Transmission of Mathematics into Greek education,1800-1840: from individual choices to institutional

frames

Iason Kastanis and Nikos Kastanis

Outline of the presentation

• Modern Greek School 1800-1821

• Channels between Greece and Europe

• Thessaly and Eastern Aegian

• Epistemological elements of the transmission

• Three main institutions after 1821

Modern Greek Schools

• In the Ottoman Empire towards the end of the 18th 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

Reasons for the modern schools

• Economic development

• Influenced by the liberal ideas of Enlightenment and especially the French Revolution

Economic development

• Thessaly (Ampelakia)– Development of cotton-

yarns in the second half of the 18th 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)

Trading activities

Thessaly – Vienna and Prussia Eastern Aegian - France

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

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”

Kavras’ translation

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

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 19th century

C.Koumas (1777-1836)

C. Koumas’ translation

• Under the influence of the professor of Mathematics in the University of Vienna, Remigius Döttler (1748-1812), 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 (1715-1807)

Austria and translations

• Elements of Arithmetic and Algebra by the Jesuit Ignaz Metzburg (1735-1798)

• Used in the modern school of Ioannina and in the Academy of Bucharest

Greek translation of Metzburg’s Arithmetic and Algebra

Eastern Aegian teachers

• Dorotheos Proios• Veniamin Lesvian• Ioannis Tselepis• Theofilos Cairis• They taught

Mathematics in Chios, Kydonies and Smyrna

Theofilos Cairis (1784-1853)

Veniamin Lesvian (1762-1824)

Eastern Aegian teachers

• They studied in Pisa and most continued in Paris

• They were influenced by French Mathematics of the period

Tselepis teaching

• Tselepis taught Mathematics in Chios

• He used Cours complet de mathématiques pures (Paris, 1809) by L.-B. Francoeur.

Epistemological elements

• Analytic method in French epistemology of Mathematics

• Combinatorial view of Mathematics in Prussia

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

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. 763-771, 785-800

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

Greek War for Independency 1821

Ionian Academy

• Founded in 1824 by Lord Guildford in Corfu

• First professor of Mathematics Ioannis Carandinos

• Carandinos influenced by Cherles Dupin(1784-1873)

• Studied in Ecole Polytechnique with the support of Lord Guildford

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)

Carandinos’ translation of Legendre 1829

Carandinos’ research 1827

Central Military School

• It opened in 1829 under the direction of the French captain J.H. Pauzié (1792-1848)

• 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

Carandinos’ translation 1828

Central Military School

• D.Despotopopulos was a student of Carandinos in the Ionian Academy

• He taught Mathematics in the Central Military School from 1829-1854

• He contributed in the spread of French Mathematics

Bavarians came to govern 1833

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

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

Gerakis’ translation of Carl Koppe 1855

University of Athens - 1837

• 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 (1804-1880)

Final remarks

• Greek mathematical education was deeply influenced by the French mathematical textbooks in the first half of the 19th 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