On known and less known relations of Leonhard Euler with Poland

Authors

  • Roman Sznajder Bowie State University

DOI:

https://doi.org/10.4467/23921749SHS.16.005.6148

Keywords:

Jowin Bystrzycki, complex numbers, Danzig Academic Gymnasium, Carl Gottlieb Ehler, Leonhard Euler, Königsberg bridge problem, Heinrich Kühn, King Stanisław August Poniatowski, Józef Rogaliński, Nathanael Matthaeus von Wolf

Abstract

In this work we focus on research contacts of Leonhard Euler with Polish scientists of his era, mainly with those from the city of Gdańsk (then Gedanum, Danzig). L. Euler was the most prolific mathematician of all times, the most outstanding mathematician of the 18th century, and one of the best ever. The complete edition of his manuscripts is still in process (Kleinert 2015; Kleinert, Mattmüller 2007).

Euler’s contacts with French, German, Russian, and Swiss scientists have been widely known, while relations with Poland, then one of the largest European countries, are still in oblivion. Euler visited Poland only once, in June of 1766, on his way back from Berlin to St. Petersburg. He was hosted for ten days in Warsaw by Stanisław II August Poniatowski, the last king of Poland. Many Polish scientists were introduced to Euler, not only from mathematical circles, but also astronomers and geographers. The correspondence of Euler with Gdańsk scientists and officials, including Carl L. Ehler, Heinrich Kühn and Nathanael M. von Wolf, originated already in the mid-1730s. We highlight the relations of L. Euler with H. Kühn, a professor of mathematics at the Danzig Academic Gymnasium and arguably the best Polish mathematician of his era. It was H. Kühn from whom Euler learned about the Königsberg Bridge Problem; hence one can argue that the beginning of the graph theory and topology of the plane originated in Gdańsk. In addition, H. Kühn was the first mathematician who proposed a geometric interpretation of complex numbers, the theme very much appreciated by Euler.

Findings included in this paper are either unknown or little known to a general mathematical community.

Author Biography

Roman Sznajder, Bowie State University

References

Archiwum Główne Akt Dawnych, Central Archives of Historical Records, Warsaw, Poland. Zbiór Popielów (Popiel Collection).

Bernoulli, Johann III 1779: Reisen durch Brandenburg, Pommern, Preussen, Curland, Russland und Polen in Jahren 1777 und 1778. Leipzig:

Caspar Fritsch. Bd. I, pp. 282–287, 298–299, Bd. II, pp. 212–213. Available online: https://books.google.pl/books?id=t0hCAAAAcAAJ (Bd. I.); https://books.google.pl/books?id=xEhCAAAAcAAJ (Bd. II.) (retrieved: 28/12/2016).

Calinger, Ronald S. 2016: Leonhard Euler. Mathematical Genius in the Enlightenment. Princeton, USA: Princeton University Press. ISBN 978-0-691-11927-4.

Cieślak, Edmund (ed.) 1993: History of Gdańsk (in Polish). Vol. III (1): 1655–1793. Gdańsk, Poland: Polish Academy of Sciences, Institute of History. ISBN 83-215-3251-9.

Czerniakowska, Małgorzata 1998: Titius (Tietz) Jan Daniel (1729–1796). Słownik Biograficzny Pomorza Nadwiślańskiego, supl. I, pp. 320–321. Gdańsk: Gdańskie Towarzystwo Naukowe, Uniwersytet Gdański.

Czerniakowska, Małgorzata 2006: Leonard Euler (1707–1783) and Poland (in Polish). Gdańsk: Published by the author. ISBN 83-924379-2-6.

Czerniakowska, Małgorzata 2012: Davisson, Daniel Bogumił (1729–ca. 1789). Słownik Biograficzny Pomorza Nadwiślanskiego, supl. III, pp. 64–65. Gdańsk: Gdańskie Towarzystwo Naukowe, Uniwersytet Gdański.

Eneström, Gustaf 1910–1913: Verzeichnis der Schriften Leonhard Eulers. Leipzig: Teubner (Jahresbericht der Deutschen Mathematiker-Vereinigung, Ergänzungsband 4). [A simplified version of the Eneström Index is available at http://eulerarchive.maa.org/index/enestrom.html] (retrieved: 28/12/2016).

Euler, Leonhard 1736: Solutio problematis ad geometriam situs pertinentis. Commentarii Academiae Scientiarum Imperialis Petropolitanae 8, pp. 128–140.

Euler, Leonhard 1740: Letter to Carl G. Ehler (Petropolis, October 5, 1740). Preserved in the Manuscripts and Rare Books Department of the University of Tartu Library. Available online at the University of Tartu Library, DSpace Repository: http://dspace.ut.ee/bitstream/handle/10062/5555/euler_10_05_1740.pdf (retrieved: 28/12/2016).

Euler, Leonhard 1768: Lettres a une princesse d’Allemagne sur divers sujets de physique et de philosophie. St. Petersbourg: Imprimerie de l’Academie Imperiale des Sciences.

Euler, Leonhard 1963: Pis’ma k uchenym. Moscow–Leningrad: Izd. Akademii Nauk SSSR.

Euler, Leonhard 1975: Opera omnia, Series IVA Commercium epistolicum, vol. 1. Leonhardi Euleri Commercium Epistolicum. Descriptio Commercii Epistolici / Leonhard Euler Briefwechsel. Beschreibung Zusammenfassungen der Briefe und Verzeichnisse. Edited by Adolf P. Juškevič, Vladimir I. Smirnov, Walter Habicht. Basel: Birkhäuser.

Fellmann, Emil A. 1995: Leonhard Euler (rororo Biographie). Hamburg: Rowohlt. ISBN 3-499-50387-5. English translation (by Erika and Walter Gautschi), Birkhäuser, 2007. ISBN 978-3-7643-7538-6.

Folkerts, Menso 1976/2008: Titius (Tietz) Johann Daniel. Dictionary of Scientific Biography vol. 13, pp. 424–426. New York: Charles Scribner’s Sons. Electronic edition.

Folkerts, Menso 2008: Complete Dictionary of Scientific Biography. Encyclopedia.com. Available online: http://www.encyclopedia.com/doc/1G2-2830904338.html (retrieved: 28/12/2016).

Fuss, Nicolas 1783: Éloge de monsieur Léonard Euler, lu a l’Academié Impériale des Sciences. St. Petersburg. Available online: http://www.gap-system.org/~history/Extras/Euler_Fuss_Eulogy.html (retrieved: 28/12/2016).

Gdańsk Library of the Polish Academy of Sciences: Johann Friedrich Jacobsen’s Diary, MS 2512.

Hanow, Michael Christoph 1741: Impossibilitas Quadraturae circluli, a

priori adserta. Gedani: Schreiberus. Available online: https://books.google.pl/books?id=xyZQAAAAcAAJ (retrieved: 28/12/2016).

Hanow, Michael Christoph 1763: Letter to Johann Daniel Titius (December 17, 1763). Preserved in the Manuscript Department of the University Library of Tartu. Available online at the University Library of Tartu, DSpace Repository: http://dspace.ut.ee/bitstream/handle/10062/5421/hanov_17_12_1763.pdf (retrieved: 28/12/2016).

Hanow, Michael Christoph 1764: Letter to Johann Daniel Titius (August 17, 1764). Preserved in the Manuscript Department of the University Library of Tartu. Available online at the University Library of Tartu, DSpace Repository: http://dspace.ut.ee/bitstream/handle/10062/5421/hanov_17_08_1764.pdf (retrieved: 28/12/2016).

Hopkins, Brian; Wilson, Robin J. 2004: The Truth about Königsberg. The College Mathematics Journal 35(3), pp. 198–207. Available online: https://www.maa.org/sites/default/files/pdf/upload_library/22/Polya/hopkins.pdf (retrieved: 28/12/2016).

Hube, Jan Michał 1759: Versuch einer analytischen Abhandlung von den Kegelschnitten mit einer Vorrede von A. G. Kästner. Göttingen.

Hube, Jan Michał 1783: Introduction to Physics for national schools. Part I. Mechanics, textbook. Polish translation from Latin) by Jan Koc. Kraków.

Hube, Jan Michał 1791/1801: Letters in Physics or natural sciences adopted for a general use. Part I (in Polish). Warszawa: Drukarnia P. Zawadzkiego. Available online: http://jbc.bj.uj.edu.pl/Content/323426/NDIGSTDR014485.pdf (retrieved: 28/12/2016). A German translation – 1801: Vollständiger und fasslicher Unterricht in der Naturlehre in einer Reihe von Briefen an einen jungen Herrn vom Stande. Leipzig (4 volumes).

Hube, Jan Michał 1792: Physics for national schools (Part I. Mechanics), teacher’s manual. Polish translation from Latin) by Jan Koc. Kraków.

Gautschi, Walter 2008: Leonhard Euler: His Life, the Man, and His Works. SIAM Review 50(1), pp. 3–33. Available online: http://euler-2007.ch/doc/EulerLec.pdf (retrieved: 28/12/2016).

Januszajtis, Andrzej 2001: Scientists in old Gdańsk: and centuries. Task Quarterly 5(3), pp. 389–399. Available online: http://euler-2007.ch/doc/EulerLec.pdf (retrieved: 28/12/2016).

Januszajtis, Andrzej 2002: Societas Physicae Experimentalis – the first Physics Society in Poland. The origins of the Society. Task Quarterly 6(2), pp. 323–330. Available online: http://task.gda.pl/files/quart/TQ2002/02/TQ0206Z3.PDF (retrieved: 28/12/2016).

Januszajtis, Andrzej 2011: A Walk Around Gdańsk for Physicists. Physics in Perspective 13/4, pp. 456–480. DOI: 10.1007/s00016-011-0066-5. Available online: http:/link.springer.com/article/10.1007/s00016-011-0066-5 (retrieved: 28/12/2016).

Januszajtis, Andrzej 2015: Z dziejów gdańskiej nauki, 2nd Edition (in Polish). Gdańsk, Poland: Wydawnictwo Politechnki Gdańskiej. ISBN 978-83-7348-605-8.

Kleinert, Andreas 2015: Leonhardi Euleri Opera Omnia: Editing the works and correspondence of Leonhard Euler. Prace Komisji Historii Nuki PAU XIV, pp. 13–35. Available online: http://pau.krakow.pl/PKHN-PAU/pkhn-pau-XIV-2015-2.pdf (retrieved: 28/12/2016).

Kleinert, Andreas; Mattmüller, Martin 2007: Leonhardi Euleri Opera Omnia: a centenary project. European Mathematical Society, 65, pp. 25–32. Available online: https://www.ems-ph.org/journals/newsletter/pdf/2007-09-65.pdf (retrieved: 28/12/2016).

Klyve, Dominic; Stemkoski, Lee; Tou, Erik 2016: The Euler Archive. A digital library dedicated to the work and life of Leonhard Euler. Hosted by the Mathematical Association of America. Available online: http://eulerarchive.maa.org/index.html (retrieved: 28/12/2016).

Kłado Tatiana; Wołoszyński, Ryszard W. 1965: Korespondencja Stanisława Augusta z Leonardem Eulerem, petersburską Akademią Nauk 1766-1783. Studia i Materiały do Dziejów Nauki Polskiej. Seria C, zeszyt 10 (1965), ss. 3-41.

Kopelevich, Judith Ch. 1978: The beginnings of ties of the Saint Petersburg Academy of Sciences with the scholars of Gdańsk (in Polish). Kwartalnik Historii Nauki i Techniki 23/2, pp. 323–331. Available online: http://bazhum.muzhp.pl/media//files/Kwartalnik_Historii_Nauki_i_Techniki/Kwartalnik_Historii_Nauki_i_Techniki-r1978-t23-n2/Kwartalnik_Historii_Nauki_i_Techniki-r1978-t23-n2-s323-331/Kwartalnik_Historii_Nauki_i_Techniki-r1978-t23-n2-s323-331.pdf (retrieved: 28/12/2016).

Kraitchik, Maurice 1953: Mathematical Recreations. New York: Dover Publications, Inc.

Kucharzewski, Feliks 1928: Michał Jan Hube and his work on river regulation (in Polish). Przegląd Techniczny 42, pp. 811–816. Available online: http://bcpw.bg.pw.edu.pl/dlibra/docmetadata?id=3453&from=publication (retrieved: 28/12/2016).

Kühn, Heinrich 1746: Vernünftige Gedancken von dem Ursprung der Qvellen, und des Grund-Wassers, auch von andern damit verknüpften Sachen: den Liebhabern der Wahrheit mitgetheilet, aus der lateinischen in die deutsche Sprache übersetzet, und mit dienlichen Beysätzen vermehret, auch mit nöthigen Registern versehen. Berlin, Leipzig: Haude & Spener. Available online: http://reader.digitale-sammlungen.de/de/fs1/object/display/bsb11272058_00001.html (retrieved: 28/12/2016).

Kühn, Heinrich 1747: Ausführliche Beschreibung einer neuen und vollkommeneren Art von Wagen, etc. . Versuche und Abhandlungen der Naturforschenden Gesellschaft in Danzig. Erster Theil [Teil], pp. 1–76. Available online: http://echo.mpiwg-berlin.mpg.de/ECHOdocuView?url=/permanent/library/MV5541KC/index.meta (retrieved: 28/12/2016).

Kühn, Heinrich 1753: Meditationes de quantitatibus imaginariis construendis et radicibus imaginariis exhibendis. Novi Commentarii Academiae Scientiarum Imperialis Petropolitanae 3, pp. 170–223. Available online: https://babel.hathitrust.org/cgi/pt?id=ucm.5324351545. See also: http://www.biodiversitylibrary.org/item/38563#page/7/mode/1up (retrieved: 28/12/2016).

Kühn, Heinrich 1758: Der Einfluss der Mathematick und Natur-Lehre in die zeitliche Glückseeligkeit des menschlichen Geschlechtes, bei Gelegenheit der zum Andecken des vor zwey hundert Jahren gestifteten Danziger Gymnasii den 13 Junii 1758 angestellten Jubel Feyer. Acta jubilaei secundi gymnasii Gedanensis Anno Domini LDCCLVIII die XIII. Juni solenniter celebrati, pp. 265–284.

L’Huillier, Simon Antoine Jean 1778: Eléments d’arithmétique et de géométrie pour les écoles palatinales. Varsovie.

L’Huillier, Simon Antoine Jean 1780: Jeometrya dla szkół narodowych. Cz. 1. Translated by Andrzej Gawroński (Warszawa: w Drukarni Nadworney J. K. Mci). Available online (II wyd. z 1785): Biblioteka Cyfrowa UMCS; http://dlibra.umcs.lublin.pl/dlibra/docmetadata?id=15608 (retrieved: 28/12/2016).

L’Huillier, Simon Antoine Jean 1781a: Geometrya dla szkół narodowych. Część II. Translated by Andrzej Gawroński (Warszawa: w Drukarni Nadworney J. K. Mci). Available online: Pedagogiczna Biblioteka Cyfrowa; http://pbc.up.krakow.pl/Content/1490/geometrya.djvu (retrieved: 28/12/2016).

L’Huillier, Simon Antoine Jean 1781b: Arytmetyka dla szkół narodowych. Translated by Andrzej Gawroński (Warszawa: w Drukarni Nadworney J. K. Mci, 1781): Available online: http://www.dbc.wroc.pl/Content/25763/index.djvu.

L’Huillier, Simon Antoine Jean 1782: Algiebra dla szkół narodowych. Translated by Andrzej Gawroński (Warszawa (Marywil): Michał Gröll). Available online at Pokarpacka Biblioteka Cyfrowa: http://www.pbc.rzeszow.pl/dlibra/doccontent?id=8926 (retrieved: 28/12/2016).

L’Huillier, Simon Antoine Jean 1789: Polygonométrie et abrégé d’ isopérimétrie élémentaire. Genève.

L’Huillier, Simon Antoine Jean 1812–1813: Géométrie. Mémoire sur la polyédrométrie; contenant une démonstration directe du théorème d’Euler sur les polyèdres, et un examen des diverses exceptions auxquelles ce théorème est assujetti (Extracted by M. Gergonne). Annales de Mathématiques Pures et Appliquées 3, pp. 169–189. Available online: http://archive.numdam.org/ARCHIVE/AMPA/AMPA_1812 1813__3_/AMPA_1812-1813__3__169_0/AMPA_1812-1813__3__169_0.pdf (retrieved: 28/12/2016).

Linde, M. Samuel Bogumił 1814: Słownik języka polskiego. T. 6: U–Z. Warszawa: M. Samuel Bogumił Lindei Drukarnia XX. Piiarów. Availabile online at Kujawsko-Pomorska Biblioteka Cyfrowa: http://kpbc.umk.pl/dlibra/docmetadata?id=13054 (retrieved: 28/12/2016).

Memin Encyclopedia 2016: Vincetoxicum. Available online: http://memim.com/vincetoxicum.html (retrieved: 28/12/2016).

Mrozowska, Kamilla 1961: Szkoła Rycerska Stanisława Augusta Poniatowskiego (1765–1794). Wrocław– Warszawa – Kraków: Zakład Narodowy Imienia Ossolińskich Wydawnictwo Polskiej Akademii Nauk. Komitet Nauk Pedagogicznych i Psychologicznych Polskiej Akademii Nauk. „Monografie Pedagogiczne” VIII. Pod Redakcją Bogdana Suchodolskiego.

Mrozowska, Kamilla 1962–1964: Hube Jan Michał (1737–1807). Polski Słownik Biograficzny, vol. 10, ss. 67–69.

Mrozowska, Kamilla 1980: Pfleiderer Christian (1736–1821). Polski Słownik Biograficzny, vol. 25, ss. 763–764.

Odlanicki-Poczobutt, Marcin 1802: Letter to Nicolaus Fuss (Wilno, May 5, 1802). Preserved in the Manuscripts and Rare Books Department of the University of Tartu Library. Available online at the University of Tartu Library, DSpace Repository: http://dspace.ut.ee/bitstream/handle/10062/13980/odlanickipoczobutt.pdf (retrieved: 28/12/2016).

Pfleiderer, Christoph Friedrich 1782: Prorector Academiae Eberhardinae Carolinae L. S. Available online at the Eberhard Karls Universität Tübingen Universitätsbibliothek: http://idb.ub.uni-tuebingen.de/cgi-bin/digi-downloadPdf-hpdfimage.fcgi?projectname=LXV8_fol_81 (retrieved: 28/12/2016).

Pfleiderer, Christoph Friedrich 1792: Letter to Johann Albrecht Euler (Tübingen, January 12, 1792). Preserved in the Manuscript Department of the University Library of Tartu. Available online at the University Library of Tartu, DSpace Repository: http://dspace.ut.ee/bitstream/handle/10062/12018/pfleiderer.pdf (retrieved: 28/12/2016).

Pinterest 2016: Leonhard Euler. Available online: https://www.pinterest.com/eulerstalker/leonhard-euler/ (retrieved: 28/12/2016).

Przytycki, Józef Henryk 2007: KNOTS: From combinatorics of knot diagrams to the combinatorial topology based on knots. Chapter II: History of Knot Theory. Cambridge University Press, pp. 600, accepted for publication, e-print: http://arxiv.org/abs/ math/0703096 (retrieved: 28/12/2016).

Przytycki, Józef Henryk 2010: From Goeritz matrices to quasi-alternating links; A Book Chapter (Chapter 9) in The Mathematics of Knots: Theory and Applications, M. Banagl, D. Vogel, editors; Springer- Verlag, 2010, pp. 257–315. ISBN 3-642-15636-3; e-print: http://front.math.ucdavis.edu/0909.1118 (retrieved: 28/12/2016).

Przytycki, Józef Henryk 2016: Knot Theory and related with knots distributive structures. Gdańsk Lectures (in Polish). Gdańsk: Gdańsk University Press, pp. 188. Second extended edition. ISBN 978-83-7865-330-1.

Richeson, David S. 2008: Euler’s Gem. The Polyhedral Formula and the Birth of Topology . Princeton and Oxford: Princeton University Press. ISBN 978-0-691-12677-7.

Sandifer, C. Edward 2007: The Early Mathematics of Leonhard Euler. Washington, D.C.: MAA Spectrum, Mathematical Association of America. ISBN 978-0-88385-559-1.

Schubring, Gert 2006: Conflicts Between Generalization, Rigor, and Intuition: Number Concepts: Number Concepts Underlying the Development of Analysis in 17th-19th Century France and Germany. New York, USA: Springer Science & Business Media. ISBN-10:0-387-22836-5; ISBN-13: 978-0387-22836-5.“Sources and Studies in the History of Mathematics and Physical Sciences”. Available online: https://books.google.pl/books?id=rMWe3okqPOcC (retrieved: 28/12/2016).

Smirnov, Vladimir Ivanoich; JUŠKEVIČ, Adol’f Pavlovich (eds.) 1967: Leonard Eiler; perepiska. Annotirovannyi ukazatel’. (Institut istorii estestvoznaniia i tekhniki, Akademiia Nauk SSSR). Leningrad: Nauka, Leningradskoe otd-nie.

Śniadecki, Jan 1814a: Pisma rozmaite, vol. 1. Wilno – Warszawa: Nakładem i Drukiem Józefa Zawadzkiego, Typografa Uniwersytetu. Available online: http://ebuw.uw.edu.pl/Content/2090/directory.djvu (retrieved: 28/12/2016).

Śniadecki, Jan 1814b: Pisma rozmaite, vol. 2. Wilno – Warszawa: Nakładem i Drukiem Józefa Zawadzkiego, Typografa Uniwersytetu. Available online: http://ebuw.uw.edu.pl/Content/2091/directory.djvu (retrieved: 28/12/2016).

Śniadecki, Jan 1815: Letter to Nicolaus Fuss (Wilno, January 17, 1815). Preserved in the Manuscript Department of the University Library of Tartu. Available online at the University Library of Tartu, DSpace Repository: http://dspace.ut.ee/bitstream/handle/10062/12115/sniadecki1.pdf (retrieved: 28/12/2016).

Thornische Wöhentliche Nachrichten und Anzeigen nebst einem Anhange von Gelehrten Sachen 1766: Euler’s visit in Warsaw (3 VII, 1766, p. 210). Available online at Kujawsko- Pomorska Biblioteka Cyfrowa: http://kpbc.umk.pl/publication/30619 (retrieved: 28/12/2016).

Titius (Tietz), Johann Daniel 1752: Dissertatio Inauguralis, Luminis lunaris theoria nova, argumentis CL. Euleri superstructa. Leipzig: Gabriel Büschel. Available online: https://books.google.pl/books?id=XDsNs7e5zcIC (retrieved: 28/12/2016).

Titius (Tietz), Johann Daniel 1763: Die gänzliche Ergebung der Lande Preussen an Polen, mittelst des A. 1466, nach der Einnahme von Comitz, zwischen König Casimir dem IV und dem Hochmeister Ludwig von Ehrlichshausen geschlossenen Friedens, historisch vorgestellet. Wittenberg.

Wiese, Ludwig Adolf 1864: Das Höhere Schulwesen in Preussen. Historisch-statistische Darstellung. Berlin: Verlag von Wiegandt und Grieben. Available online: http://reader.digitale-sammlungen.de/de/f1/object/display/bsb10735613_00005.html. See also: https://archive.org/download/bub_gb_cIvCZ9igRzUC/bub_gb_cIvCZ9igRzUC.pdf (retrieved: 28/12/2016).

Wikipedia 2016: Finow Canal. Available online: https://de.wikipedia.org/wiki/Finowkanal (retrieved: 28/12/2016).

Wilson, Robin J. 2012: Introduction to Graph Theory, 5th Ed. Upper Saddle River, New Jersey: Pearson. ISBN 978-0-27-372889-4.

Von Wolf, Nathanael Matthaeus 1767: Letter to Johann Albrecht Euler (Gdańsk, March 8, 1767). Preserved in the Manuscript Department of the University Library of Tartu. Available online at the Library of Tartu, DSpace Repository: http://dspace.ut.ee/bitstream/handle/10062/14058/wolf3.pdf (retrieved: 28/12/2016).

Downloads

Published

24-11-2016

How to Cite

Sznajder, R. (2016). On known and less known relations of Leonhard Euler with Poland. Studia Historiae Scientiarum, 15, 75–110. https://doi.org/10.4467/23921749SHS.16.005.6148

Issue

Section

RESEARCH PAPERS AND COMMUNICATIONS