th powers and related texts from Seleucid Babylon'. Journal of Cuneiform Studies 43-45, 71-78. Includes survey of all known LB table texts.

 Friberg, J. (1993). 'On the structure of cuneiform metrological table texts from the -1st millennium'. in Die Rolle der Astronomie in Kulturen Mesopotamiens (Grazer Morgenländische Studien 3), (ed. H. D. Galter), Graz, 383-405.

 Friberg, J., Hunger, H. and Al-Rawi, F. (1990). ' "Seed and reeds", a metro-mathematical topic text from Late Babylonian Uruk'. Baghdader Mitteilungen 21, 483-577. First major discussion of LB maths for decades - and some OB too.

 Horowitz, W. (1993). 'The reverse of the Neo-Assyrian planisphere CT 33 11'. in Die Rolle der Astronomie in Kulturen Mesopotamiens (Grazer Morgenländische Studien 3), (ed. H. D. Galter), Graz, 149-159. Which turns out to be a survivor of OB maths tradition, including very OB terminology. The following article is on the same tablet (now recatalogued as HS 245).

 Powell, M. A. (1984). 'Late Babylonian surface mensuration: a contribution to the history of Babylonian agriculture and arithmetic'. Archiv für Orientforschungen 31, 32-66.

Rochberg-Halton, F. (1983). 'Stellar distances in early Babylonian astronomy: a new perspective on the Hilprecht text (HS 229)'. Journal of Near Eastern Studies 42, 209-217.
 

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TRANSMISSION TO OTHER CULTURES

Høyrup, J. (1985). 'Varieties of mathematical discourse in pre-modern socio-cultural contexts: Mesopotamia, Greece and the Latin Middle Ages'. Science and Society 49, 4-41.

 Høyrup, J. (1990). 'Dynamis, the Babylonians and Theaetetus 147c7-148d7', Historia Mathematica 17, 201-222; 18, 19. But see Fowler, D. H. (1992). 'Dynamis, mithartum and square'. Historia Mathematica 19, 418-419.

 Høyrup, J. (1990). 'On parts of parts and ascending continued fractions. An investigation of the origins and spread of a peculiar system', Centaurus 33, 293-324.

 *Høyrup, J. (1990). 'Sub-scientific mathematics. Observations on a pre-modern phenomenon', History of Science 28, 63-86.

 *Høyrup, J. (1996). ' "The four sides and the area". Oblique light on the prehistory of algebra', in Vita mathematica. Historical research and integration with teaching (ed. R. Calinger), Washington, 45-65.

 Neugebauer, O. (1963). 'The survival of Babylonian methods in the exact sciences of Antiquity and the Middle Ages', Proceedings of the Americal Philosophical Society 107, 528-535.
 

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GENERAL HISTORY AND CULTURE OF MESOPOTAMIA: 
the best and most widely available.

Black, J. A. and Green, A. (1992), Gods, demons and symbols of ancient Mesopotamia, London: British Museum Press.

 Caplice, R. (1988), Introduction to Akkadian (Studia Pohl: Series Maior 9), Rome: Biblical Institute Press.

Collon, D. (1995) Ancient Near Eastern art, London: British Museum Press.

 Dalley, S. M. (1989). Myths from Mesopotamia, Oxford: OUP World's Classics.

 Foster, B. (1993) Before the muses: an anthology of Akkadian literature I-II, Bethesda: CDL Press.

 Freedman, D. N. (ed.) (1992), The Anchor Bible Dictionary I-V, New York : Anchor Doubleday.

 Kuhrt, A. (1995), The ancient Near East : c. 3000-330 BC I-II, London: Routledge .

 Postgate, J. N. (1992), Early Mesopotamia: society and economy at the dawn of history, London: Routledge.

 Roaf, M. (1990), Cultural atlas of Mesopotamia and the ancient Near East, Oxford: Facts on File.

 Roux, G. (1992), Ancient Iraq, Harmondsworth: Penguin.

 Saggs, H. W. F. (1995), The Babylonians. Peoples of the past, London: British Museum Press.

 Sasson, J. M. (ed.) (1995), Civilizations of the ancient Near East I-IV, New York: Scribner's.

 Thomsen, M.-L. (1994), The Sumerian language (Mesopotamia 10), Copenhagen: Akademisk Forlag.

 Walker, C. B. F. (1987),Cuneiform. Reading the past, London: British Museum Press.


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Created on 1.iii.96. Latest version (improved formatting; some additions, marked with *) 8.i.97

 eleanor.robson@wolfson.ox.ac.uk