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Transmission of Mathematics into Greek education, : from individual choices to institutional frames Iason Kastanis and Nikos Kastanis

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Outline of the presentation Modern Greek School Channels between Greece and Europe Thessaly and Eastern Aegian Epistemological elements of the transmission Three main institutions after 1821

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Modern Greek Schools In the Ottoman Empire towards the end of the 18 th century Their curriculum included: –Advanced Mathematics –Scientific Subjects –Elements of Modern Philosophy New ideals, new programs unlike traditional, religious- centred Greek schools Jassy Ampelakia Chios, Smyrna, Kydonies

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Reasons for the modern schools Economic development Influenced by the liberal ideas of Enlightenment and especially the French Revolution

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Economic development Thessaly (Ampelakia) –Development of cotton- yarns in the second half of the 18 th century –Exports to Austria, Central and Northern Europe Eastern Aegian (Chios, Smyrna, Kydonies) –Trade of grains and cotton with France –Embargo of England against France Jassy Thessaly (Ampelakia)Eastern Aegian (Chios, Smyrna, Kydonies)

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Trading activities Thessaly – Vienna and PrussiaEastern Aegian - France

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Studying activities Young Greeks followed the same directions to study in Europe From Thessaly they went to Prussia and Vienna From Eastern Aegian they went to Livorno, Pisa and then France Adaptation to economic capabilities and therefore the trading orientations

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Thessaly studying Kavras and Dougas went to Prussia Govdelas went to Pesti Koumas went to Vienna Important contribution to the Greek mathematical education First three carried German (Prussian) influences Koumas was influenced by the “Austrian scholastics”

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Kavras’ translation Elements of Arithmetic and Algebra (translation from German), Jena, 1800

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C. Koumas and Austria Austrian “scholastics”, “that is the traditional representatives of the Catholic Church” Koumas from Thessaly played an important role in the teaching of Mathematics in Smyrna during the first decades of the 19 th century C.Koumas ( )

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C. Koumas’ translation Under the influence of the professor of Mathematics in the University of Vienna, Remigius Döttler ( ), a monk of the Catholic order of Piaristen Koumas translated Cours Encyclopédique et Élémentaire de Mathématique et de Physique (Vienna, 1800) by Jean-Claude Fontaine ( )

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Austria and translations Elements of Arithmetic and Algebra by the Jesuit Ignaz Metzburg ( ) Used in the modern school of Ioannina and in the Academy of Bucharest Greek translation of Metzburg’s Arithmetic and Algebra

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Eastern Aegian teachers Dorotheos Proios Veniamin Lesvian Ioannis Tselepis Theofilos Cairis They taught Mathematics in Chios, Kydonies and Smyrna Theofilos Cairis ( ) Veniamin Lesvian ( )

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Eastern Aegian teachers They studied in Pisa and most continued in Paris They were influenced by French Mathematics of the period

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Tselepis teaching Tselepis taught Mathematics in Chios He used Cours complet de mathématiques pures (Paris, 1809) by L.-B. Francoeur.

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Epistemological elements Analytic method in French epistemology of Mathematics Combinatorial view of Mathematics in Prussia

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Analytic method Condillac’s Logique translated in Greek by Daniel Philippidis in 1801, who taught Mathematics in the Academy of Bucharest Condillac was also an influence to Vienamin Lesvian

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Analytic method A translation of an article by Em. Develey was published in 1819 in “Logios Hermes”. This was about the Didactic of Geometry, where the analytic method is epxlained “Pure Mathematics or Logic of Mathematics teaching” by Em. Develey, Logios Hermis, 9, 1819, pp ,

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Combinatorial view There was an extensive presentation of technical elements of the Combinatorial Theory. Mainly influenced by German writers A review of the combinatorial school was published in 1821 “On Mathematics “Syntaxiology” [Combinationslehre (sic)]”, Logios Hermis, 11(6), 1821, pp. 187

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Greek War for Independency 1821

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Ionian Academy Founded in 1824 by Lord Guildford in Corfu First professor of Mathematics Ioannis Carandinos Carandinos influenced by Cherles Dupin( ) Studied in Ecole Polytechnique with the support of Lord Guildford

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Carandinos and the Ionian Academy He translated parts from the Lacroix series, Bourdon’s Algebra, Biot’s Analytic Geometry, Lagrange’s Analytic Functions and Poisson’s Mechanics. He used Monge’s Descriptive Geometry and Lacroix’s Applications of Algebra in Geometry. Later on, he translated and published the following books: –1) Elements of Arithmetic of Bourdon (Vienna, 1828) –2) Elements of Geometry of Legendre (Corfu, 1829) –3) Analysis Geometrical of John Leslie (Corfu, 1829) –4) Treatise of Trigonometry of Legendre (Corfu, 1830)

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Carandinos’ translation of Legendre 1829

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Carandinos’ research 1827

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Central Military School It opened in 1829 under the direction of the French captain J.H. Pauzié ( ) Its model was École Polytechnique The teaching of Mathematics included: –Arithmetic and Algebra of L.P. Bourdon –Geometry and Trigonometry of A.M. Legendre –Descriptive Geometry of G.Monge First two were translated by Carandinos and published when the Military School began its function

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Carandinos’ translation 1828

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Central Military School D.Despotopopulos was a student of Carandinos in the Ionian Academy He taught Mathematics in the Central Military School from He contributed in the spread of French Mathematics

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Bavarians came to govern 1833

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Bavarian Legislation of 1836 The Bavarians legislated secondary education Publication of mathematical textbooks Vafas, another student of Carandinos, translated French books and composed books based on French material Lecons D’Algebre of Lefebure De Fourcy

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G. Gerakis More teachers of Mathematics, that had studied in the Ionian Academy, wrote books being influenced by French books or translated French books Gerakis was the only exception He studied in Germany with a state scholarship He taught for many years Mathematics in the secondary education He translated and then published German textbooks He composed his own books influenced by German mathematics

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Gerakis’ translation of Carl Koppe 1855

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University of Athens Founded in 1837 by the Bavarians First professor of Mathematics was Constantinos Negris Negris studied in École Polytechnique He taught Mathematics based on books like Geometry of Legendre, Descriptive Geometry of Hachette Negris was a supporter of the Positive Philosophy Constantinos Negris ( )

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Final remarks Greek mathematical education was deeply influenced by the French mathematical textbooks in the first half of the 19 th century Koppe, translated by Gerakis, was a follower of the ideas of Martin Ohm, an important representative of the combinatorial school The transmission of German Mathematics was limited, even though they were more developed and structured in a cognitive level

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