The Phrontistery

Books by Stephen Chrisomalis
Numerical Notation: A Comparative History Human Expeditions: Inspired by Bruce Trigger

Numerical Notation Bibliography

This is a bibliography of 1047 academic publications about numerals, numeral systems, numerical notation and numeration. It is a working bibliography for my doctoral dissertation, The Comparative History of Numerical Notation (McGill, 2003), and related papers. The references primarily focus on numeral symbols (like Roman numerals) rather than number words, but there is plenty of information on numeration in general. Most of the sources are in English, but a few are in other languages. If you know of any source that I have not listed, or are interested in this topic, feel free to contact me.

Of course, you may not be looking for hundreds of obscure papers, but simply wish to find some general sources. If so, please check out my Numeration Books page, where I review about 20 interesting and important books on numerals and numeration. If you would like to purchase any of them, they are available for sale through on that page, with any proceeds going to defray the cost of maintaining this site.

Note (Jan 24/08): ANTH357 students, you will not find what you are looking for here!

  1. Aaboe, Asger. 1964. Episodes from the Early History of Mathematics. New York.
  2. Abramian, R., ed. 1965. Pekhleviisko-persidsko-armiano-russko-angliiskii slovar. Erevan Mitk.
  3. Acharya, Subrata Kumar. 1993. The transition from the numerical from the decimal system in the inscriptions of Orissa. Journal of the Epigraphical Society of India 19: 52-62.
  4. Adams, G.B. 1965. Counting-rhymes and systems of numeration. Ulster Folklife 11: 87-98.
  5. Adams, R.F.G. 1947. Obåri Okaimå: a new African language and script. Africa 17: 24-34.
  6. Adkins, Julia E. 1956. Historical and analytical study of the tally, the knotted cord, the fingers, and the abacus. Ph.D. dissertation, Ohio State University.
  7. Aghali-Zakara, Mohammed. 1993. Les lettres et les chiffres: écrire en berbère. In A la croisée des études libyco-berbères: mélanges offerts à Paulette Galand-Pernet et Lionel Galand, ed. Jeannine Drouin and Arlette Roth, pp. 141-155. Paris: Librairie Orientaliste Paul Geuthner.
  8. Aharoni, Yohanan. 1966. The use of hieratic numerals in Hebrew ostraca and the shekel weights. Bulletin of the American School of Oriental Research 184: 13-19.
  9. Ahmad, Qeyamuddin. 1973. Corpus of Arabic and Persian Inscriptions of Bihar. Patna: K.P. Jayaswal Research Institute.
  10. Alföldi-Rosenbaum, Elisabeth. 1971. The finger calculus in antiquity and in the Middle Ages. Frühmittelalterliche Studien 5: 1-9.
  11. Allard, André. 1973. Les procédés de multiplication des nombres entiers dans le calcul indien à Byzance. Bulletin de l'historique belge de Rome 43: 111-143.
  12. Allard, André. 1977. Le premier traité byzantin de calcul indien: classement des manuscrits et édition critique du texte. Revue d'histoire des textes 7: 57-107.
  13. Allrik, H.L. 1954. The lists of Zerubabel (Nehemiah 7 and Ezra 2) and the Hebrew numeral notation. Bulletin of the American Schools of Oriental Research 136: 21-27.
  14. Alvis, Robert Lee. 1985. Speculations on the Interpretation of Number Systems as a Historically Diffused Cultural Element. M.A. thesis, University of Oregon.
  15. Anderson, W. French. 1956. Arithmetical computations in Roman numerals. Classical Philology 51(3): 145-150.
  16. Anderson, W. French. 1958. Arithmetical procedure in Minoan Linear A and in Minoan-Greek Linear B. American Journal of Archaeology 62: 363-369.
  17. Anderson, W. French. 1971. Arithmetic in Maya numerals. American Antiquity 36(1): 54-63.
  18. Ang Tian-Se and Frank J. Swetz. 1986. A Chinese mathematical classic of the third century: the Sea Island Manual of Liu Hui. Historia Mathematica 13: 99-117.
  19. Ang Tian-Se. 1978. Chinese interest in right-angled triangles. Historia Mathematica 5: 253-266.
  20. Anonymous. 1960. Precious Watches from the 16th to the 19th century. Omega Publications.
  21. Anonymous. 1994. The right to inscribe non-Hebrew characters on tombstones. Justice 1: 28-29.
  22. Anonymous. 1996. The Vitale Collection of Highly Important European Clocks, part II. London, Tues. Nov. 26, 1996. London: Christie's.
  23. Araujo, Frank P. 1975. Counting sheep in Basque. Anthropological Linguistics 17 (4): 139-145.
  24. Archibald, R.C. 1921. 1321, 1471, 1521, 1571, 1621, 1671, 1721, 1771, 1821. American Mathematical Monthly 28(11-12): 423-427.
  25. Archibald, R.C. 1936. Babylonian mathematics. Isis 26: 63-81.
  26. Armstrong, Robert G. 1962. Yoruba Numerals. London: Oxford University Press.
  27. Arnett, William S. 1982. The Predynastic Origin of Egyptian Hieroglyphs. Washington: University Press of America.
  28. Ascher, Marcia and Robert Ascher. 1972. Numbers and relations from ancient Andean quipus. Archive for History of Exact Sciences 8: 288-320.
  29. Ascher, Marcia and Robert Ascher. 1980. Code of the Quipu: A Study in Media, Mathematics and Culture. Ann Arbor: University of Michigan Press.
  30. Ascher, Marcia and Robert Ascher. 1986. Ethnomathematics. History of Science 24: 125-144.
  31. Ascher, Marcia and Robert Ascher. 1989. Are there numbers in the sky? IN Time and Calendars in the Inca Empire, Mariusz S. Ziolkowski and Robert M. Sadowski, pp. 35-48. BAR International Series 479.
  32. Ascher, Marcia and Robert Ascher. 1997. Ethnomathematics. IN Ethnomathematics: Challenging Eurocentrism in Mathematics Education, Arthur B. Powell and Marilyn Frankenstein, eds., pp. 25-50. Albany: SUNY Press.
  33. Ascher, Marcia. 1983. The logical-numerical system of Inca quipus. Annals of the History of Computing 5(3): 268-278.
  34. Ascher, Marcia. 1988a. Graphs in cultures: a study in ethnomathematics. Historia Mathematica 15: 201-227.
  35. Ascher, Marcia. 1988b. Graphs in cultures (II): a study in ethnomathematics. Archive for History of Exact Sciences 39: 75-95.
  36. Ascher, Marcia. 1991. Ethnomathematics. Pacific Grove, CA: Brooks/Cole.
  37. Attié Attié, Bachir. 1975. La numération de "position" et l'arabe preislamique. Hesperis Talmuda 16: 7-23.
  38. Aveni, Anthony F. and Horst Hartung. 1982. Precision in the layout of Maya architecture. Annals of the New York Academy of Sciences 385: 63-80.
  39. Aveni, Anthony F., ed. 1975. Archaeoastronomy in Pre-Columbian America. Austin: University of Texas Press.
  40. Aveni, Anthony F., ed. 1982. Archaeoastronomy in the New World. Cambridge: Cambridge University Press.
  41. Aveni, Anthony. 1997. Stairways to the Stars: Skywatching in Three Great Ancient Cultures. New York: John Wiley.
  42. Avigad, N. 1975. A bulla of Jonathan the High Priest. Israel Exploration Journal 25: 8-12.
  43. Avital, S. and I. Kleiner. 1992. Themes in the evolution of number systems. International Journal of Mathematical Education in Science and Technology 23(3): 445-461.
  44. Bag, A.K. 1990. Indian arithmetic in Central Asia. IN Interaction between Indian and Central Asian Science and Technology in Medieval Times, vol. 1., W.H. Abdi et al., eds., pp. 288-296. New Delhi: Indian National Science Academy.
  45. Bag, A.K. 1990. Ritual geometry in India and its parallelism in other cultural areas. Indian Journal of History of Science 25(1-4): 4-19.
  46. Bag, Amulya Kumar. 1979. Mathematics in Ancient and Medieval India. Delhi: Chaukhambha Orientalia.
  47. Bagheri, Mohammad. 1998. Siyaqat accounting: its origin, history, and principles. Acta Orientalia Academia Scientiarum Hungaricae 51(3): 297-301.
  48. Baillargeon, Richard, Gérard Noelting, Louis-Jacques Dorais, and Bernard Saladin D'Anglure. 1977. Aspects semantiques et structuraux de la numération chez les Inuit. Études Inuit 1: 93-128.
  49. Ball, W.W. Rouse. 1908. A Short Account of the History of Mathematics. New York: Macmillan. Dover reprint, 1960.
  50. Barcenilla Mena, Alejandro. 1995. La numeracion romana y arabiga. Perficit 19: 63-95.
  51. Bariero Saguier, Rubén. 1986. La numeracion en guarani. Amerindia 11: 145-154.
  52. Barnard, F. P. 1916. The Casting-Counter and the Counting Board. A Chapter in the History of Numismatics and Early Arithmetic. Oxford: Oxford University Press.
  53. Barnes, R.H. 1980. Fingers and numbers. Journal of the Anthropological Society of Oxford 11(3): 197-206.
  54. Barnes, R.H. 1982. Number and number use in Kedang, Indonesia. Man (N.S.) 17: 1-22.
  55. Barradas de Carvalho, Joaquim. 1957. Sur l'introduction et la diffusion des chiffres arabes au Portugal. Bulletin des études portugaises 20: 110-151.
  56. Barrow, John D. 1992. Pi in the Sky. Oxford: Clarendon Press.
  57. Barthel, Thomas S. 1962. Zählweise und Zahlenglaube der Osterinsulaner. Abhandlungen und Berichte des staatlichen Museum für Volkerkunde (Dresden) 21: 1-22.
  58. Barthel, Thomas S. 1971. Pre-contact writing in Oceania. In Current Trends in Linguistics, vol. 8, part 2, Thomas Sebeok, ed., pp. 1165-1186. The Hague: Mouton.
  59. Bartholomew, Doris A. 1980. Cornfield: a loan translation for the number thousand in some Mexican languages. International Journal of American Linguistics 46(4): 315-316.
  60. Bauer, Friedrich L. 1996. Reckoning brings good order. Interdisciplinary Science Reviews 23(1): 18-28.
  61. Baxter, W.T. 1989. Early accounting: the tally and checkerboard. The Accounting Historians Journal 16(2): 43-83.
  62. Beaujouan, Guy. 1947. Étude paléographique sur la "rotation" des chiffres et l'emploi des apices du Xe au XIIe siècle. Revue d'histoire des sciences 1: 301-313.
  63. Beaujouan, Guy. 1950. Les soi-disant chiffres grecs ou chaldéens (XIIe - XVIe siècles). Revue d'histoire des sciences 3: 170-174.
  64. Bechtel, Edward A. 1909. Finger-counting among the Romans in the fourth century. Classical Philology 4: 25-31.
  65. Becker, Wilhelm. 1995. Frühformen indisch-arabischer Ziffern in einer Handschrift des Soester Stadtarchivs. Soest: Institut für Technologie- und Wissenstransfer an der Uni-GH Paderborn.
  66. Beckmann, Petr. 1974. A history of Pi. New York: St. Martin's Press.
  67. Bede. 1999. The Reckoning of Time. Edited and translated with commentary by Faith Wallis. Liverpool: Liverpool University Press.
  68. Beeston, A.F.L. 1984. Sabaic Grammar. Manchester: Journal of Semitic Studies.
  69. Bell, Eric T. 1946. The Magic of Numbers. New York: McGraw-Hill.
  70. Bendall, Cecil. 1896. On a system of letter-numerals used in South India. Journal of the Royal Asiatic Society 28: 789-792.
  71. Bender, Marvin L., Sydney W. Head and Roger Cowley. 1976. The Ethiopian writing system. In Language in Ethiopia, M.L. Bender, J.D. Bowen, R.L. Cooper, and C.A. Ferguson, eds., pp. 120-129. London: Oxford University Press.
  72. Bengtson, John D. 1987. Notes on Indo-European '10', '100', and '1000'. Diachronica 4(1-2): 257-262.
  73. Bennett, Emmett L., Jr. 1950. Fractional quantities in Minoan bookkeeping. American Journal of Archaeology 54: 204-222.
  74. Bennett, Wendell C. 1963. Lore and learning: Numbers, measures, weights and calendars. IN Handbook of South American Indians, vol. 5., ed. Julian Steward, pp. 601-619. New York: Cooper Square.
  75. Berlin, Brent. 1968. Tzeltal Numeral Classifiers. The Hague: Mouton.
  76. Bernal, Martin. 1997. Animadversions on the origins of Western science. IN Ethnomathematics: Challenging Eurocentrism in Mathematics Education, Arthur B. Powell and Marilyn Frankenstein, eds., pp. 83-100. Albany: SUNY Press.
  77. Bernal-Garcia, Maria Elena, James B. Buchanan, Donald H. Green and Richard E. Johnson. 1988. The Dresden Codex pages 61-69: the serpent numbers, multiplication tables and almanacs. U Mut Maya 1: 83-94.
  78. Berthelot, R. 1956. Sistemas de numeración. Revista de Educación 1(5): 363-74.
  79. Bertin, George. 1882. The Assyrian numerals. Transactions of the Society for Biblical Archaeology 7: 370-389.
  80. Besner, Derek and Max Coltheart. 1979. Ideographic and alphabetic processing in skilled reading of English. Neuropsychologia 17: 467-472.
  81. Bharati Krishna Tirtha, Swami. 1971. Vedic Mathematics. Delhi: Motilal Banarsidass.
  82. Bialystok, Ellen and Judith Codd. 1996. Developing representations of quantity. Canadian Journal of Behavioural Science 28(4): 281-291.
  83. Bianco, Jean. 1990. Une numération de Polynésie Occidentale dans les tablettes de l'Ile de Pâques? In Circumpacifica: Festschrift für Thomas S. Barthel, vol. 2., Bruno Illius and Matthias Laubscher, eds., pp. 39-53. Frankfurt: Peter Lang.
  84. Bibé, Celia. 1984. Numerología Egipcia, I. Aegyptus Antiqua 5: 5-12.
  85. Bidwell, James K. 1967 [1994]. Mayan arithmetic. In From Five Fingers to Infinity, Frank J. Swetz, ed., pp. 71-79.
  86. Biella, Joan Copeland. 1982. Dictionary of Old South Arabic, Sabaean Dialect. Harvard Semitic Series, no. 25. Chico, CA: Scholars Press.
  87. Biersack. A. 1982. The logic of misplaced concreteness: Paiela body counting and the nature of primitive mind. American Anthropologist 84(4).
  88. Biot, Edouard. 1839. Notes sur la connaissance que les Chinois ont eue de la valeur de position des chiffres. Journal Asiatique (Dec. 1839): 497-502.
  89. Bischoff, Bernard. 1990. Latin Palaeography. Cambridge: Cambridge University Press.
  90. Blanchet, Louis-Émile. 1972. La maturation de l'écriture et de la numération. Laval Théologique et Philosophique 28: 118-128.
  91. Boltz, William O. 1994. The Origin and Early Development of the Chinese Writing System. New Haven: American Oriental Society.
  92. Bonfante, Larissa. 1990. Etruscan. Berkeley: University of California Press.
  93. Bonfioli, Mara. 1974-75. In margine ai mosaici di via Madonna del Mare a Trieste: osservazioni sui numerali. Aquileia Nostra 45-46: 575-596.
  94. Bonvini, Emilio. 1984. Les numéraux en kasim. Afrique et Langage 22: 35-69.
  95. Boone, Elizabeth Hill. 2000. Stories in Red and Black: Pictorial Histories of the Aztecs and Mixtecs. Austin: University of Texas.
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  97. Bos, H.J.M. and H. Mehrtens. 1977. The interactions of mathematics and society in history: some explanatory remarks. Historia Mathematica 4: 7-30.
  98. Bowditch, Charles P. 1910. The numeration, calendar systems and astronomical knowledge of the Mayas. Cambridge: Cambridge University Press.
  99. Bowers, Nancy and Pundia Lepi. 1975. Kaugel Valley systems of reckoning. Journal of the Polynesian Society 84 (3): 309-324.
  100. Bowers, Nancy. 1977. Kapauku numeration: Reckoning, racism, scholarship, and Melanesian counting systems. Journal of the Polynesian Society 86 (1): 105-116.
  101. Boyer, Carl B. 1944. Fundamental steps in the development of numeration. Isis 35: 153-165.
  102. Boyer, Carl B. 1959. Note on Egyptian numeration. Mathematics Teacher 52: 127-129.
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