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CARL FRIEDRICH GEISER AND FERDINAND RUDIO: THE MEN BEHIND THE FIRST INTERNATIONAL CONGRESS OF MATHEMATICIANS Stefanie Ursula Eminger A Thesis Submitted for the Degree of PhD at the University of St Andrews 2015 Full metadata for this item is available in Research@StAndrews:FullText at: http://research-repository.st-andrews.ac.uk/ Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/6536 This item is protected by original copyright Carl Friedrich Geiser and Ferdinand Rudio: The Men Behind the First International Congress of Mathematicians Stefanie Ursula Eminger This thesis is submitted in partial fulfilment for the degree of PhD at the University of St Andrews 2014 Table of Contents Abstract 7 Acknowledgements 9 1. Introduction 11 2. Carl Friedrich Geiser (1843 – 1934) 15 2.1 Life 15 2.2 Connection with Steiner 33 2.3 Impact at the Polytechnic and on Education 39 3. Ferdinand Karl Rudio (1856 – 1929) 49 3.1 Life 49 3.2 Contribution to Euler’s Opera Omnia 53 4. The First International Congress of Mathematicians, Zurich 1897 57 4.1 Background and Organisation 57 4.1.1 Historical Developments 57 4.1.2 Organising the Congress 62 4.1.3 The Congress Itself 67 4.1.4 Geiser’s Contribution 76 4.1.5 Rudio’s Contribution 77 4.2 The Swiss Organising Committee 79 4.2.1 Ernst Julius Amberg (1871 – 1952) 79 4.2.2 Christian Beyel (1854 – 1941) 82 4.2.3 Hermann Bleuler (1837 – 1912) 83 4.2.4 Heinrich Burkhardt (1861 – 1914) 86 4.2.5 Fritz Bützberger (1862 – 1922) 89 4.2.5.1 Bützberger’s Work on Steiner 92 4.2.6 Gustave Dumas (1872 – 1955) 98 4.2.7 Ernst Fiedler (1861 – 1954) 100 4.2.8 Jérôme Franel (1859 – 1939) 103 4.2.9 Walter Gröbli (1852 – 1903) 106 4.2.10 Salomon Eduard Gubler (1845 – 1921) 109 4.2.11 Albin Herzog (1852 – 1909) 111 4.2.12 Arthur Hirsch (1866 – 1948) 113 4.2.13 Adolf Hurwitz (1859 –1919) 115 4.2.14 Adolf Kiefer (1857 – 1929) 121 4.2.15 Gustav Künzler 123 4.2.16 Marius Lacombe (1862 – 1938) 123 4.2.17 Hermann Minkowski (1864 – 1909) 125 4.2.18 Johann Jakob Rebstein (1840 – 1907) 130 4.2.19 Heinrich Friedrich Weber (1843 – 1912) 134 4.2.20 Adolf Weiler (1851 – 1916) 137 5. Geiser’s Schoolbook and Letters to a Schoolteacher 145 5.1 Einleitung in die synthetische Geometrie 145 5.1.1 Background and Motivation 145 5.1.2 Structure and Content 150 5.1.3 Geiser’s Style and Method 165 5.1.3.1 §18: Pole and Polar with Respect to a Circle 167 5.1.4 Reception 169 5.2 Letters to Julius Gysel 175 5.2.1. Julius Gysel (1851 – 1935) 176 5.2.1.1 Letters from Ludwig Schläfli 181 5.2.2. Letters from Geiser 182 6. Rudio as a Historian of Mathematics 193 6.1 Archimedes, Huygens, Lambert, Legendre 193 6.1.1 Background and Motivation 193 6.1.2 Chapter One 196 6.1.3 Chapter Two 198 6.1.4 Chapter Three 205 6.1.5 Chapter Four 207 6.1.6 Reception 212 6.1.7 Comparison of Rudio’s AHLL and Hobson’s Squaring the Circle 215 6.2 The Commentary of Simplicius and Related Papers 224 6.2.1 Motivation 224 6.2.2 Overview of Relevant Papers 228 6.2.3 References to his Papers 238 6.3 Rudio’s Popular Lectures: Leonhard Euler and Über den Antheil der mathematischen Wissenschaften an der Kultur der Renaissance 240 6.3.1 Rathausvorträge 240 6.3.2 Publication 241 6.3.3 Euler Talk 243 6.3.4 Renaissance Talk 246 7. Conclusion 259 Appendix A – Glossary 261 Appendix B – The Federal Polytechnic 265 Appendix C – Publication Lists 273 C.1 – Geiser’s Publications 273 C.2 – Rudio’s Publications 275 Appendix D – Friedrich Robert Scherrer (1854 – 1935) 279 Appendix E – Translations 281 E.1 Material relating to the 1897 ICM 281 E.1.1 Letter from C F Geiser to fellow mathematicians in Zurich 281 E.1.2 Welcoming Speech by Adolf Hurwitz 281 E.1.3 Opening Speech by Carl Friedrich Geiser 282 E.1.4 Closing Speech by Carl Friedrich Geiser 285 E.1.5 Über die Aufgaben und die Organisation internationaler mathematischer Kongresse by Ferdinand Rudio 286 E. 2 Letters 291 E.2.1 Letters from Carl Friedrich Geiser to Julius Gysel (1874 – 1890) 291 E.2.2 Letters from Carl Friedrich Geiser to Fritz Bützberger (1895 – 1907) 301 E.2.3 Letters from Ludwig Schläfli to Julius Gysel (1874 – 1888) 303 E.3 Papers 311 E.3.1 C F Geiser: In Memoriam Jakob Steiner 311 E.3.2 C F Geiser: In Memoriam Theodor Reye 330 E.3.3 F Rudio: Leonhard Euler 348 E.3.4 F Rudio: On the Contribution of Mathematics to the Culture of the Renaissance 357 Bibliography 373 Abstract The first International Congress of Mathematicians (ICM) was held in Zurich in 1897, setting the standards for all future ICMs. Whilst giving an overview of the congress itself, this thesis focuses on the Swiss organisers, who were predominantly university professors and secondary school teachers. As this thesis aims to offer some insight into their lives, it includes their biographies, highlighting their individual contributions to the congress. Furthermore, it explains why Zurich was chosen as the first host city and how the committee proceeded with the congress organisation. Two of the main organisers were the Swiss geometers Carl Friedrich Geiser (1843-1934) and Ferdinand Rudio (1856-1929). In addition to the congress, they also made valuable contributions to mathematical education, and in Rudio’s case, the history of mathematics. Therefore, this thesis focuses primarily on these two mathematicians. As for Geiser, the relationship to his great-uncle Jakob Steiner is explained in more detail. Furthermore, his contributions to the administration of the Swiss Federal Institute of Technology are summarised. Due to the overarching theme of mathematical education and collaborations in this thesis, Geiser’s schoolbook Einleitung in die synthetische Geometrie is considered in more detail and Geiser’s methods are highlighted. A selection of Rudio’s contributions to the history of mathematics is studied as well. His book Archimedes, Huygens, Lambert, Legendre is analysed and compared to E W Hobson’s treatise Squaring the Circle. Furthermore, Rudio’s papers relating to the commentary of Simplicius on quadratures by Antiphon and Hippocrates are considered, focusing on Rudio’s translation of the commentary and on Die Möndchen des Hippokrates. The thesis concludes with an analysis of Rudio’s popular lectures Leonhard Euler and Über den Antheil der mathematischen Wissenschaften an der Kultur der Renaissance, which are prime examples of his approach to the history of mathematics. 7 8 Acknowledgements Firstly, I would like to thank my supervisors, Prof Edmund Robertson and Dr John O’Connor, for taking me on as a research student. Their knowledge, experience, and words of advice and encouragement were invaluable during the past four years. A big thank you also goes to Dr Colva Roney-Dougal for officially supervising me – without her support my PhD would not have been possible. I would like to thank all those who helped me along the way by providing information, pointing out sources, and generally offering advice. They are too numerous for me to name them all individually, but I am grateful for all their contributions as each of them added a little piece to the jigsaw puzzle that is this thesis. Particular thanks go to: The staff at the ETH Library Archive; the staff at the Stadtarchiv Schaffhausen; Rev Simon Kuert, town historian in Langenthal, canton Bern; Roland Berger and Tina Mark of the Staatsarchiv Schaffhausen, Anita Bruder of the Kantonsschule Schaffhausen, and Urs Uehlinger of the Naturforschende Gesellschaft Schaffhausen; the staff at the University of St Andrews Library; the staff at the Library of the Freie Universität Berlin. I would also like to thank all those nameless individuals who digitise journals and books, and make them available online. Without these resources my research would have been much slower and certainly much more laborious. Thanks go to the BSHM Research in Progress conference organisers and to Peter Körtesi, Miskolc, Hungary, for inviting me to speak at conferences, thus providing me with invaluable experience of sharing my research with others. Thank you to Valerie Sturrock, Tricia Watson, Tricia Heggie, and Peter Lindsay, for their help with admin, PC equipment, and any other queries. A big Merci and thank you goes to my godfather, Roman Krapf, and Sylvie Beurret-Krapf, with Léonie and Eloi, for their generous hospitality during my visits to Zurich. 9 Thank you to Anna Schröder and Liz Lewis for their company, words of encouragement, and many conversations about anything from PhD worries to explaining tutorial questions, and anything not to do with mathematics. A special thank you goes to my partner Hannah Mace for always being there for me, cheering me up and telling me to stop being silly when I needed it, and keeping me grounded (and supplying me with tea and cake!). Lastly I must thank my family – my parents Wolfgang and Elisabeth Eminger, and my sister Katharina – for supporting me and caring about my education, and showing me how wonderful it is to explore different cultures, past and present. Without their help (not least financial support) I would not have been able to study at St Andrews, let alone embark on a PhD. 10 1. Introduction The first International Congress of Mathematicians (ICM) took place in Zurich in 1897.
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