DOCSLIB.ORG

The Transcendence of Pi Has Been Known for About a Century

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
The Transcendence of Pi Has Been Known for About a Century Results in Mathematics Contents 117 J. Bair/F. Jongmans Volume 7/No. 2/1984 Some remarks about recent result Pages 117-250 on the asymptotic cone 119 W. Beekmann/S. C Chang On the structure of summability fields 130 P. Bundschuh/1. Shiokawa A measure for the linear inde- pendence of certain numbers 145 P. L. Butzer/R. J. Nessel/E. L. Stark Eduard Helly (1884-1943) in memoriam 154 A. S. Cavaretta jr./H. P. Dikshit/ A. Sharma An extension of a theorem of Walsh 164 R. Fritsch The transcendence of ir has been known for about a century-but who was the man who discovered it? 184 Y. Hirano/H. Tominaga On simple ring extensions gener- ated by two idempotents 190 J. Joussen Eine Bemerkung zu einem Satz von Sylvester 192 H. Karzel/C. J. Maxson Fibered groups with non-trivial centers 209 H. Meiert G. Rosenberger Hecke-Integrale mit rationalen periodischen Funktionen und Dirichlet-Reihen mit Funk• tionalgleichung 234 G. Schiffels/M. Stemel Einbettung von topologischen Ringen in Quotientenringe Short Communications on Mathematical Dissertations 249 G. BaszenskijW. Schempp TAXT Konvergenzbeschleunigung von Orthogonal-Doppelreihen The Journal Copyright RESULTS IN MATHEMATICS It is a fundamental condition of publication that submitted RESULTATE DER MATHEMATIK manuscripts have not been published, nor will be simulta- publishes mainly research papers in all Heids of pure and applied mathematics. In addition, it publishes summaries of any mathematical neously submitted or published elsewhere. By submitting a field and surveys of any mathematical subject provided they are de- manuscript, the authors agree that the Copyright for their signed to advance some recent mathematical development. Finally, it article is transferred to the publisher if and when the arti- publishes short Communications on mathematical dissertations. Such cle is accepted for publication. The Copyright Covers the short Communications should be written by the author of the disserta• exclusive rights to reproduce and distribute the article, in- tions and by the Supervisor. They should not exceed two printed cluding reprints, Photographie reproduetions, microform pages. or any other reproduetions of similar nature, and transla- RESULTS IN MATHEMATICS tions. RESULTATE DER MATHEMATIK Photographie reproduetion, microform, or any other re- veröffentlicht Forschungsbeiträge zu allen Gebieten der reinen und produetion of text, figures or tables from this Journal is angewandten Mathematik. Darüber hinaus können auch in begrenz• prohibited without permission obtained from the pub• tem Ausmass Beiträge, welche eine Zusammenfassung eines mathema• lisher. tischen Gebietes oder eine Übersicht über einen mathematischen Problemkreis geben, veröffentlicht werden, sofern sie geeignet sind, © 1984 Birkhäuser Verlag, P.O. Box 133, CH-4010 Basel/ neuere Entwicklungen der Mathematik zu fördern. Schliesslich kön• nen kurze Mitteilungen über mathematische Dissertationen veröffent• Switzerland licht werden. Diese sollten vom Autor der Dissertation und einem Gutachter verfasst sein und eine Darstellung der Resultate in ihrem Bezug zu umfassenderen Forschungsvorhaben enthalten. Sie sollten For users in the USA: einen Umfang von zwei Druckseiten nicht überschreiten. The appearance of the code immediateiy before each arti• cle in this Journal indicates the Copyright owner's consent Editor in Chief that copies of articles may be made for personal or inter• Prof. Dr. Hans-Joachim Arnold nal use, or for the personal or internal use of specific Cli• Fachbereich Mathematik der Universität Duisburg ents. However this consent is given on the condition that the copier pay the stated per copy fee through the Copy• (Federal Republic of Germany) right Clearance Center, Inc., 21 Congress St., Salem. Mass. 01970, for copying beyond that permitted by Sec- Editorial Board tions 107 or 108 of the U.S. Copyright Law. This consent Prof. Dr. Hans-Joachim Arnold does not extend to other kinds of copying, such as copying Prof. Dr. Franz Pittnauer for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. Prof. Dr. Heinrich Wefelscheid For copying from back volumes of this Journal see Per• Fachbereich Mathematik der Universität Duisburg missions to Photo-Copy: Publisher's Fee List of the CCC. Editorial Office Fachbereich Mathematik, For users in the Federal Republic of Germany: Universität Duisburg, All rights reserved (including those of translation into for- Lotharstrasse 65, eign languages). No part of this Journal may be repro- D-4100 Duisburg duced in any form - by photoprint, microfilm, or any other means - nor transmitted or translated into a ma• Editors chine language without the written permission of the pub- lishers. Only Single copies of contributions, or parts there- Prof. Dr. J. Aczel, Waterloo of, may be reproduced for personal use. Copies repro- Prof. Dr. R. Artzy, Haifa duced and used for other than private purposes in an in- Prof. Dr. A. Barlotti, Bologna dustrial or commercial undertaking are subject to Copy• Prof. Dr. W. Benz, Hamburg right and, in such cases, a Copyright fee must be paid to Prof. Dr. P. L. Butzer, Aachen the VG WORT, Abteilung Wissenschaft, Goethestrasse 49, Prof. Dr. S.S. Chern, Berkeley 8000 München 2, from whom conditions of payment can Prof. Dr. P.M. Cohn, London be obtained on request. Prof. Dr. G. Ewald, Bochum Prof. Dr. G. Frank, Dortmund ISSN 0378-6218 Prof. Dr. P. Henrici, Zürich Prof. Dr. F. Hering, Dortmund Prof. Dr. E. Hewitt, Seattle Subscription Information 1 Prof. Dr. H. Karzel, München This Journal appears in 2 issues per year Prof. Dr. K. Leichtweiß, Stuttgart Annual subscription: Sfr. 104-, DM 120.-, approx. US$ 55.00 Prof. Dr. M. Mikoläs, Budapest postage included Prof. Dr. L. Nachbin, Rio de Janeiro and Rochester Single issue: Sfr. 58.-, DM 66.-, approx. US$ 29.00 postage not included Prof. Dr. M.Z. Nashed, Newark Subscription Orders should be placed with Birkhäuser Verlag, Prof. Dr. M. Reimer, Dortmund P.O. Box 133, CH-4010 Basel/Switzerland, or through your book• Prof. Dr. H. Rund, Tucson sei ler of subscription agency. Prof. Dr. W. Schempp, Siegen Additional charges for airmail to other countries are available on Prof. Dr.Dr.h.c. E. Sperner, Hamburg! request. Claims for underlivered issues must be made promptly - at the very latest, immediateiy following receipt of the issue sueeeeding Prof. Dr. Hisao Tominaga, Okayama the missing number. Annual subscriptions cannot be cancelled be• Prof. Dr. L. Tzafriri, Jerusalem fore the fixed date of expiration. Cancellations of standing orders Prof. Dr. W. Wasow, Madison must be effected 2 months before the end of the Publishing year. Prof. Dr. K. Zeller, Tübingen Printed in Switzerland 0378-6218/84/020164-20 $01.50 + 0.20/0 Results in Mathematics, Vol. 7 (1984) © 1984 Birkhäuser Verlag, Basel The transcendence of TT has been known for about a Century - but who was the man who discovered it? RUDOLF FRITSCH Freiburg, April 12, 1882 A very well known German mathematical Institution is the "Mathematische Forschungsinstitut Oberwolf ach". Its director Professor Martin Barner of the University of Freiburg im Breisgau, built his private house on the Loretto hill, a part of the Black Forest belonging to the city of Freiburg. It Stands on a place of extreme mathematical interest, because a young man had an important idea here. It was his 30th birthday, and he was alone on a stroll to Günterstal, a small village with a medieval monastery, today also part of Freiburg. Five years beforehand, in October 1877 as associate professor in Freiburg he had been invited to take similar walks in the Company of the (füll) professors Thomae1 from Freiburg and du Bois-Reymond2 from Tübingen, Thomae's friend and predecessor, who often came back for short visits. On the first of these walks he was unsuitably dressed, hiking through the creeks and brushwood of the Black Forest with top-hat and tails, whereas his colleagues looked like todays equivalent of "green-peacers". Besides enjoying the wonderful landscape, the group engaged in mathematical discussions. Thomae and du Bois-Reymond were specialists in (complex) analysis; our young man was brilliant in geometry, having learned a lot from Clebsch3 and Felix Klein4, especially the tools which he used so effectively a short time later. One topic touched on in their talks was the problem of the transcendence of TT. Euler5 and Lambert6 had conjectured that TT was transcendental. If this could be proved, then the very old question of squaring the circle would be settled7. Thomae and du Bois-Reymond proposed to attack this problem by means of continued fractions, a device which the French mathematician Liouville8 had very successfully used in order to clarify the notion of transcendental numbers and to exhibit some of such numbers. But our young friend was not attracted to this approach. Some years previously he had spent a winter term (1876/77) in Paris, where Hermite9 had shown him how to prove the transcendence of e using integration of real functions. He feit that this must be the right path leading to the goal, although for a long time he had had no idea how to begin. Meanwhile his personal circumstances had changed. On October 1, 1879 he had taken over the 165 166 RUDOLF FRITSCH chair of Thomae who had moved to Jena, and was too far away to come back just for walks. Reminiscing about the past, he frequently made such strolls alone now, just like the one on this pleasant day. Some weeks beforehand he had looked through his collection of reprints for Hermite's famous paper on the Solution of the general equation of degree 5 by means of elliptic functions10. By chance, the proof of the transcendence of e caught his eye and he started to study it again. Hermite himself regarded this paper as his own most significant accomplishment. At the place where Barner's house Stands today, the long hoped for idea flashed through his mind: e™ = — 1! He rushed home and wrote down the paper: "Über die Zahl 7r" (On the number -rr)11.
Load more

Recommended publications
  • Mollweide Projection and the ICA Logo Cartotalk, October 21, 2011 Institute of Geoinformation and Cartography, Research Group Cartography (Draft Paper)
    Mollweide Projection and the ICA Logo CartoTalk, October 21, 2011 Institute of Geoinformation and Cartography, Research Group Cartography (Draft paper) Miljenko Lapaine University of Zagreb, Faculty of Geodesy, [email protected] Abstract The paper starts with the description of Mollweide's life and work. The formula or equation in mathematics known after him as Mollweide's formula is shown, as well as its proof "without words". Then, the Mollweide map projection is defined and formulas derived in different ways to show several possibilities that lead to the same result. A generalization of Mollweide projection is derived enabling to obtain a pseudocylindrical equal-area projection having the overall shape of an ellipse with any prescribed ratio of its semiaxes. The inverse equations of Mollweide projection has been derived, as well. The most important part in research of any map projection is distortion distribution. That means that the paper continues with the formulas and images enabling us to get some filling about the liner and angular distortion of the Mollweide projection. Finally, the ICA logo is used as an example of nice application of the Mollweide projection. A small warning is put on the map painted on the ICA flag. It seams that the map is not produced according to the Mollweide projection and is different from the ICA logo map. Keywords: Mollweide, Mollweide's formula, Mollweide map projection, ICA logo 1. Introduction Pseudocylindrical map projections have in common straight parallel lines of latitude and curved meridians. Until the 19th century the only pseudocylindrical projection with important properties was the sinusoidal or Sanson-Flamsteed.
    [Show full text]
  • Arnold Sommerfeld in Einigen Zitaten Von Ihm Und Über Ihn1
    K.-P. Dostal, Arnold Sommerfeld in einigen Zitaten von ihm und über ihn Seite 1 Karl-Peter Dostal, Arnold Sommerfeld in einigen Zitaten von ihm und über ihn1 Kurze biographische Bemerkungen Arnold Sommerfeld [* 5. Dezember 1868 in Königsberg, † 26. April 1951 in München] zählt neben Max Planck, Albert Einstein und Niels Bohr zu den Begründern der modernen theoretischen Physik. Durch die Ausarbeitung der Bohrschen Atomtheorie, als Lehrbuchautor (Atombau und Spektrallinien, Vorlesungen über theoretische Physik) und durch seine „Schule“ (zu der etwa die Nobelpreisträger Peter Debye, Wolfgang Pauli, Werner Heisenberg und Hans Bethe gehören) sorgte Sommerfeld wie kein anderer für die Verbreitung der modernen Physik.2 Je nach Auswahl könnte Sommerfeld [aber] nicht nur als theoretischer Physiker, sondern auch als Mathematiker, Techniker oder Wissenschaftsjournalist porträtiert werden.3 Als Schüler der Mathematiker Ferdinand von Lindemann, Adolf Hurwitz, David Hilbert und Felix Klein hatte sich Sommerfeld zunächst vor allem der Mathematik zugewandt (seine erste Professur: 1897 - 1900 für Mathematik an der Bergakademie Clausthal). Als Professor an der TH Aachen von 1900 - 1906 gewann er zunehmendes Interesse an der Technik. 1906 erhielt er den seit Jahren verwaisten Lehrstuhl für theoretische Physik in München, an dem er mit wenigen Unterbrechungen noch bis 1940 (und dann wieder ab 19464) unterrichtete. Im Gegensatz zur etablierten Experimen- talphysik war die theoretische Physik anfangs des 20. Jh. noch eine junge Disziplin. Sie wurde nun zu
    [Show full text]
  • Transnational Mathematics and Movements: Shiing- Shen Chern, Hua Luogeng, and the Princeton Institute for Advanced Study from World War II to the Cold War1
    Chinese Annals of History of Science and Technology 3 (2), 118–165 (2019) doi: 10.3724/SP.J.1461.2019.02118 Transnational Mathematics and Movements: Shiing- shen Chern, Hua Luogeng, and the Princeton Institute for Advanced Study from World War II to the Cold War1 Zuoyue Wang 王作跃,2 Guo Jinhai 郭金海3 (California State Polytechnic University, Pomona 91768, US; Institute for the History of Natural Sciences, Chinese Academy of Sciences, Beijing 100190, China) Abstract: This paper reconstructs, based on American and Chinese primary sources, the visits of Chinese mathematicians Shiing-shen Chern 陈省身 (Chen Xingshen) and Hua Luogeng 华罗庚 (Loo-Keng Hua)4 to the Institute for Advanced Study in Princeton in the United States in the 1940s, especially their interactions with Oswald Veblen and Hermann Weyl, two leading mathematicians at the IAS. It argues that Chern’s and Hua’s motivations and choices in regard to their transnational movements between China and the US were more nuanced and multifaceted than what is presented in existing accounts, and that socio-political factors combined with professional-personal ones to shape their decisions. The paper further uses their experiences to demonstrate the importance of transnational scientific interactions for the development of science in China, the US, and elsewhere in the twentieth century. Keywords: Shiing-shen Chern, Chen Xingshen, Hua Luogeng, Loo-Keng Hua, Institute for 1 This article was copy-edited by Charlie Zaharoff. 2 Research interests: History of science and technology in the United States, China, and transnational contexts in the twentieth century. He is currently writing a book on the history of American-educated Chinese scientists and China-US scientific relations.
    [Show full text]
  • Real Proofs of Complex Theorems (And Vice Versa)
    REAL PROOFS OF COMPLEX THEOREMS (AND VICE VERSA) LAWRENCE ZALCMAN Introduction. It has become fashionable recently to argue that real and complex variables should be taught together as a unified curriculum in analysis. Now this is hardly a novel idea, as a quick perusal of Whittaker and Watson's Course of Modern Analysis or either Littlewood's or Titchmarsh's Theory of Functions (not to mention any number of cours d'analyse of the nineteenth or twentieth century) will indicate. And, while some persuasive arguments can be advanced in favor of this approach, it is by no means obvious that the advantages outweigh the disadvantages or, for that matter, that a unified treatment offers any substantial benefit to the student. What is obvious is that the two subjects do interact, and interact substantially, often in a surprising fashion. These points of tangency present an instructor the opportunity to pose (and answer) natural and important questions on basic material by applying real analysis to complex function theory, and vice versa. This article is devoted to several such applications. My own experience in teaching suggests that the subject matter discussed below is particularly well-suited for presentation in a year-long first graduate course in complex analysis. While most of this material is (perhaps by definition) well known to the experts, it is not, unfortunately, a part of the common culture of professional mathematicians. In fact, several of the examples arose in response to questions from friends and colleagues. The mathematics involved is too pretty to be the private preserve of specialists.
    [Show full text]
  • Robert De Montessus De Ballore's 1902 Theorem on Algebraic
    Robert de Montessus de Ballore’s 1902 theorem on algebraic continued fractions : genesis and circulation Hervé Le Ferrand ∗ October 31, 2018 Abstract Robert de Montessus de Ballore proved in 1902 his famous theorem on the convergence of Padé approximants of meromorphic functions. In this paper, we will first describe the genesis of the theorem, then investigate its circulation. A number of letters addressed to Robert de Montessus by different mathematicians will be quoted to help determining the scientific context and the steps that led to the result. In particular, excerpts of the correspondence with Henri Padé in the years 1901-1902 played a leading role. The large number of authors who mentioned the theorem soon after its derivation, for instance Nörlund and Perron among others, indicates a fast circulation due to factors that will be thoroughly explained. Key words Robert de Montessus, circulation of a theorem, algebraic continued fractions, Padé’s approximants. MSC : 01A55 ; 01A60 1 Introduction This paper aims to study the genesis and circulation of the theorem on convergence of algebraic continued fractions proven by the French mathematician Robert de Montessus de Ballore (1870-1937) in 1902. The main issue is the following : which factors played a role in the elaboration then the use of this new result ? Inspired by the study of Sturm’s theorem by Hourya Sinaceur [52], the scientific context of Robert de Montessus’ research will be described. Additionally, the correlation with the other topics on which he worked will be highlighted,
    [Show full text]
  • The History of the Abel Prize and the Honorary Abel Prize the History of the Abel Prize
    The History of the Abel Prize and the Honorary Abel Prize The History of the Abel Prize Arild Stubhaug On the bicentennial of Niels Henrik Abel’s birth in 2002, the Norwegian Govern- ment decided to establish a memorial fund of NOK 200 million. The chief purpose of the fund was to lay the financial groundwork for an annual international prize of NOK 6 million to one or more mathematicians for outstanding scientific work. The prize was awarded for the first time in 2003. That is the history in brief of the Abel Prize as we know it today. Behind this government decision to commemorate and honor the country’s great mathematician, however, lies a more than hundred year old wish and a short and intense period of activity. Volumes of Abel’s collected works were published in 1839 and 1881. The first was edited by Bernt Michael Holmboe (Abel’s teacher), the second by Sophus Lie and Ludvig Sylow. Both editions were paid for with public funds and published to honor the famous scientist. The first time that there was a discussion in a broader context about honoring Niels Henrik Abel’s memory, was at the meeting of Scan- dinavian natural scientists in Norway’s capital in 1886. These meetings of natural scientists, which were held alternately in each of the Scandinavian capitals (with the exception of the very first meeting in 1839, which took place in Gothenburg, Swe- den), were the most important fora for Scandinavian natural scientists. The meeting in 1886 in Oslo (called Christiania at the time) was the 13th in the series.
    [Show full text]
  • The Intellectual Journey of Hua Loo-Keng from China to the Institute for Advanced Study: His Correspondence with Hermann Weyl
    ISSN 1923-8444 [Print] Studies in Mathematical Sciences ISSN 1923-8452 [Online] Vol. 6, No. 2, 2013, pp. [71{82] www.cscanada.net DOI: 10.3968/j.sms.1923845220130602.907 www.cscanada.org The Intellectual Journey of Hua Loo-keng from China to the Institute for Advanced Study: His Correspondence with Hermann Weyl Jean W. Richard[a],* and Abdramane Serme[a] [a] Department of Mathematics, The City University of New York (CUNY/BMCC), USA. * Corresponding author. Address: Department of Mathematics, The City University of New York (CUN- Y/BMCC), 199 Chambers Street, N-599, New York, NY 10007-1097, USA; E- Mail: [email protected] Received: February 4, 2013/ Accepted: April 9, 2013/ Published: May 31, 2013 \The scientific knowledge grows by the thinking of the individual solitary scientist and the communication of ideas from man to man Hua has been of great value in this respect to our whole group, especially to the younger members, by the stimulus which he has provided." (Hermann Weyl in a letter about Hua Loo-keng, 1948).y Abstract: This paper explores the intellectual journey of the self-taught Chinese mathematician Hua Loo-keng (1910{1985) from Southwest Associ- ated University (Kunming, Yunnan, China)z to the Institute for Advanced Study at Princeton. The paper seeks to show how during the Sino C Japanese war, a genuine cross-continental mentorship grew between the prolific Ger- man mathematician Hermann Weyl (1885{1955) and the gifted mathemati- cian Hua Loo-keng. Their correspondence offers a profound understanding of a solidarity-building effort that can exist in the scientific community.
    [Show full text]
  • European Influences in the Fine Arts: Melbourne 1940-1960
    INTERSECTING CULTURES European Influences in the Fine Arts: Melbourne 1940-1960 Sheridan Palmer Bull Submitted in total fulfilment of the requirements of the degree ofDoctor ofPhilosophy December 2004 School of Art History, Cinema, Classics and Archaeology and The Australian Centre The University ofMelbourne Produced on acid-free paper. Abstract The development of modern European scholarship and art, more marked.in Austria and Germany, had produced by the early part of the twentieth century challenging innovations in art and the principles of art historical scholarship. Art history, in its quest to explicate the connections between art and mind, time and place, became a discipline that combined or connected various fields of enquiry to other historical moments. Hitler's accession to power in 1933 resulted in a major diaspora of Europeans, mostly German Jews, and one of the most critical dispersions of intellectuals ever recorded. Their relocation to many western countries, including Australia, resulted in major intellectual and cultural developments within those societies. By investigating selected case studies, this research illuminates the important contributions made by these individuals to the academic and cultural studies in Melbourne. Dr Ursula Hoff, a German art scholar, exiled from Hamburg, arrived in Melbourne via London in December 1939. After a brief period as a secretary at the Women's College at the University of Melbourne, she became the first qualified art historian to work within an Australian state gallery as well as one of the foundation lecturers at the School of Fine Arts at the University of Melbourne. While her legacy at the National Gallery of Victoria rests mostly on an internationally recognised Department of Prints and Drawings, her concern and dedication extended to the Gallery as a whole.
    [Show full text]
  • Arxiv:1803.01386V4 [Math.HO] 25 Jun 2021
    2009 SEKI http://wirth.bplaced.net/seki.html ISSN 1860-5931 arXiv:1803.01386v4 [math.HO] 25 Jun 2021 A Most Interesting Draft for Hilbert and Bernays’ “Grundlagen der Mathematik” that never found its way into any publi- Working-Paper cation, and 2 CVof Gisbert Hasenjaeger Claus-Peter Wirth Dept. of Computer Sci., Saarland Univ., 66123 Saarbrücken, Germany [email protected] SEKI Working-Paper SWP–2017–01 SEKI SEKI is published by the following institutions: German Research Center for Artificial Intelligence (DFKI GmbH), Germany • Robert Hooke Str.5, D–28359 Bremen • Trippstadter Str. 122, D–67663 Kaiserslautern • Campus D 3 2, D–66123 Saarbrücken Jacobs University Bremen, School of Engineering & Science, Campus Ring 1, D–28759 Bremen, Germany Universität des Saarlandes, FR 6.2 Informatik, Campus, D–66123 Saarbrücken, Germany SEKI Editor: Claus-Peter Wirth E-mail: [email protected] WWW: http://wirth.bplaced.net Please send surface mail exclusively to: DFKI Bremen GmbH Safe and Secure Cognitive Systems Cartesium Enrique Schmidt Str. 5 D–28359 Bremen Germany This SEKI Working-Paper was internally reviewed by: Wilfried Sieg, Carnegie Mellon Univ., Dept. of Philosophy Baker Hall 161, 5000 Forbes Avenue Pittsburgh, PA 15213 E-mail: [email protected] WWW: https://www.cmu.edu/dietrich/philosophy/people/faculty/sieg.html A Most Interesting Draft for Hilbert and Bernays’ “Grundlagen der Mathematik” that never found its way into any publication, and two CV of Gisbert Hasenjaeger Claus-Peter Wirth Dept. of Computer Sci., Saarland Univ., 66123 Saarbrücken, Germany [email protected] First Published: March 4, 2018 Thoroughly rev. & largely extd. (title, §§ 2, 3, and 4, CV, Bibliography, &c.): Jan.
    [Show full text]
  • Life and Work of Egbert Brieskorn (1936-2013)
    Life and work of Egbert Brieskorn (1936 – 2013)1 Gert-Martin Greuel, Walter Purkert Brieskorn 2007 Egbert Brieskorn died on July 11, 2013, a few days after his 77th birthday. He was an impressive personality who left a lasting impression on anyone who knew him, be it in or out of mathematics. Brieskorn was a great mathematician, but his interests, knowledge, and activities went far beyond mathematics. In the following article, which is strongly influenced by the authors’ many years of personal ties with Brieskorn, we try to give a deeper insight into the life and work of Brieskorn. In doing so, we highlight both his personal commitment to peace and the environment as well as his long–standing exploration of the life and work of Felix Hausdorff and the publication of Hausdorff ’s Collected Works. The focus of the article, however, is on the presentation of his remarkable and influential mathematical work. The first author (GMG) has spent significant parts of his scientific career as a arXiv:1711.09600v1 [math.AG] 27 Nov 2017 graduate and doctoral student with Brieskorn in Göttingen and later as his assistant in Bonn. He describes in the first two parts, partly from the memory of personal cooperation, aspects of Brieskorn’s life and of his political and social commitment. In addition, in the section on Brieskorn’s mathematical work, he explains in detail 1Translation of the German article ”Leben und Werk von Egbert Brieskorn (1936 – 2013)”, Jahresber. Dtsch. Math.–Ver. 118, No. 3, 143-178 (2016). 1 the main scientific results of his publications.
    [Show full text]
  • An Inquiry Into Alfred Clebsch's Geschlecht
    ”Are the genre and the Geschlecht one and the same number?” An inquiry into Alfred Clebsch’s Geschlecht François Lê To cite this version: François Lê. ”Are the genre and the Geschlecht one and the same number?” An inquiry into Alfred Clebsch’s Geschlecht. Historia Mathematica, Elsevier, 2020, 53, pp.71-107. hal-02454084v2 HAL Id: hal-02454084 https://hal.archives-ouvertes.fr/hal-02454084v2 Submitted on 19 Aug 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. “Are the genre and the Geschlecht one and the same number?” An inquiry into Alfred Clebsch’s Geschlecht François Lê∗ Postprint version, April 2020 Abstract This article is aimed at throwing new light on the history of the notion of genus, whose paternity is usually attributed to Bernhard Riemann while its original name Geschlecht is often credited to Alfred Clebsch. By comparing the approaches of the two mathematicians, we show that Clebsch’s act of naming was rooted in a projective geometric reinterpretation of Riemann’s research, and that his Geschlecht was actually a different notion than that of Riemann. We also prove that until the beginning of the 1880s, mathematicians clearly distinguished between the notions of Clebsch and Riemann, the former being mainly associated with algebraic curves, and the latter with surfaces and Riemann surfaces.
    [Show full text]
  • From Riemann Surfaces to Complex Spaces Reinhold Remmert∗
    From Riemann Surfaces to Complex Spaces Reinhold Remmert∗ We must always have old memories and young hopes Abstract This paper analyzes the development of the theory of Riemann surfaces and complex spaces, with emphasis on the work of Rie- mann, Klein and Poincar´e in the nineteenth century and on the work of Behnke-Stein and Cartan-Serre in the middle of this cen- tury. R´esum´e Cet article analyse le d´eveloppement de la th´eorie des surfaces de Riemann et des espaces analytiques complexes, en ´etudiant notamment les travaux de Riemann, Klein et Poincar´eauXIXe si`ecle et ceux de Behnke-Stein et Cartan-Serre au milieu de ce si`ecle. Table of Contents 1. Riemann surfaces from 1851 to 1912 1.1. Georg Friedrich Bernhard Riemann and the covering principle 1.1∗. Riemann’s doctorate 1.2. Christian Felix Klein and the atlas principle 1.3. Karl Theodor Wilhelm Weierstrass and analytic configurations AMS 1991 Mathematics Subject Classification: 01A55, 01A60, 30-03, 32-03 ∗Westf¨alische Wilhelms–Universit¨at, Mathematisches Institut, D–48149 Munster,¨ Deutschland This expos´e is an enlarged version of my lecture given in Nice. Gratias ago to J.-P. Serre for critical comments. A detailed exposition of sections 1 and 2 will appear elsewhere. SOCIET´ EMATH´ EMATIQUE´ DE FRANCE 1998 204 R. REMMERT 1.4. The feud between G¨ottingen and Berlin 1.5. Jules Henri Poincar´e and automorphic functions 1.6. The competition between Klein and Poincar´e 1.7. Georg Ferdinand Ludwig Philipp Cantor and countability of the topology 1.8.
    [Show full text]