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Mathematics Education in Antiquity


This chapter is derived from highly heterogeneous sources both in their nature and in their geographic and chronological distribution. These sources represent different environments and refer to different cultural and institutional codes. Whereas ancient sources do not describe a coherent picture of teaching mathematics in Antiquity, some details from the better documented educational contexts of Mesopotamia, Egypt, and the Greco-Roman World provide impressionistic insight into these traditions. This approach shows that modern knowledge of these contexts is limited and that even the kinds of questions framing the topic depend strictly on the nature of the surviving sources.


  • Mathematical Curriculum
  • Mathematical Text
  • Late Antiquity
  • Ancient Education
  • Hellenistic Period

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  1. 1.

    This methodological approach is developed in Bernard and Proust (2014); see in particular the introduction.

  2. 2.

    The presence of school tablets in a house is not always a proof that this house served as a school; in particular, school tablets may have been brought from other places to be reused as construction material. Thus, the archaeological context must be analyzed carefully for each context. See, for example, the case of the “schools” in Ur analyzed by Charpin (1986, pp. 432–434) and Friberg (2000), the case of the houses of “Aire II” of Tell Haddad analyzed by Cavigneaux (1999, pp. 251–252), the case of “House F” in Nippur analyzed by Robson (2001, pp. 39–40), and the case of the house of the “gala-mah” in Sippar-Amnânum analyzed by Tanret (2002, p. 5). About bins for recycling tablets, see Tanret (2002, pp. 145–153).

  3. 3.

    The studies of the curriculum in the edubba are mainly based on Nippur sources; from the abundant literature on the subject, see Cavigneaux (1983), Civil (1985), Tinney (1999), Vanstiphout (1996), Veldhuis (1997), Robson (2001), George (2005), Proust (2007), and Delnero (2010).

  4. 4.

    About the role of memorization in learning process and transmission, see Veldhuis (1997, pp. 131–132, 148–149) and Delnero (2012).

  5. 5.

    One example of text not clearly linked with teaching is the famous tablet Plimpton 322 (see Britton et al. 2011); other examples are found among the so-called series texts, which are lists of problem statements written on numbered suites of tablets (see Proust 2012).

  6. 6.

    This typology comes from the classification of tablets used in OB Nippur for learning Sumerian literary (Tinney 1999, p. 160).

  7. 7.

    These tablets are six catalogue texts conserved at Yale University and two related procedure texts (including YBC 4663). See Proust (2012).

  8. 8.

    Rochberg (2004, Chap. 6), Robson (2008, Chap. 8), Clancier (2009, pp. 81–103, 205–211), Steele (2011), Ossendrijver (2012, Chap. 1), and Beaulieu (2006).

  9. 9.

    For a reliable guide to the bibliography and contents of the specific texts, see Clagett (1999).

  10. 10.

    For an accessible discussion of “The House of Life,” see Strouhal (1992, pp. 235–243).

  11. 11.

    For ancient scholarship and the history of texts and their transmission, see Reynolds, Leighton and Wilson (1968).

  12. 12.

    For the question of our sources of knowledge on ancient mathematics, see Fowler (1999, pp. 199–221), particularly the list in pp. 268–275.

  13. 13.

    For Greek literature, see Fowler, op. cit. For Latin technical literature (corpus agrimensorum, on which more below), see Dilke (1971, 128ff) as well as Chouquer and Favory (2001) (esp. Chap. 1).

  14. 14.

    Including copying, annotating, and writing memoranda, summaries, and abridgements (epitomai)

  15. 15.

    For more detail, see, for example, Aelius Theon’s Progymnasmata, which is basically a handbook for teachers of rhetoric.

  16. 16.

    On the uncertainty of the date and context of Euclid – uncertainty that already dates from Late Antiquity – see Vitrac (1990, pp. 13–18).

  17. 17.

    Vitrac (1990, pp. 114–148). Other treatises by Euclid besides the Elements might be more legitimately suspected to contain some kind of exercises in demonstration or in the technique of analysis (Pseudaria and Dedomena, respectively); see Vitrac (1990, pp. 21–23).

  18. 18.

    Not only were they teachers, but, in the case of late Platonist commentators like Proclus, they considered themselves as the successors (diadochoi) of a Platonic tradition that included such famous mathematicians as Euclid or Nicomachus. Thus, according to his biographer Marinus, Proclus believed he was the reincarnation of the latter.

  19. 19.

    Pappus probably did not author the collection as such, but only the constituent individual treatises which were put together long after Pappus’s time.

  20. 20.

    For more detailed discussions of this event and Pappus’s account of it, see Knorr (1989, pp. 63–76), Lloyd 1996, Cuomo (2000, 127ff), and Bernard (2003).

  21. 21.

    He answers not only by demonstrating his own capacity to analyze the shortcomings of the construction but also by suggesting that the students could have proceeded otherwise if they had possessed more knowledge of the underlying problems.

  22. 22.

    Entitled “Proclus or On Happiness” = Vita Procli. This “biography” is better termed a hagiography. For the nature of Marinus’s discourse, see Vita Procli XLI-C (Saffrey and Segonds).

  23. 23.

    Such an approach to mathematics is already distinctly represented by Theon of Smyrna in the second century A.D. (Delattre 2010). For the noninstitutionalized framework of Late Antique education, see Derda et al. (2007, pp. 177–185) (E. Szabat) See also Watts (2006).

  24. 24.

    This particularity is best explained by the fact that this period is characterized by, among other things, the violent confrontation of various cultural and didactic models, especially between Christian and pagan models, which led each party to highlight and effectively represent these values.

  25. 25.

    H.I. Marrou, in his short discussion on the teaching of elementary calculation, already warned against the too easy identification of papyri with mathematical content as corresponding to school exercises (Marrou 1964 6, note 10, pp. 398–399). Modern discussions confirm this.

  26. 26.

    This standard and traditional view is found, among others, in the influential syntheses of Marrou (1965), Bonner (1977), and Clarke (1971).

  27. 27.

    For a more detailed account of the contents of each level, see Cribiore (2001, Chaps. 6, 7 and 8, pp. 160–244); in those chapters, she focuses on only the basic contents of each level. See also the lucid and updated synthesis provided in Szabat (2007), with many references to the debates on these issues.

  28. 28.

    The term “grammaticus” should not be understood as equivalent to our modern “grammarian,” which now designates a distinct discipline. Although the latter was first constructed in antiquity, the competence of the “grammaticus” as a teacher extended much beyond mere “grammatical” analysis of literary and poetic texts: this teaching included a thorough initiation in the reading and analysis of a characteristic corpus of poets and classical writers. See Szebat (2007, pp. 185–187) for a synthetic summary and Kaster (1988) and Cribiore (2001, pp. 185–219) for more detailed explanations.

  29. 29.

    Some “idealized” accounts allude to the existence of such “separate” professionals, but these accounts are uncertain and ambiguous. There is some, albeit scanty, evidence of such mathematical teaching at the secondary level. See Kaster (1983, p. 335) and Cribiore (2001, pp. 40–42).

  30. 30.

    For a discussion of the thorny and interesting issue of the “technical” terminology of ancient education, see again Kaster (1983, pp. 329–331) and Szabat (2007), with references to other studies on the same subject.

  31. 31.

    On the analysis of Marrou’s precautions on this issue, see the insightful discussion of Kaster (1983, p. 324).

  32. 32.

    Booth paid attention to the situation in first-century AD Rome. His theses (Booth 1979) are conveniently summarized in Kaster (1983), who expands on his argumentation.

  33. 33.

    For an efficient summary, see Szabat (2007, pp. 178–181), who draws on previous studies, esp. Kaster (1983).

  34. 34.

    Kaster (1983, p. 346). The same point is made in Cribiore (2001, Chap. 1) (pp. 15–44) for the sole case of Hellenistic and Roman Egypt and Szabat, op.cit. Even the imperial state did not heavily intervene in educational institutions. At best, laws would oblige cities to finance municipal chairs, without intervention in and regulation of their study. The majority of teachers, though, worked privately and directly depended on fees from students and their parents.

  35. 35.

    Kaster (1983, pp. 337–338) summarizes the “positive” reasons to believe that Booth’s model is better adapted in general to antiquity, although it should not be viewed as an alternative model applicable to all ancient situations.

  36. 36.

    On the uniformity and strong identity of the grammatikoi’s teaching, the classic study is Kaster (1988).

  37. 37.

    This idea of “concentric” studies, in which the same elements and methods are retrieved at each level but with a different depth and difficulty, is central to the argument of Cribiore (2001).

  38. 38.

    This point is made in Szabat (2007, pp. 180–181) and Cribiore (2001), Chap. 1 (on school accommodations) and Chap. 2 (on teachers).

  39. 39.

    Fowler (1999)gives the sole extensive discussion on the papyrological evidence concerning mathematics.

  40. 40.

    Cribiore (2001, pp. 180–183). This short discussion is devoted to the question of the acquisition of numeracy at the elementary level.

  41. 41.

    For an account of ancient Greek astrology, the standard reference remains Bouché-Leclercq (1899). See also the more recent Barton (1994), especially pp. 134–142 as far as astrological training is concerned.

  42. 42.

    For an updated extensive study on this question, see Hadot (2005), especially the fourth “étude complémentaire,” pp. 431–455, concerning mathematics. Note, however, that Hadot has a tendency to reduce any ancient mathematical teaching to being basically dependent in all cases on a philosophical ideal, an idea which is somewhat open to criticism.

  43. 43.

    See Isocrates’s ideas in Antid. pp. 258–269. For Quintilianus, see Inst. Orat. I.10, especially pp. 34–49.

  44. 44.

    Even by those, like Firmicus, who obviously had little command of the mathematical contexts of their art.

  45. 45.

    These commentaries can indeed be seen, at least in part, as conscious imitations of the Almagest; see Bernard( 2014) on this point.

  46. 46.

    As far as the corpus agrimensorum is concerned, the work of Toneatto (1994-5) has drastically improved our understanding of its history; see Chouquer and Favory (2001, Chap. 1).

  47. 47.

    Is Hero’s Dioptra, for example, an exercise in land surveying, as the kinds of problems treated therein strongly suggest, or the skillful description of an instrument, as the preface and many technological details indicate? Is Vitruvius’s treatise merely a work on monuments and house-building, or also on machine-building (book 10), the science of sundials and astronomy in general (book 9), and many related subjects, as the contents suggest?

  48. 48.

    Like Hyginus “gromaticus,” the second Hyginus or Siculus Flaccus. For translations of these authors, see Campbell (2000) or the various annotated editions published in French by J.Y. Guillaumin, in particular Guillaumin (2005, 2010).

  49. 49.

    It has even become commonplace in scholarship on these kinds of sources that they represent didactic efforts and are scholastic “manuals,” a qualification difficult to dismiss because of the vague and multifarious meanings of this category. The idea is discussed and nuanced in Chouquet and Favory (2001, p. 38).

  50. 50.

    Acerbi and Vitrac forthcoming: introduction, A4. A preliminary version of this detailed analysis is available online on hal-SHS (consulted 5.1.12).

  51. 51.

    For a list of such documents, see Fowler (1999, pp. 269–276). The list is focused on tables rather than problems.


Ancient Sources

  • Antidosis. 2003. Isocrate: sur l’échange. In Isocrates, Discours, tome III, ed. and transl. by G. Mathieu. Paris: Belles Lettres.

    Google Scholar 

  • Arithm. 1974. Diophanti Alexandrini Opera Omnia cum Graeciis commentariis, ed. and Latin Transl. by Paul Tannery, 2 vols. Leipzig: B.G. Teubner 1893–95. Repr. Teubner.

    Google Scholar 

  • Inst. Orat. 2001. The Orator’s education: Books 1–2, ed. and transl. by D.A. Russell. Loeb.

    Google Scholar 

  • Progymn. 1997. Aélius Théon, Progymnasmata. Trans. M. Patillon. Paris: Belles Lettres.

    Google Scholar 

  • Vita Procli. 2002. Marinus: Proclus ou sur le Bonheur, text edited, translated and annotated by H.D. Saffrey and A.P. Segonds. Paris: Belles Lettres.

    Google Scholar 

Modern Studies

  • Acerbi, Fabio, and Bernard Vitrac. Forthcoming. Héron: Metrica. Intr., ed., transl. and comm. Fabio Acerbi et Bernard Vitrac. Coll. Mathematica Graeca Antiqua. Pisa-Roma: Fabrizio Serra Editore.

    Google Scholar 

  • Acerbi, Fabio, Nicolas Vinel, and Bernard Vitrac. 2010. Les ‘Prolégomènes à l’Almageste’. Une édition à partir des manuscrits les plus anciens. Introduction générale-Parties I-III. Sciamvs 11: 53–210.

    MATH  MathSciNet  Google Scholar 

  • Baillet, Jules. 1892. Le papyrus mathématique d’Akhmim. Paris: E. Leroux.

    Google Scholar 

  • Barton, Tamsyn. 1994. Ancient astrology. London/New York: Routledge.

    CrossRef  Google Scholar 

  • Beaulieu, Paul-Alain. 2006. De l’Esagil au Mouseion: l’organisation de la recherche scientifique au 4e siècle av. J.C. In La transition entre l’empire achéménide et les royaumes hellénistiques, vol. 9, Persika, ed. Pierre Briant and Francis Joannès. Paris: De Boccard.

    Google Scholar 

  • Bernard, Alain. 2003. Sophistic aspects of Pappus’s collection. Archive for History of Exact Sciences 57(2): 93–150.

    CrossRef  MATH  MathSciNet  Google Scholar 

  • Bernard, Alain. 2010a. The historical significance of Ptolemy’s Almagest for its early readers. Revue de synthèse 131, 6e série: n°4, 495–521.

    Google Scholar 

  • Bernard, Alain. 2010b. L’arrière-plan rhétorique de la théorie de l’activité mathématique chez Proclus. In Études sur le commentaire de Proclus au Ier livre des Éléments d’Euclide, Dir. Alain Lernoult, 67–85. Lille: Presses universitaires du Septentrion.

    Google Scholar 

  • Bernard, Alain. 2011. Les Arithmétiques de Diophante: Introduction à la lecture d’une oeuvre ancrée dans différentes traditions antiques. In Circulation, transmission, heritage, ed. Evelyin Barbin and Pierre Ageron, 557–582. Caen: IREM de Basse-Normandie.

    Google Scholar 

  • Bernard, Alain. 2014. In what sense did Theon’s commentary on the Almagest have a didactic purpose? In ed. Bernard and Proust.

    Google Scholar 

  • Bernard, Alain, and Christine Proust. 2014. Studying ancient scientific sources produced in an educational context: Problems and perspectives. Boston Studies.

    Google Scholar 

  • Bernard, Alain, and Christine Proust (eds.). Forthcoming. Scientific sources and teaching contexts throughout history: Problems and perspectives. Springer.

    Google Scholar 

  • Bernard, Alain, and Jean Christianidis. 2011. A new analytical framework for the understanding of Diophantus’s Arithmetica I–III. Archive for History of Exact Sciences 66: 1–69.

    CrossRef  MathSciNet  Google Scholar 

  • Bonner, Stanley F. 1977. Education in ancient Rome: From the elder Cato to the younger Pliny. Berkeley: University of California Press.

    Google Scholar 

  • Booth, Alain D. 1979. Elementary and secondary education in the Roman Empire. Florilegium 1: 1–14.

    Google Scholar 

  • Bouché-Leclerc, Auguste. 1899. L’astrologie grecque. Paris: E. Leroux.

    Google Scholar 

  • Britton, John P., Christine Proust, and Steve Shnider. 2011. Plimpton 322: A review and a different perspective. Archive for History of Exact Sciences 65: 519–566.

    CrossRef  MATH  MathSciNet  Google Scholar 

  • Campbell, B. 2000. The writings of the Roman land surveyors. Intr., text, transl. and com. by Brian Campbell. London: Society for the Promotion of Roman Studies.

    Google Scholar 

  • Cavigneaux, Antoine. 1983. Lexikalische listen. Reallexikon der Assyriologie 6: 609–641.

    Google Scholar 

  • Cavigneaux, Antoine. 1999. A scholar’s library in Meturan? In Mesopotamian magic, ed. T. Abusch and K. van der Toorn. Groningen: Styx Publications.

    Google Scholar 

  • Charpin, Dominique. 1986. Le clergé d’Ur au siècle d’Hammurabi. Genève: Droz.

    Google Scholar 

  • Chouquet, Gérard, and François Favory. 2001. L’arpentage romain. Histoire des textes – Droit – Techniques. Paris: Errance.

    Google Scholar 

  • Christianidis, Jean. 2007. The way of Diophantus: Some clarifications on Diophantus’ method of solution. Historia Mathematica 34: 289–305.

    CrossRef  MATH  MathSciNet  Google Scholar 

  • Civil, Miguel. 1985. Sur les “livres d’écoliers” à l’époque paléo-babylonienne. In Miscellanea Babylonica, Mélanges offerts à M. Birot, ed. J.-M. Durand and J.-R. Kupper. Paris: Editions Recherche sur les Civilisations.

    Google Scholar 

  • Clagett, Marshall. 1999. Ancient Egyptian science: A sourcebook, Ancient Egyptian mathematics, vol. 3. Philadelphia: American Philosophical Society.

    Google Scholar 

  • Clancier, Philippe. 2009. Les bibliothèques en Babylonie dans la deuxième moitié du Ier millénaire, Alter Orient und Altes Testament vol. 363. Münster: Ugarit-Verlag.

    Google Scholar 

  • Clarke, Martin L. 1971. Higher education in the ancient world. London : Routledge and Kegan Paul.

    Google Scholar 

  • Couchoud, Sylvia. 1993. Mathématiques égyptiennes: Editions Le Léopard d’Or.

    Google Scholar 

  • Cribiore, Raffaella. 2001. Gymnastics of the mind: Greek education in Hellenistic and Roman Egypt. Princeton: Princeton University Press.

    Google Scholar 

  • Cuomo, Serafina. 2000. Pappus of Alexandria and the mathematics of Late Antiquity. Cambridge: Cambridge University Press.

    MATH  Google Scholar 

  • Cuomo, Serafina. 2007. Technology and culture in Greek and Roman antiquity. Cambridge: Cambridge University Press.

    Google Scholar 

  • Delattre, Joëlle (trad.). 2010. Théon de Smyrne: lire Platon. Trans. Joëlle Delattre. Toulouse: Anacharsis.

    Google Scholar 

  • Delnero, Paul. 2010. Sumerian extract tablets and scribal education. Journal of Cuneiform Studies 62: 53–69.

    Google Scholar 

  • Delnero, Paul. 2012. Memorization and the transmission of Sumerian literary compositions. Journal of Near Eastern Studies 71(2): 189–208.

    CrossRef  Google Scholar 

  • Derda, Tomasz, Tomasz Markiewicz, and Ewa Wipszycka. 2007. Alexandria: Auditoria of Kom El-Dikka and late antique education. The Journal of Juristic Papyrology, Supplement 8. Warsaw: the Raphael Taubenschlag foundation.

    Google Scholar 

  • Dilke Oswald, A.W. 1971. The Roman land surveyors. New York: David and Charles.

    Google Scholar 

  • Dorandi, Tiziano. 2000. Le stylet et la tablette, dans le secret des auteurs antiques. Paris: Belles Lettres.

    Google Scholar 

  • Feke, Jacqueline, and Alexander Jones. 2010. Ptolemy. In The Cambridge history of philosophy in Late Antiquity, ed. Lloyd Gerson, 197–209. Cambridge: Cambridge University Press.

    CrossRef  Google Scholar 

  • Fowler, David. 1999. The mathematics of Plato’s academy: A new reconstruction, 2nd ed. New York: Oxford University Press.

    MATH  Google Scholar 

  • Friberg, Jöran. 2000. Mathematics at Ur in the old Babylonian period. Revue d’Assyriologie 94: 98–188.

    Google Scholar 

  • Fried, Michael N. Forthcoming. History of mathematics in mathematics education. In History, philosophy and science teaching handbook. Boston: Springer.

    Google Scholar 

  • George, Andrew R. 2005. In search of the é 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. Yitschak Sefati, Pinhas Artzi, Chaim Cohen, Barry L. Eichler, and Victor A. Hurowitz, 127–137. Bethesda: CDL Press.

    Google Scholar 

  • Goldstein, Catherine, Jeremy Gray, and Jim Ritter (eds.). 1996. L’Europe mathématique. Paris: Maison des Sciences de l’Homme.

    MATH  Google Scholar 

  • Guillaumin, Jean-Yves. 2005. Les arpenteurs romains1: Hygin le Gromatique, Frontin. Text establ. and transl. by Jean-Yves Guillaumin. Paris: Belles Lettres.

    Google Scholar 

  • Guillaumin, Jean-Yves. 2010. Les arpenteurs romains 2: Hygin, Siculus Flaccus. Text establ. and transl. by Jean-Yves Guillaumin. Paris: Belles Lettres.

    Google Scholar 

  • Hadot, Pierre. 2002. Exercices spirituels et philosophie antique. Paris: Albin Michel.

    Google Scholar 

  • Hadot, Ilsetraut. 2005. Arts libéraux et philosophie dans la pensée antique, 2nd ed. Paris: Vrin.

    Google Scholar 

  • Hilprecht, Hermann V. 1906. Mathematical, metrological and chronological tablets from the temple library of Nippur, vol. 20–1. Philadelphia: University of Pennsylvania.

    Google Scholar 

  • Hinrichs, Focke T. 1989. Histoire des institutions gromatiques. Die Geschichte der gromatischen Institutionen (trans: Minary, Daniel). Centre d’histoire ancienne de Besançon. Paris: Geuthner.

    Google Scholar 

  • Jones, Alexander. 1994. The place of astronomy in Roman Egypt. In The sciences in Greco-Roman society, ed. Timothy D. Barnes, 25–54. Edmonton: Academic.

    Google Scholar 

  • Jones, Alexander. 1999. Uses and users of astronomical commentaries in antiquity, 147–172.

    Google Scholar 

  • Karivieri, Arja. 1994. The ‘House of Proclus’ on the Southern slope of the acropolis: A contribution. In Post-Herulian Athens: Aspects of life and culture in Athens A.D. 267–529, ed. Paavo Castrén. Helsinki: Suomen Ateenan-instituutin säätiö. 115–139.

    Google Scholar 

  • Kaster, Robert A. 1983. Notes on “Primary” and “Secondary” schools in Late Antiquity. Transactions of the American Philological Association 113: 323–346.

    CrossRef  Google Scholar 

  • Kaster, Robert A. 1988. Guardians of language: The grammarian and society in Late Antiquity. Berkeley: University of California Press.

    Google Scholar 

  • Knorr, Wilbur R. 1989. Textual studies in ancient and medieval geometry. Boston: Birkhaüser.

    CrossRef  MATH  Google Scholar 

  • Lernoult, Alain (ed.). 2010. Etudes sur le commentaire de Proclus au premier livre des Eléments d’Euclide. Lille: Presses Universitaires du Septentrion.

    Google Scholar 

  • Lloyd, Geoffrey E.R. 1996. Adversaries and authorities. Investigations into ancient Greek and Chinese science. Cambridge: Cambridge University Press.

    Google Scholar 

  • Marrou, Henri-Irénée. 1965. Histoire de l’éducation dans l’Antiquité, 6th ed. Paris: Seuil.

    Google Scholar 

  • Michalowski, Piotr. 1987. Charisma and control: On continuity and change in early Mesopotamian bureaucratic systems. In The organization of power, aspects of bureaucracy in the near east, ed. McGuire Gibson and Robert D. Biggs, 55–68. Chicago: The Oriental Institute of the University of Chicago.

    Google Scholar 

  • Neugebauer, Otto, and Abraham J. Sachs. 1945. Mathematical cuneiform texts, vol. 29. New Haven: American Oriental Series/American Schools of Oriental Research.

    MATH  Google Scholar 

  • Ossendrijver, Mathieu. 2012. Babylonian mathematical astronomy: Procedure texts, sources and studies in the history of mathematics and physical sciences. New York: Springer.

    CrossRef  Google Scholar 

  • Proust, Christine. 2007. Tablettes mathématiques de Nippur, vol. XVIII. Istanbul: IFEA, De Boccard.

    MATH  Google Scholar 

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

    CrossRef  Google Scholar 

  • Reynolds, Leighton D., and Nigel G. Wilson. 1968. Scribes and scholars: A guide to the transmission of Greek and Latin literature. London: Oxford University Press.

    Google Scholar 

  • Robson, Eleanor. 2001. The tablet house: A scribal school in old Babylonian Nippur. Revue d’Assyriologie 95: 39–66.

    Google Scholar 

  • Robson, Eleanor. 2002. More than metrology: Mathematics education in an old Babylonian scribal school. In Under one sky. Astronomy and mathematics in the ancient near east, ed. John M. Steele and Annette Imhausen. Münster: Ugarit-Verlag.

    Google Scholar 

  • Robson, Eleanor. 2008. Mathematics in ancient Iraq: A social history. Princeton: Princeton University Press.

    Google Scholar 

  • Rochberg, Francesca. 2004. The heavenly writing: Divination, horoscopy, and astronomy in Mesopotamian culture. Cambridge: Cambridge University Press.

    CrossRef  Google Scholar 

  • Sidoli, Nathan. 2004. Ptolemy’s mathematical approach: Applied mathematics in the second century. Ph.D. thesis. Available online on the site of the University of Toronto (consulted 19 Jan 2012).

    Google Scholar 

  • Sluiter, Ineke. 1999. Commentaries and the didactic tradition. In Commentaries—Kommentare, Aporemata, Bd. 4, ed. Glenn Most, 173–205. Göttingen: Vandenhoeck und Ruprecht.

    Google Scholar 

  • Steele, John M. 2011. Astronomy and culture in late Babylonian Uruk. International Astronomical Union, 331–342.

    Google Scholar 

  • Strouhal, Eugen. 1992. Life of the ancient Egyptians. Norman: University of Oklahoma Press.

    Google Scholar 

  • Szabat, Elżbieta. 2007. Teachers in the Eastern Roman Empire, In Derda et alii, 177–208.

    Google Scholar 

  • Tanret, Michel. 2002. Per aspera ad astra. L’apprentissage du cunéiforme à Sippar-Amnanum pendant la période paléo-babylonienne tardive, vol. I/2. Gand: Université de Gand.

    Google Scholar 

  • Taub, Liba C. 1993. Ptolemy’s universe, the natural philosophical and ethical foundations of Ptolemy’s astronomy. Chicago: Open Court.

    Google Scholar 

  • Tihon, Anne. 1992. Propos sur l’édition de textes astronomiques grecs des IVè et Vè siècles de notre ère. In Les problèmes posés par l’édition critique des textes anciens et médiévaux, ed. Jacqueline Hamesse, 113–137. Louvain-la-Neuve: Brepols.

    Google Scholar 

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

    CrossRef  Google Scholar 

  • Toneatto, Lucio. 1994–1995. Codices Artis Mensoriæ. I Manoscritti degli Antichi Opuscoli Latini d’Agrimensura (V-XIX SEC.). Vol. I: Tradizione diretta, Il Medioevo. II: Tradizione diretta, l’età moderna. III: Tradizione indiretta. Spoleto: Centro Italiano di Studi sull’Alto Medioevo.

    Google Scholar 

  • Vanstiphout, Herman L.J. 1996. On the old Babylonian Eduba curriculum. In Centres of learning: Learning and location in the pre-modern Europe and the near east, ed. Jan W. Drijvers and Alasdair A. MacDonald. Leiden/New York/Köln: E.J. Brill.

    Google Scholar 

  • Veldhuis, Niek. 1997. Elementary education at Nippur, the lists of trees and wooden objects. Ph.D. dissertation thesis. University of Groningen, Groningen.

    Google Scholar 

  • Vitrac, Bernard. 1990. Euclide: Les éléments. 1: Introduction. Livres I à IV: Géométrie plane. French transl. with comm. and notes. Gen. intr. by Maurice Caveing. Paris: PUF.

    Google Scholar 

  • Vitrac, Bernard. 2005. Les classifications des sciences mathématiques en Grèce ancienne. Archives de Philosophie 68: 269–301.

    Google Scholar 

  • Watts, Edward J. 2006. City and school in late antique Athens and Alexandria. Berkeley: Los Angeles.

    CrossRef  Google Scholar 

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Correspondence to Alain Bernard .

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Bernard, A., Proust, C., Ross, M. (2014). Mathematics Education in Antiquity. In: Karp, A., Schubring, G. (eds) Handbook on the History of Mathematics Education. Springer, New York, NY.

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