Research article

Which kind of mathematics was known and referred to by those who wanted to integrate mathematics in «Wisdom» –Neopythagoreans and others?

  • Received: 29 March 2016 Accepted: 08 April 2016 Published: 17 May 2016
  • Plato, so the story goes, held mathematics in high esteem, and those philosopher-kings that ought to rule his republic should have a thorough foundation in mathematics. This may well be true – but an observation made by Aristotle suggests that the mathematics which Plato intends is not the one based on theorems and proofs which we normally identify with “Greek mathematics”. Most other ancient writers who speak of mathematics as a road toward Wisdom also appear to be blissfully ignorant of the mathematics of Euclid, Archimedes, Apollonios, etc. – though not necessarily of their names. The aim of the paper is to identify the kinds of mathematics which were available as external sources for this current (on the whole leaving out of consideration Liberal-Arts mathematics as not properly external). A number of borrowings can be traced to various practitioners' traditions – but always as bits borrowed out of context.

    Citation: Jens Høyrup. Which kind of mathematics was known and referred to by those who wanted to integrate mathematics in «Wisdom» –Neopythagoreans and others?[J]. AIMS Mathematics, 2016, 1(2): 77-95. doi: 10.3934/Math.2016.2.77

    Related Papers:

  • Plato, so the story goes, held mathematics in high esteem, and those philosopher-kings that ought to rule his republic should have a thorough foundation in mathematics. This may well be true – but an observation made by Aristotle suggests that the mathematics which Plato intends is not the one based on theorems and proofs which we normally identify with “Greek mathematics”. Most other ancient writers who speak of mathematics as a road toward Wisdom also appear to be blissfully ignorant of the mathematics of Euclid, Archimedes, Apollonios, etc. – though not necessarily of their names. The aim of the paper is to identify the kinds of mathematics which were available as external sources for this current (on the whole leaving out of consideration Liberal-Arts mathematics as not properly external). A number of borrowings can be traced to various practitioners' traditions – but always as bits borrowed out of context.


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    [1] Babbitt, F. C. (ed., trans.) (1936) Plutarch's Moralia, vol. IV.London: Heinemann/ New York: Putnam. .
    [2] Barnes, J. (ed.) (1984) The Complete Works of Aristotle. The Revised Oxford Translation.2 vols. Princeton: Princeton University Press .
    [3] Boncompagni, B. (ed.) (1862) Scritti di Leonardo Pisano matematico del secolo decimo-terzo. II. Practica geometriae et Opusculi.Roma: Tipografia delle Scienze Matematiche e Fisiche .
    [4] Bubnov, N. (ed.) (1899) Gerberti postea Silvestri II papae Opera mathematica (972- 1003).Berlin: Friedl?nder. .
    [5] Cantor, M (1875) Die römischen Agrimensoren und ihre Stellung in der Geschichte der Feldmess-kunst. Eine historisch-mathematische Untersuchung.Leipzig: Teubner. .
    [6] Chemla, K ., & Guo S. (ed., trans.) (2004) Les neuf chapitres. Le Classique mathématique de la Chine ancienne et ses commentaires.Paris: Dunod .
    [7] Clark, W. E. (ed., trans.) (1930) The āryabha?īya of āryabha?a.Chicago: University of Chicago Press. .
    [8] Colebrooke, H. T. (ed., trans.) (1817) Algebra, with Arithmetic and Mensuration from the Sanscrit of Brahmagupta and Bhascara.London: John Murray. .
    [9] Cullen, C. (ed., trans.) (2004) The Suàn shù shū, “Writings on Reckoning”: A Translation of a Chinese Mathematical Collection of the Second Century bc, with Explanatory Commentary. (Needham Research Institute Working Papers, 1). Cambridge: Needham Research Institute.Web edition available from: http://www.nri.org.uk/suanshushu.html. .
    [10] de Falco, V. (ed.) (1975) [Iamblichi] Theologumena arithmeticae. Stuttgart: 2Teubner.
    [11] Diels, H . (1912) Die Fragmente der Vorsokratiker, Griechisch und Deutsch.Dritte Auflage, erster Band. Berlin: Weidmann. .
    [12] Dupuis, J. (ed., trans.) (1892) Théon de Smyrne, philosophe platonicien, Exposition des connaissances mathématiques utiles pour la lecture de Platon.Traduite pour la première fois du grec en fran?ais. Paris: Hachette. .
    [13] Fowler, D. H., & E. Robson (1998) Square Root Approximations in Old Babylonian Mathematics: YBC 7289 in Context.Historia Mathematica 366-378.
    [14] Friedlein, G. (ed.) (1873) Procli Diadochi In primum Euclidis Elementorum librum commentarii.Leipzig: Teubner .
    [15] Heath, T. L (1921) A History of Greek Mathematics.2 vols. Oxford: The Clarendon Press. .
    [16] Heath, T. L. (ed., trans.) (1926) The Thirteen Books of Euclid's Elements. 2nd revised edition. 3 vols.Cambridge: Cambridge University Press/ New York: Macmillan .
    [17] Heiberg, J. L. (ed., trans.) (1912) Heronis Definitiones cum variis collectionibus. Heronis quae feruntur Geometrica.Leipzig: Teubner .
    [18] Heiberg, J. L. (ed., trans.) (1914) Heronis quae feruntur Stereometrica et De mensuris.Leipzig: Teubner .
    [19] H?yrup, J (1990a) Sub-Scientific Mathematics. Observations on a Pre-Modern Phenomenon.History of Science 28: 63-86.
    [20] H?yrup, J (1990b) Sub?scientific Mathematics: Undercurrents and Missing Links in the Mathematical Technology of the Hellenistic and Roman World. Filosofi og videnskabsteori p? Roskilde Universitetscenter. 3. R?kke: Preprints og Reprints 1990 nr. 3. To appear in Aufstieg und Niedergang der r?mischen Welt.II vol. 37,3 (if, by miracle, that volume is ever going to appear). Manuscript available from http://ruc.dk/~jensh/Publications/????1990%7bg%7d?_??Undercurrents.PDF .
    [21] H?yrup, J (1997a) Mathematics, Practical and Recrea-tional, pp. 660-663 in Helaine Selin (ed.).Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Dordrecht etc.: Kluwers. .
    [22] H?yrup, J (1997b) Hero, Ps.-Hero, and Near Eastern Practical Geometry. An Investi-gation of Metrica, Geometrica, and other Treatises, pp. 67-93 in Klaus D?ring, Bernhard Herzhoff & Georg W?hrle (eds).Antike Naturwissen-schaft und ihre Rezeption, Band 7. Trier: Wissenschaftlicher Verlag Trier. .
    [23] H?yrup, J (2001) On a Collection of Geometrical Riddles and Their Role in the Shaping of Four to Six ‘Algebras.Science in Context 14: 85-131.
    [24] H?yrup, J (2002) Seleucid Innovations in the Babylonian ‘Algebraic’ Tradition and Their Kin Abroad, pp. 9-29 in Yvonne Dold-Samplonius et al (eds), From China to Paris: 2000 Years Transmission of Mathematical Ideas.Stuttgart: Steiner. .
    [25] H?yrup, J (2004) Mahāvīra's Geometrical Problems: Traces of Unknown Links between Jaina and Mediterranean Mathematics in the Classical Ages, pp. 83-95 in Ivor Grattan-Guinness & B. S. Yadav (eds).History of the Mathematical Sciences .
    [26] H?yrup, JJacopo da Firenze's Tractatus Algorismi and Early Italian Abbacus Culture.Basel etc.: Birkh?user. .
    [27] H?yrup, J (2009) The Rare Traces of Constructional Procedures in ‘Practical Geometries’, pp. 367-377 in Horst Nowacki & Wolfgang Lefèvre (eds), Creating Shapes in Civil and Naval Architecture.Leiden & Boston: Brill. .
    [28] Jü r?, F. (ed., trans.) (2001) Sextus Empiricus, Gegen die Wissenschaftler, Buch 1-6.Würzburg: K?nigshausen & Neumann. .
    [29] Krasnova, S. A. (ed., trans.) (1966) Abu-l-Vafa al-Buzd?ani, Kniga o tom, ?to neobxodimo remeslenniku iz geometri?eskix postroenij, pp. 42-140 in A. T. Grigor'jan & A. P. Ju?kevi?, Fiziko-matemati?eskie nauki v stranax vostoka..Sbornik statej i publikacij. Vypusk I (IV). Moskva: Izdatel'stvo ?Nauka?. .
    [30] Kroll, W. (ed.) (1899) Procli Diadochi In Platonis Rem publicam commentarii.2 vols. Leipzig: Teubner .
    [31] MCT: O (1945) Neugebauer & A. Sachs, Mathematical Cuneiform Texts.New Haven, Connecticut: American Oriental Society .
    [32] MKT: O (1935) Neugebauer, Mathematische Keilschrift-Texte.I-III. Berlin: Julius Springer .
    [33] Morrow, G. R. (ed., trans.) (1970) Proclus, A Commentary on the First Book of Euclid's Elements.Princeton, New Jersey: Princeton University Press .
    [34] Ne tz, R (1999) The Shaping of Deduction in Greek Mathematics: A Study in Cognitive History.Cambridge: Cambridge University Press. .
    [35] Parker, R. A (1972) Demotic Mathematical Papyri.Providence & London: Brown University Press. .
    [36] Pistelli, H. (ed.) (1975) Iamblichos, In Nicomachi Introductionem Arithmeticam..2Stuttgart: Teubner .
    [37] PL: J. P. Migne (ed.)Patrologiae cursus completus, series latina.221 vols. Paris 1844-1864.
    [38] Sesiano, J (1998) An Early Form of Greek Algebra.Centaurus 40: 276-302.
    [39] Sesiano, J (1999) Sur le Papyrus graecus genevensis 259.Museum Helveticum 56: 26-32.
    [40] Shelby, L. R. (ed.) (1977) Gothic Design Techniques. The Fifteenth-Century Design Book-lets of Mathes Roriczer and Hanns Schmuttermayer.Carbondale & Edwardsville: Southern Illinois University Press .
    [41] Shorey, P. (ed., trans.) (1930) Plato, The Republic. 2 vols.2 vols. London: Heinemann / New York: Putnam, 1930, 1935. .
    [42] Tannery, P. (ed., trans.) (1893) Diophanti Alexandrini Opera omnia cum graecis commen-tariis. 2 vols.Leipzig: Teubner 1893-1895.
    [43] Thomas, I. (ed., trans.) (1939) Selections Illustrating the History of Greek Mathematics.Selections Illustrating the History of Greek Mathematics .
    [44] To th, I (1998) Aristotele e i fondamenti assiomatici della geometria. Prolegomeni alla comprensione dei frammenti non-euclidei nel ?Corpus Aristotelicum? nel loro contesto matematico e filosofico.Milano: Vita e Pensiero. .
    [45] Tropfke, J./Vogel, K ., et al. (1980) Geschichte der Elementarmathematik. 4. Auflage. Band 1: Arithmetik und Algebra. Vollst?ndig neu bearbeitet von Kurt Vogel, Karin Reich, Helmuth Gericke.Berlin & New York: W. de Gruyter. .
    [46] Vitrac, B. (ed., trans.) (1990) Euclide d'Alexandrie, Les éléments. Traduits du texte de Heiberg.4 vols. Paris: Presses Universitaires de France .
    [47] Vogel, K (1936) Beitr?ge zur griechischen Logistik. Erster Theil. Sitzungsberichte der mathematisch-naturwissenschaftlichen Abteilung der Bayerischen Akademie der Wissenschaften zu München.
    [48] Vogel, K. (ed., trans.) (1968) Chiu chang suan shu. Neun Bücher arithmetischer Technik. Ein chinesisches Rechenbuch für den praktischen Gebrauch aus der frühen Hanzeit (202 v. Chr. bis 9 n. Chr.).Braunschweig: Friedrich Vieweg & Sohn. .
    [49] Waterfield, R. (trans.) (198) The Theology of Arithmetic. On the Mystical, mathematical and Cosmological Symbolism of the First Ten Number.Attributed to Iamblichus. Grand Rapids, Michigan: Phanes. .
    [50] Woepcke, F (1853) Extrait du Fakhr?, traité d'algèbre par Abo? Bekr Mohammed ben Alha?an Alkarkh?; précédé d'un mémoire sur l'algèbre indéterminé chez les Arabes..Paris: L'Imprimerie Impériale. .
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