Title: The Transmission of Mathematics into Greek Education, 1800–1840: From Individual Initiatives to Institutionalization
Abstract: Abstract In the early nineteenth century, a number of Greek communities developed a remarkable education in mathematics. The subject matter for this instruction was drawn mainly from French textbooks, although some teachers displayed a preference for Prussian mathematical sources. These efforts, however, were thwarted by the religious conservatism of the Greek establishment of the time, which did not favor the emergence of a Greek mathematical discourse. As a consequence, the reception of mathematical knowledge was a fragmented, random process lacking cohesion, collectivity and transitivity. The situation changed radically during the second and third decades of the nineteenth century. The Ionian Academy in Corfu, and the Military School in Nafplio, founded in 1824 and 1828 respectively, created the first institutional frame for a Greek education in which post‐revolutionary French mathematics was established as the basis of Greek mathematical discourse. The French background of Greek mathematical education was further reinforced after 1837, subsequent to the institutionalization of secondary education, and to the founding of the University of Athens in 1836–1837. At the same time, along with this French infusion into Greek mathematical discourse, some noteworthy translations of Prussian textbooks were promoted as well. The first half of the nineteenth century also witnessed the transmission of the respective epistemological trends of that era, i.e. of the analytical model, of the positivism dominating French mathematics, and of the combinatorial ‘paradigm’ of Prussian mathematics, to the historical setting of Greek mathematical education. Notes 1 The authors would like to thank Dr Maria Panteki and Dr Gert Schubring for their critical comments on an earlier draft of this work, and translator Günter Seib for his revision. 2 The education provided by the Orthodox Church. 3 Chatzopoulos, K. 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Berkeley: University of California Press, 1982: 163. 10 For instance, Lacaille’s volume Lectiones elementares astronomiae, geometricae, et physicae (first published in Paris, 1755) had been translated into Latin by the Jesuit Karl Scherffer (1716–1783) and published in Vienna in 1757. In the same year, Lacaille’s Lectiones elementares opticae, edited by the eminent Jesuit Rudjer Boscovich (1711–1787), were published in Vienna, and re‐edited in Venice in 1773. 11 Zisis Kavras (c.1765–1844) of Ampelakia studied medicine in Jena, and translated a German book on arithmetic and algebra, his translation having been anonymously published in Jena in 1800. The second young scholar was Dimitrios Govdelas (1780–1831) of Rapsani (a village near Ampelakia), who studied science and philosophy in Pest, and wrote a volume on algebra largely inspired by German sources and published in Halle in 1806, bearing the title Stoicheia Algebras (Elements of Algebra). Later, he wrote a book on arithmetic published in Jassy in 1818. The third was Stefanos Dougas (c.1765–1829) of Tyrnavo (a village near Ampelakia), who studied science and philosophy in Halle, Jena and Göttingen, and who published a four‐volume arithmetic and algebra inspired by German tradition in Vienna in 1816. 12 Kastanis, N. “Algebra [in Neo‐Hellenic Culture]” (in Greek). In History and Philosophy in the Greek Area (17th–19th century) (in Greek), edited by I. Karas. Athens: Ekdoseis Metaichmio, 2003: 144–96. 13 Ibid., 167, 194. 14 Ibid., 178. 15 Ibid., 197. 16 Tomadakis, N. “Churches and Institutions of the Greek Community in Livorno” (in Greek). Yearbook of Byzantine Studies Association 16 (1940): 81–127. 17 Kastanis, Aspects of the Neo‐Hellenic Mathematical Culture, 189. 18 Stassinopoulou, M. A. “Weltgeschichte im Denken eines griechischen Aufklärers – Konstantinos Michail Koumas als Historiograph.” Studien zur Geschichte Südosteuropas 9, no. 122 (1992): 32. 19 Ibid., no. 115 (1992): 31. 20 Kastanis, N. “An Introduction of Mathematics in the Neo‐Hellenic Culture. The Cases of Algebra and Calculus” (in Greek). Ph.D., University of Thessaloniki, 2001: 119, 174. 21 That book was probably Abbé J. Sauri’s Cours complet de mathématique I–V. Paris: 1974; or Institutions mathématiques. Paris: Froullé, 1777. 22 Cantor, M. Vorlesungen über Geschichte der Mathematik, Vierter Band. Leipzig: Teubner: 1908/New York: Johnson Reprint, 1965: 327. 23 Ibid., 332–6; Schubring, G. Analysis of the Historical Textbooks in Mathematics. Lecture Notes. Pontificia Universida de Católica do Rio De Janeiro: Departamento de Mathemática, 1999: 34. 24 Roudometof, V. “From Rum Millet to Greek Nation: Enlightenment, Secularization, and National Identity in Ottoman Balkan Society, 1453–1821.” Journal of Modern Greek Studies 16 (1998): 11–48. 25 Tatakis, B. “La Philosophie Byzantine.” Fascicule Supplémentaire N° II in Histoire de la Philosophie, edited by Émile Bréhier. Paris: Presses Universitaires de France, 1949: 274. 26 Tacquet, André. The Elements of Geometry. Vienna: 1805. Translated by the eminent Greek man of letters Evgenios Voulgaris. It is well known that all Byzantine manuscripts of ancient Greek origin were pillaged, destroyed or sold after the fall of Constantinople (an abomination beginning with the crusades from 1204 to 1261). Thus, the scientific works of the Greek civilization of antiquity, like Euclid’s Elements, were missing both in the libraries of Neo‐Hellenic communities and in those of the Orthodox monasteries, and it was extremely difficult for Greek scholars to access them. A typical statement by an eminent Greek man of letters, around 1780, was: ‘I do not have my ancient heritage’ [Katartzis, D. The Findings (in Greek). Athens: Ekdoseis Ermis, 1970: 55]. 27 The first volume of Institutiones mathematicae, tomus I–V (Vienna, 1775–1790) which contained Elementa arithmeticae. Elementa algebrae. Other volumes of this work were probably also used, including Geometry, Mechanics, Optics, etc. 28 The textbook Arithmetic for use in Greek Schools, translated into ‘our vernacular’ (into Greek) from Latin (Vienna: Typography of Gebrüder Pouliou, 1794) (Karas, 1992: 153). 29 Michael Christaris (1773–1851), who studied medicine in Padova in the early nineteenth century. The textbook Elements of Arithmetic and Algebra, compiled … by Metzburg …, see Karas, I. Sciences during the Period of the Turkish Occupation. Manuscripts and Printed Matters. Vol. A mathematics (in Greek). Athens: Bibliopoleion tis ‘Estias’, 1992: 151–2. 30 Camariano‐Cioran. Les Académies Princières, 233, 457. 31 Heliou, P. The Social Struggles and the Enlightenment. The Case of Smyrna (in Greek). Athens: Etaireia Meletis Neou Ellinismou‐Mnimon, 1981; Heliou, P. Blind, Lord, thy People (in Greek). Athens: Ekdoseis ‘Poreia’, 1988. 32 With the exception of Tselepis, who did not study in Paris. 33 In the first period of his teaching, he used his Pisa tutor’s Pietro Paoli (1759–1838) books, probably the latter’s two‐volume Elementi d’ Algebra. Pisa: 1794 (Sotirakis, N. Veniamin Lesvios, Part A Biography (in Greek). Mytilene, reprint from the journal ‘Poimin’, 1939). 34 Dragona‐Monachou, M. “The reception of Aristotle by Veniamin of Lesvos in his Elements of Ethics.” In The Neo‐Hellenic Philosophy (in Greek), edited by K. Voudouris. Athens: Ekdoseis Ellinika Grammata, 2000: 79–94. 35 Veniamin Lesvios. Stoicheia Arithmitikis (Elements of Arithmetic). Vienna: Typography of Johann Schneirer, 1818: 85, 115, 134, 138; Veniamin Lesvios. Geometrias Eycleidoy Stoicheia (Euclid’s Elements of Geometry). Vienna: Typography of Johann Schneirer, 1820: 15. It should also be noted that the notation applied in Veniamin’s Geometry bears resemblance to that found in Legendre’s Geometry, see also Karas. Sciences during the Period of the Turkish Occupation. Vol. A: Mathematics (in Greek), 57–59. 36 Palamiotou‐Thomaidou, K. The logical cognition in the Philosophy of Th. Cairis. In The Neo‐Hellenic Philosophy (in Greek), edited by K. Voudouris. Athens: Ekdoseis Ellinika Grammata, 2000: 221–33; Kastanis. “An Introduction of Mathematics,” 140, 178, 195. 37 Such historical analysis is absent in contemporary Greek publications. 38 Kitromilides, P. M. “The Idea of Science in the Modern Greek Enlightenment.” In Greek Studies in the Philosophy and History of Science, edited by P. Nicolacopoulos. Dordrecht: Kluwer, 1990: 187–200; Henderson, G. P. The Revival of Greek Thought, 1620–1830. Albany NY: State University of New York Press, 1970: 127–41. 39 Sotirakis, Veniamin Lesvios, Part A: Biography. 40 Valetas, G. “A History of Kydonies’ Academy. Part A: The Enlightening Period of Veniamin Lesvios (1798–1812)” (in Greek). Near East Annals 4 (1948): 145–208. 41 Terdimou, M. “The Confrontation of Mathematics on Behalf of the Eastern Orthodox Church During the Ottoman Period.” In Multicultural Science in the Ottoman Empire, edited by E. Ihsanoglou et al. Turnhout: Brepols, 2003: 53–62. 42 Karas, I. Natural Sciences in Greece During the 18th Century (in Greek). Athens: Ekdoseis Gutenberg, 1977: 99. 43 Terdimou, M. “The Confrontation of Mathematics,” 62. 44 Economidis, D. B. “Athanasios Parios” (in Greek). Yearbook Cycladic Islands Studies Association 1 (1961): 347–422. 45 Philippidis studied in Vienna and Paris and taught mathematics at the Academy of Jassy, in around 1801. He used the textbooks of A. R. Mauduit (1731–1815). Konstantas studied in Halle, Padua and Vienna. He taught mathematics in Bucharest (1782–1787), in Ampelakia (1795–1803), and in Milies in Pilio (1812–1821). It is a known fact that he used French textbooks. 46 Kastanis, Aspects of the Neo‐Hellenic Mathematical Culture, 183–4; Phili, Chr. “La reconstruction des mathématiques en Grèce: l’apport de Ioannis Carandinos (1784–1834).” In Mathematical Europe, edited by C. Goldstein et al. Paris: Maison des Sciences de l’Homme, 1996: 303–19. 47 Camariano‐Cioran, Les Académies Princières, 543–5. 48 The article was by Cyrillos Liberios, who studied at the Universities of Leipzig, Jena, Würzburg and Göttingen, from 1816 to 1820. 49 Argyropoulou, R. “Condillac in Greece (18th–19th cent.)” (in Greek). Newsletter of the Greek Society for the History of Sciences and Technology 19 (1999): 44–53. 50 Logios Hermes 9 (1819): 763–71, 785–800. 51 Logios Hermes 11 (1821): 187. 52 Manning, K. R. “The Emergence of the Weierstrassian Approach to Complex Analysis.” Archive for History of Exact Sciences 14 (1974): 297–383; Jahnke, H. N. “Algebraic Analysis in Germany, 1780–1840: Some Mathematical and Philosophical Issues.” Historia Mathematica 20 (1993): 265–84. 53 For example: Hindenburg, D. Burckhardt, Klügel, Fischer, Rothe, Thibaut, and others. 54 These were Kavras’s Stoicheia Arithmitikis kai Algebras (Elements of Arithmetic and Algebra) translated from German, Dougas’s Stoicheia Arithmitikis kai Algebras (Elements of Arithmetic and Algebra), and the Greek translation of Metzburg’s Algebra. 55 Kitromilides, “The Idea of Science in the Modern Greek Enlightenment,” 187–200. 56 Kitromilides, P. M. Neo‐Hellenic Enlightenment (in Greek). Athens: Ekdoseis Morfotikou Idrimatos Ethnikis Trapezis, 1996: 466 [English origin: “Tradition, Enlightenment and Revolution: Ideological Change in Eighteenth and Nineteenth Century Greece.” Ph.D. diss., Harvard University, 1978]. 57 At the time, which is from 1815 to 1864, Corfu and the other islands of the Eptanese formed part of the British protectorate. 58 The British lord was Frederick North, 5th Earl of Guilford (1766–1827), son of a prime minister of the United Kingdom. 59 Aggelomati‐Tsougaraki, H. The Ionian Academy. The Chronicle of the Constitution of the First Greek University (1811–1824) (in Greek). Athens: Ekdoseis ‘M. Romios’, 1997: 231. 60 He was initiated to French mathematics by Charles Dupin (1784–1873), when the latter organized and directed the Society of General Intellectual Culture in Corfu from 1808 to 1810, while the Ionian Islands were under Napoleon’s rule. Carandinos adopted the French system while teaching mathematics at a public school in Corfu from 1812 to 1820. From 1820 to 1823, he studied at the Ecole Polytechnique with Lord Guilford’s support. 61 His Arithmetic, Algebra, Trigonometry, the Elementary Treatise of Differential and Integral Calculus, and the first volume and part of the second volume of his three‐volume Treatise of Differential and Integral Calculus. 62 Kastanis, Aspects of the Neo‐Hellenic Mathematical Culture, 185–6. 63 Phili, Chr. “La reconstruction des mathématiques en Grèce,” 303–19. 64 From a French translation of this book, published by Hachette. 65 Legendre had added a separate volume on trigonometry to his geometry textbook, from the second edition on. This additional part has been published in several foreign editions as a separate volume. 66 Kastanis, Aspects of the Neo‐Hellenic Mathematical Culture, 186. 67 Two of them were on combinatorics, one on algebraic equations, one on the foundation of differential calculus, and one on angles of polygons. 68 Kastanis, Aspects of the Neo‐Hellenic Mathematical Culture, 188; Phili, “La reconstruction des mathématiques en Grèce,” 303–19. 69 Kastanis, A. The Military School of Cadets in the First Years of its Foundation, 1828–1834 (in Greek). Athens: Ekdoseis Ellinika Grammata, 2000: 228. 70 Kastanis, A. “The Teaching of Mathematics in the Greek Military Academy During the First Years of its Foundation (1828–1834).” Historia Mathematica 30, no. 3 (2003): 123–39. 71 Ibid., 136. 72 He had also translated Bourdon’s Algebra, and Monge’s Descriptive Geometry, which for unknown reasons never saw publication. 73 Kastanis, A. “The Mathematics Books During the Period 1828–1832” (in Greek). In In Honor of Antonis Antonakopoulos, edited by K. Aroni‐Tsichli. Athens: Ekdoseis Papazisi, 1997: 531–40. 74 Kastanis, A. “The Teaching of Mathematics in the Greek Military Academy”, 123–39. 75 Kastanis, Aspects of the Neo‐Hellenic Mathematical Culture, 196. 76 Kyprianos, P. A Comparative History of Greek Education (in Greek). Athens: Ekdoseis Bibliorama, 2004: 97. 77 Antoniou, D. The Origin of Educational Planning in the Neo‐Hellenic State: The Plan of the Commission of 1833 (in Greek). Athens: Ekdoseis Pataki, 1992: 109. 78 Ibid., 33. 79 Education in liberated Greece was provided by 49 non‐elementary schools in 1829, a number reduced to 39 by 1831. 80 Toumasis, Ch. “The Epos of Euclidean Geometry in Greek Secondary Education (1836–1985): Pressure for Change and Resistance.” Educational Studies in Mathematics 21 (1990): 491–508. 81 Toumasis, Ch. “Trends and Characteristics of Secondary School mathematics in New Greece, in Relation to Socio‐Economic Changes and the Developments of Mathematical Science (1836–1985)” (in Greek). Ph.D., Department of Mathematics, University of Patra, 1989: 131. 82 Zorbala, K. “A Greek Geometry Textbook of the 19th Century: Influences of Mathematical Science on Axiomatic in School.” Sudhoffs Archiv 86, no. 2 (2002): 198–219. 83 The textbook: Leichter Leitfaden der Elementargeometrie und Trigonometrie. Giessen: 1799, 1819. 84 The textbook: Die Arithmetik, Algebra und allgemeine Grössenlehre für Schulunterricht. Bädeker: Essen, 1836. 85 The textbook: Die Planimetrie und Stereometrie für Schulunterricht. Bädeker: Essen, 1836. 86 Koppe’s Solid Geometry and Plane Geometry had been published in one volume in German; see previous note. 87 Some of them came from the Ionian Academy, like Antonios Fatseas (1821–1872) and Gerasimos Zochios (1821–1881). Others came from the Military School, like V. Nikolaidis and Michael Sofianos (1811–1888). 88 Phili, Chr. “Some Aspects of Scientific Society in Athens at the End of the xixth Century: Mathematics and Mathematicians.” Archives Internationales d’Histoire des Sciences 50, no. 145 (2000): 302–20. 89 Kastanis, Aspects of the Neo‐Hellenic Mathematical Culture, 197. 90 Loc. cit. 91 It should be noted that Carandinos made a minor meta‐theoretical contribution in the preface of his translation of Leslie’s book; he quoted the analytical method. 92 The preface of Die Arithmetik, Algebra und allgemeine Grössenlehre für Schulunterricht says that he followed the ideas of Martin Ohm (1792–1872). 93 Mehrtens, H. “Mathematics in Germany circa 1800.” In Epistemological and Social Problems of Sciences in the Early 19th Century, edited by H. N. Jahnke and M. Otte. Dordrecht: Reidel, 1981: 401–20.