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Babylonian Mathematics

From the Yale Babylonian Collection, with the assistance and permission of William Hallo, Curator, and Ulla Kasten, Associate Curator. Provenance unknown, dated approximately to between 1800 B.C. and 1600 B.C. Purchased around 1912 A.D. by an agent of J. P. Morgan, who contributed it to Yale University as part of the foundation of its Babylonian Collection. The images are very close to life-size (about 8 cm on a side).

"The photographs( by Prof. Bill Casselman,department of Mathematics,U British Columbia ), were made with a Nikon CoolPix 990, a portable floodlight, a Benbo tripod, and a special cable release designed for this camera. I wish to acknowledge not only the extraordinarily friendly reception from the Curators of the Babylonian Collection, but also the help of Christopher Anagnostakis in making the photographs"



Babylonian clay tablet






Content of Babylonian Mathematics

Comparison with Greek and Vedic-Indic mathematics

Relative antiquity of Babylonian Mathematics vs. the mathematics of the Vedics







From, Otto Neugebauer The exact sciences in Antiquity,Plate 13 and 14




  1. A Aaboe, Episodes from the Early History of Mathematics (1964).
  2. R Calinger, A conceptual history of mathematics (Upper Straddle River, N. J., 1999).
  3. J Friberg, The third millenium roots of Babylonian mathematics. I. A method for the decipherment, through mathematical and metrological analysis, of proto-Sumerian and proto-Elamite semipictographic inscriptions, Department of Mathematics, University of Göteborg No. 9 (Göteborg, 1978).
  4. G Ifrah, A universal history of numbers : From prehistory to the invention of the computer (London, 1998).
  5. G G Joseph, The crest of the peacock (London, 1991).
  6. O Neugebauer and A Sachs, Mathematical Cuneiform Texts (New Haven, CT., 1945).
  7. B L van der Waerden, Science Awakening (Groningen, 1954).
  8. B L van der Waerden, Geometry and Algebra in Ancient Civilizations (New York, 1983).



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  4. L Brack-Bernsen and O Schmidt, Bisectable trapezia in Babylonian mathematics, Centaurus 33 (1) (1990), 1-38.
  5. E M Bruins, A contribution to the interpretation of Babylonian mathematics; triangles with regular sides, Nederl. Akad. Wetensch. Proc. Ser. A. Indagationes Math. 15 (1953), 412-422.
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  9. E M Bruins, Computation in the old Babylonian period, Janus 58 (1971), 222-267.
  10. M Caveing, La tablette babylonienne AO 17264 du Musée du Louvre et le problème des six frères, Historia Math. 12 (1) (1985), 6-24.
  11. S Démare-Lafont, Les partages successoraux paléobabyloniens, Histoire de fractions, fractions d'histoire, Sci. Networks Hist. Stud. 10 (Basel, 1992), 103-114; 404; 410.
  12. J Friberg, Methods and traditions of Babylonian mathematics. II. An old Babylonian catalogue text with equations for squares and circles, J. Cuneiform Stud. 33 (1) (1981), 57-64.
  13. S Gandz, A few notes on Egyptian and Babylonian mathematics, in Studies and Essays in the History of Science and Learning Offered in Homage to George Sarton on the Occasion of his Sixtieth Birthday, 31 August 1944 (New York, 1947), 449-462.
  14. S Gandz, Studies in Babylonian mathematics. I. Indeterminate analysis in Babylonian mathematics, Osiris 8 (1948), 12-40.
  15. S Gandz, Studies in Babylonian mathematics. II. Conflicting interpretations of Babylonian mathematics, Isis 31 (1940), 405-425.
  16. S Gandz, Studies in Babylonian mathematics. III. Isoperimetric problems and the origin of the quadratic equations, Isis 32 (1940), 101-115.
  17. R J Gillings and C L Hamblin, Babylonian sexagesimal reciprocal tables, Austral. J. Sci. 27 (1964), 139-141.
  18. J Hoyrup, The Babylonian cellar text BM 85200+ VAT 6599. Retranslation and analysis, Amphora (Basel, 1992), 315-358.
  19. J Hoyrup, Babylonian mathematics, in I Grattan-Guinness (ed.), Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences (London, 1994), 21-29.
  20. S Ilic, M S Petkovic and D Herceg, A note on Babylonian square-root algorithm and related variants, Novi Sad J. Math. 26 (1) (1996), 155-162.
  21. D E Knuth, Ancient Babylonian algorithms, Twenty-fifth anniversary of the Association for Computing Machinery, Comm. ACM 15 (7) (1972), 671-677.
  22. D E Knuth, Errata: "Ancient Babylonian algorithms", Comm. ACM 19 (2) (1976), 108.
  23. H Lewy, Marginal notes on a recent volume of Babylonian mathematical texts, J. Amer. Oriental Soc. 67 (1947), 305-320.
  24. J S Liu, A general survey of Babylonian mathematics (Chinese), Sichuan Shifan Daxue Xuebao Ziran Kexue Ban 16 (1) (1993), 80-87.
  25. K Muroi, A circular field problem in the late Babylonian metrological-mathematical text W 23291-x, Ganita-Bharati 19 (1-4) (1997), 86-90.
  26. K Muroi, An enigmatic sentence in the old Babylonian table of exponents and logarithms, Historia Sci. (2) 6 (3) (1997), 229-230.
  27. K Muroi, Babylonian mathematics - ancient mathematics written in cuneiform writing (Japanese), in Studies on the history of mathematics (Kyoto, 1998), 160-171.
  28. K Muroi, Early Old Babylonian mathematical problems written in Sumerian, Historia Sci. (2) 7 (3) (1998), 199-203.
  29. K Muroi, Extraction of cube roots in Babylonian mathematics, Centaurus 31 (3-4) (1988), 181-188.
  30. K Muroi, Inheritance problems of Babylonian mathematics, Historia Sci. No. 34 (1988), 11-19.
  31. K Muroi, Interest calculation of Babylonian mathematics: new interpretations of VAT 8521 and VAT 8528, Historia Sci. No. 39 (1990), 29-34.
  32. K Muroi, Small canal problems of Babylonian mathematics, Historia Sci. (2) 1 (3) (1992), 173-180.
  33. K Muroi, The expressions of zero and of squaring in the Babylonian mathematical text VAT 7537, Historia Sci. (2) 1 (1) (1991), 59-62.
  34. K Muroi, Two harvest problems of Babylonian mathematics, Historia Sci. (2) 5 (3) (1996), 249-254.
  35. M A Powell Jr, The antecedents of old Babylonian place notation and the early history of Babylonian mathematics, Historia Math. 3 (1976), 417-439.
  36. A E Raik, From the early history of algebra. Quadratic equations among the Babylonians (Russian), Molotov. Gos. Univ. Uc. Zap. 8 (1) (1953), 31-63.
  37. A J Sachs, Babylonian mathematical texts. I. Reciprocals of regular sexagesimal numbers, J. Cuneiform Studies 1 (1947), 219-240.
  38. A J Sachs, Some metrological problems in Old-Babylonian mathematical texts, Bull. Amer. Schools of Oriental Research no. 96 (1944), 29-39.
  39. A J Sachs, Notes on fractional expressions in Old Babylonian mathematical texts, J. Near Eastern Studies 5 (1946), 203-214.
  40. G Sarton, Remarks on the study of Babylonian mathematics, Isis 31 (1940), 398-404.
  41. M Wygodski, Mathematics of the ancient Babylonians (Russian), Uspekhi Matem. Nauk 7 (1940), 102-153.
  42. M Wygodski, The mathematics of the ancient Babylonians (Russian), Uspekhi Matem. Nauk 8 (1941), 293-335.



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