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Karl Weierstraß – Zum 200. Geburtstag „Alles Im Leben Kommt Doch Leider Zu Spät“ Reinhard Bölling Universität Potsdam, Institut Für Mathematik Prolog Nunmehr Im 74
1 Karl Weierstraß – zum 200. Geburtstag „Alles im Leben kommt doch leider zu spät“ Reinhard Bölling Universität Potsdam, Institut für Mathematik Prolog Nunmehr im 74. Lebensjahr stehend, scheint es sehr wahrscheinlich, dass dies mein einziger und letzter Beitrag über Karl Weierstraß für die Mediathek meiner ehemaligen Potsdamer Arbeitsstätte sein dürfte. Deshalb erlaube ich mir, einige persönliche Bemerkungen voranzustellen. Am 9. November 1989 ging die Nachricht von der Öffnung der Berliner Mauer um die Welt. Am Tag darauf schrieb mir mein Freund in Stockholm: „Herzlich willkommen!“ Ich besorgte das damals noch erforderliche Visum in der Botschaft Schwedens und fuhr im Januar 1990 nach Stockholm. Endlich konnte ich das Mittag- Leffler-Institut in Djursholm, im nördlichen Randgebiet Stockholms gelegen, besuchen. Dort befinden sich umfangreiche Teile des Nachlasses von Weierstraß und Kowalewskaja, die von Mittag-Leffler zusammengetragen worden waren. Ich hatte meine Arbeit am Briefwechsel zwischen Weierstraß und Kowalewskaja, die meine erste mathematikhistorische Publikation werden sollte, vom Inhalt her abgeschlossen. Das Manuskript lag in nahezu satzfertiger Form vor und sollte dem Verlag übergeben werden. Geradezu selbstverständlich wäre es für diese Arbeit gewesen, die Archivalien im Mittag-Leffler-Institut zu studieren. Aber auch als Mitarbeiter des Karl-Weierstraß- Institutes für Mathematik in Ostberlin gehörte ich nicht zu denen, die man ins westliche Ausland reisen ließ. – Nun konnte ich mir also endlich einen ersten Überblick über die Archivalien im Mittag-Leffler-Institut verschaffen. Ich studierte in jenen Tagen ohne Unterbrechung von morgens bis abends Schriftstücke, Dokumente usw. aus dem dortigen Archiv, denn mir stand nur eine Woche zur Verfügung. Am zweiten Tag in Djursholm entdeckte ich unter Papieren ganz anderen Inhalts einige lose Blätter, die Kowalewskaja beschrieben hatte. -
Halloweierstrass
Happy Hallo WEIERSTRASS Did you know that Weierestrass was born on Halloween? Neither did we… Dmitriy Bilyk will be speaking on Lacunary Fourier series: from Weierstrass to our days Monday, Oct 31 at 12:15pm in Vin 313 followed by Mesa Pizza in the first floor lounge Brought to you by the UMN AMS Student Chapter and born in Ostenfelde, Westphalia, Prussia. sent to University of Bonn to prepare for a government position { dropped out. studied mathematics at the M¨unsterAcademy. University of K¨onigsberg gave him an honorary doctor's degree March 31, 1854. 1856 a chair at Gewerbeinstitut (now TU Berlin) professor at Friedrich-Wilhelms-Universit¨atBerlin (now Humboldt Universit¨at) died in Berlin of pneumonia often cited as the father of modern analysis Karl Theodor Wilhelm Weierstrass 31 October 1815 { 19 February 1897 born in Ostenfelde, Westphalia, Prussia. sent to University of Bonn to prepare for a government position { dropped out. studied mathematics at the M¨unsterAcademy. University of K¨onigsberg gave him an honorary doctor's degree March 31, 1854. 1856 a chair at Gewerbeinstitut (now TU Berlin) professor at Friedrich-Wilhelms-Universit¨atBerlin (now Humboldt Universit¨at) died in Berlin of pneumonia often cited as the father of modern analysis Karl Theodor Wilhelm Weierstraß 31 October 1815 { 19 February 1897 born in Ostenfelde, Westphalia, Prussia. sent to University of Bonn to prepare for a government position { dropped out. studied mathematics at the M¨unsterAcademy. University of K¨onigsberg gave him an honorary doctor's degree March 31, 1854. 1856 a chair at Gewerbeinstitut (now TU Berlin) professor at Friedrich-Wilhelms-Universit¨atBerlin (now Humboldt Universit¨at) died in Berlin of pneumonia often cited as the father of modern analysis Karl Theodor Wilhelm Weierstraß 31 October 1815 { 19 February 1897 sent to University of Bonn to prepare for a government position { dropped out. -
On the First Electromagnetic Measurement of the Velocity of Light by Wilhelm Weber and Rudolf Kohlrausch
Andre Koch Torres Assis On the First Electromagnetic Measurement of the Velocity of Light by Wilhelm Weber and Rudolf Kohlrausch Abstract The electrostatic, electrodynamic and electromagnetic systems of units utilized during last century by Ampère, Gauss, Weber, Maxwell and all the others are analyzed. It is shown how the constant c was introduced in physics by Weber's force of 1846. It is shown that it has the unit of velocity and is the ratio of the electromagnetic and electrostatic units of charge. Weber and Kohlrausch's experiment of 1855 to determine c is quoted, emphasizing that they were the first to measure this quantity and obtained the same value as that of light velocity in vacuum. It is shown how Kirchhoff in 1857 and Weber (1857-64) independently of one another obtained the fact that an electromagnetic signal propagates at light velocity along a thin wire of negligible resistivity. They obtained the telegraphy equation utilizing Weber’s action at a distance force. This was accomplished before the development of Maxwell’s electromagnetic theory of light and before Heaviside’s work. 1. Introduction In this work the introduction of the constant c in electromagnetism by Wilhelm Weber in 1846 is analyzed. It is the ratio of electromagnetic and electrostatic units of charge, one of the most fundamental constants of nature. The meaning of this constant is discussed, the first measurement performed by Weber and Kohlrausch in 1855, and the derivation of the telegraphy equation by Kirchhoff and Weber in 1857. Initially the basic systems of units utilized during last century for describing electromagnetic quantities is presented, along with a short review of Weber’s electrodynamics. -
Weberˇs Planetary Model of the Atom
Weber’s Planetary Model of the Atom Bearbeitet von Andre Koch Torres Assis, Gudrun Wolfschmidt, Karl Heinrich Wiederkehr 1. Auflage 2011. Taschenbuch. 184 S. Paperback ISBN 978 3 8424 0241 6 Format (B x L): 17 x 22 cm Weitere Fachgebiete > Physik, Astronomie > Physik Allgemein schnell und portofrei erhältlich bei Die Online-Fachbuchhandlung beck-shop.de ist spezialisiert auf Fachbücher, insbesondere Recht, Steuern und Wirtschaft. Im Sortiment finden Sie alle Medien (Bücher, Zeitschriften, CDs, eBooks, etc.) aller Verlage. Ergänzt wird das Programm durch Services wie Neuerscheinungsdienst oder Zusammenstellungen von Büchern zu Sonderpreisen. Der Shop führt mehr als 8 Millionen Produkte. Weber’s Planetary Model of the Atom Figure 0.1: Wilhelm Eduard Weber (1804–1891) Foto: Gudrun Wolfschmidt in der Sternwarte in Göttingen 2 Nuncius Hamburgensis Beiträge zur Geschichte der Naturwissenschaften Band 19 Andre Koch Torres Assis, Karl Heinrich Wiederkehr and Gudrun Wolfschmidt Weber’s Planetary Model of the Atom Ed. by Gudrun Wolfschmidt Hamburg: tredition science 2011 Nuncius Hamburgensis Beiträge zur Geschichte der Naturwissenschaften Hg. von Gudrun Wolfschmidt, Geschichte der Naturwissenschaften, Mathematik und Technik, Universität Hamburg – ISSN 1610-6164 Diese Reihe „Nuncius Hamburgensis“ wird gefördert von der Hans Schimank-Gedächtnisstiftung. Dieser Titel wurde inspiriert von „Sidereus Nuncius“ und von „Wandsbeker Bote“. Andre Koch Torres Assis, Karl Heinrich Wiederkehr and Gudrun Wolfschmidt: Weber’s Planetary Model of the Atom. Ed. by Gudrun Wolfschmidt. Nuncius Hamburgensis – Beiträge zur Geschichte der Naturwissenschaften, Band 19. Hamburg: tredition science 2011. Abbildung auf dem Cover vorne und Titelblatt: Wilhelm Weber (Kohlrausch, F. (Oswalds Klassiker Nr. 142) 1904, Frontispiz) Frontispiz: Wilhelm Weber (1804–1891) (Feyerabend 1933, nach S. -
A Century of Mathematics in America, Peter Duren Et Ai., (Eds.), Vol
Garrett Birkhoff has had a lifelong connection with Harvard mathematics. He was an infant when his father, the famous mathematician G. D. Birkhoff, joined the Harvard faculty. He has had a long academic career at Harvard: A.B. in 1932, Society of Fellows in 1933-1936, and a faculty appointmentfrom 1936 until his retirement in 1981. His research has ranged widely through alge bra, lattice theory, hydrodynamics, differential equations, scientific computing, and history of mathematics. Among his many publications are books on lattice theory and hydrodynamics, and the pioneering textbook A Survey of Modern Algebra, written jointly with S. Mac Lane. He has served as president ofSIAM and is a member of the National Academy of Sciences. Mathematics at Harvard, 1836-1944 GARRETT BIRKHOFF O. OUTLINE As my contribution to the history of mathematics in America, I decided to write a connected account of mathematical activity at Harvard from 1836 (Harvard's bicentennial) to the present day. During that time, many mathe maticians at Harvard have tried to respond constructively to the challenges and opportunities confronting them in a rapidly changing world. This essay reviews what might be called the indigenous period, lasting through World War II, during which most members of the Harvard mathe matical faculty had also studied there. Indeed, as will be explained in §§ 1-3 below, mathematical activity at Harvard was dominated by Benjamin Peirce and his students in the first half of this period. Then, from 1890 until around 1920, while our country was becoming a great power economically, basic mathematical research of high quality, mostly in traditional areas of analysis and theoretical celestial mechanics, was carried on by several faculty members. -
Erica Fretwell SENSORY EXPERIMENTS Sensory Experiments PSYCHOPHYSICS, RACE, and the AESTHETICS of FEELING
S E N S O R Y E X P E R I M E N T S Psychophysics, RACE, and the Aesthetics of feeling Erica Fretwell SENSORY EXPERIMENTS Sensory Experiments PSYCHOPHYSICS, RACE, AND THE AESTHETICS OF FEELING Erica Fretwell Duke University Press Durham and London 2020 © 2020 Duke University Press All rights reserved Printed in the United States of Amer i ca on acid- free paper ∞ Designed by Amy Ruth Buchanan Typeset in Arno and Avenir by Westchester Publishing Services Library of Congress Cataloging- in- Publication Data Names: Fretwell, Erica, [date] author. Title: Sensory experiments : psychophysics, race, and the aesthetics of feeling / Erica Fretwell. Description: Durham : Duke University Press, 2020. | Includes bibliographical references and index. Identifiers:lccn 2019054741 (print) | lccn 2019054742 (ebook) | isbn 9781478009863 (hardcover) | isbn 9781478010937 (paperback) | isbn 9781478012450 (ebook) Subjects: lcsh: Psychophysics. | Senses and sensation— Social aspects. | Racism—United States—Psychological aspects. | Racism—United States—History—19th century. | Science—Social aspects—United States—History—19th century. Classification:lcc bf237 .f74 2020 (print) | lcc bf237 (ebook) | ddc 152.10973/09034—dc23 lc record available at https://lccn.loc.gov/2019054741 lc ebook record available at https://lccn.loc.gov/2019054742 Duke University Press gratefully acknowl- edges the University at Albany, SUNY, which provided funds toward the publication of this book. IN MEMORY OF STEVEN FRETWELL CONTENTS Acknowl edgments ix Introduction: NEW SENSATION 1 -
Fundamental Theorems in Mathematics
SOME FUNDAMENTAL THEOREMS IN MATHEMATICS OLIVER KNILL Abstract. An expository hitchhikers guide to some theorems in mathematics. Criteria for the current list of 243 theorems are whether the result can be formulated elegantly, whether it is beautiful or useful and whether it could serve as a guide [6] without leading to panic. The order is not a ranking but ordered along a time-line when things were writ- ten down. Since [556] stated “a mathematical theorem only becomes beautiful if presented as a crown jewel within a context" we try sometimes to give some context. Of course, any such list of theorems is a matter of personal preferences, taste and limitations. The num- ber of theorems is arbitrary, the initial obvious goal was 42 but that number got eventually surpassed as it is hard to stop, once started. As a compensation, there are 42 “tweetable" theorems with included proofs. More comments on the choice of the theorems is included in an epilogue. For literature on general mathematics, see [193, 189, 29, 235, 254, 619, 412, 138], for history [217, 625, 376, 73, 46, 208, 379, 365, 690, 113, 618, 79, 259, 341], for popular, beautiful or elegant things [12, 529, 201, 182, 17, 672, 673, 44, 204, 190, 245, 446, 616, 303, 201, 2, 127, 146, 128, 502, 261, 172]. For comprehensive overviews in large parts of math- ematics, [74, 165, 166, 51, 593] or predictions on developments [47]. For reflections about mathematics in general [145, 455, 45, 306, 439, 99, 561]. Encyclopedic source examples are [188, 705, 670, 102, 192, 152, 221, 191, 111, 635]. -
The Psychophysics of Consciousness: a Hypothesis
S.R. Joye The Psychophysics of Consciousness The Psychophysics of Consciousness: A Hypothesis "Hypothesis: a very poor choice of word to designate the supreme spiritual act by which the dust-cloud of experience takes on form and is kindled at the fire of knowledge." Pierre Teilhard de Chardin August 9, 2013 S.R. Joye, B.S. Electrical Engineering, M.A. Asian Philosophy, CIIS Doctoral Candidate, Department of Philosophy & Religion Concentration in Philosophy, Cosmology, and Consciousness PARP 9600 – Doctoral Comprehensive Exam Paper Professor Allan Combs School of Consciousness and Transformation Summer Semester 2013 Comp. Exam Part II The Psychophysics of Consciousness The Psychophysics of Consciousness: A Hypothesis Abstract Gustav Fechner, the German experimental psychologist, coined the term psychophysics in 1860, publishing the first mathematical equation to model human consciousness.1 Fechner assumed that any future approaches to consciousness would include mathematical and physical underpinnings. In 1995, the cognitive scientist and philosopher David Chalmers coined the phrase "the hard problem" as being that of connecting consciousness with some physical substrate. According to Chalmers, "The really hard problem of consciousness is the problem of experience. Most existing theories of consciousness either deny the phenomenon, explain something else, or elevate the problem to an eternal mystery."2 As Chalmers points out, unfortunately, the modern scientific community has not yet produced a model of consciousness supported by mathematics and physics, thus no progress in Fecher's "psychophysics." However there is growing interest among the scientific community in string theory, the only branch of mathematical geometry that has successfully explained recent discoveries in high energy particle physics. -
Inauguration
INAUGURATION OF THE PERMANENT SECRETARIAT OF THE INTERNATIONAL MATHEMATICAL UNION February 1, 2011, Berlin, Germany Ribbon Cutting Ceremony: Professor Dr. Martin Grötschel, Dr. Georg Schütte, Professor Dr. Ingrid Daubechies, Dr. Knut Nevermann, Professor Dr. Jürgen Sprekels (from left to right), and Gauss on the wall. Contents The IMU and Berlin ..................................................................................................................... 3 Where to find the IMU Secretariat ............................................................................................... 4 Adresses delivered at the Opening Ceremony ............................................................................. 5 Dr. Georg Schütte, State Secretary at the German Federal Ministry of Education and Research .............................. 5 Professor Dr. Jürgen Zöllner, Senator for Education, Science and Research of the State of Berlin, speech read by Dr. Knut Nevermann, State Secretary for Science and Research at the Berlin Senate .................................................... 8 Professor Dr. Ingrid Daubechies, President of the International Mathematical Union ............. 10 Professor Dr. Christian Bär, President of the German Mathematical Society (DMV) ............. 12 Professor Dr. Jürgen Sprekels, Director of the Weierstrass Institute, Berlin ............................ 13 The Team of the Permanent Secretariat ..................................................................................... 16 Impressions from the Opening -
The Book and Printed Culture of Mathematics in England and Canada, 1830-1930
Paper Index of the Mind: The Book and Printed Culture of Mathematics in England and Canada, 1830-1930 by Sylvia M. Nickerson A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Institute for the History and Philosophy of Science and Technology University of Toronto © Copyright by Sylvia M. Nickerson 2014 Paper Index of the Mind: The Book and Printed Culture of Mathematics in England and Canada, 1830-1930 Sylvia M. Nickerson Doctor of Philosophy Institute for the History and Philosophy of Science and Technology University of Toronto 2014 Abstract This thesis demonstrates how the book industry shaped knowledge formation by mediating the selection, expression, marketing, distribution and commercialization of mathematical knowledge. It examines how the medium of print and the practices of book production affected the development of mathematical culture in England and Canada during the nineteenth and early twentieth century. Chapter one introduces the field of book history, and discusses how questions and methods arising from this inquiry might be applied to the history of mathematics. Chapter two looks at how nineteenth century printing technologies were used to reproduce mathematics. Mathematical expressions were more difficult and expensive to produce using moveable type than other forms of content; engraved diagrams required close collaboration between author, publisher and engraver. Chapter three examines how editorial decision-making differed at book publishers compared to mathematical journals and general science journals. Each medium followed different editorial processes and applied distinct criteria in decision-making about what to publish. ii Daniel MacAlister, Macmillan and Company’s reader of science, reviewed mathematical manuscripts submitted to the company and influenced which ones would be published as books. -
Helmholtz's Physiological Psychology1
Helmholtz’s Physiological Psychology1 Lydia Patton [email protected] In Philosophy of Mind in the Nineteenth Century, ed. S. Lapointe (Routledge, 2018) Author’s copy. Published version available at: https://www.routledge.com/Philosophy-of- Mind-in-the-Nineteenth-Century-The-History-of-the- Philosophy/Lapointe/p/book/9781138243965 Hermann von Helmholtz (1821-1894) contributed two major works to the theory of sensation and perception in the nineteenth century. The first edition of the The Doctrine of the Sensations of Tone was published in 1863, and the first edition of the Handbook of Physiological Optics was published in toto in 1867. These works established results both controversial and enduring: Helmholtz’s analysis of mixed colors and of combination tones, his arguments against nativism, and his commitment to analyzing sensation and perception using the techniques of natural science, especially physiology and physics. This study will focus on the Physiological Optics (hereafter PO), and on Helmholtz’s account of sensation, perception, and representation via “physiological psychology”. Helmholtz emphasized that external stimuli of sensations are causes, and sensations are their effects, and he had a practical and naturalist orientation toward the analysis of phenomenal experience. 1 Above all, I would like to thank Sandra Lapointe for her insight into the configuration and promise of this project, for conceiving of this volume, and for astute and perceptive responses to earlier versions, which shaped the project as it stands now. Clinton Tolley read the penultimate version of the paper and contributed invaluable suggestions, including preventing me from making a most consequential error of translation, for which I am grateful. -
Laboratories at the Faculty of Medicine of the University of Coimbra in the XIX Century
Scientific Research and Essays Vol. 5(12), pp. 1402-1417, 18 June, 2010 Available online at http://www.academicjournals.org/SRE ISSN 1992-2248 ©2010 Academic Journals Review Laboratories at the Faculty of Medicine of the University of Coimbra in the XIX century Maria Burguete Instituto Rocha Cabra, l Calçada Bento da Rocha Cabral, 14; 1250-047 Lisboa, Portugal. E-mail: [email protected]. Accepted 25 March, 2010 The beginning of natural sciences came to predominate in medicine with the emergence of natural scientific thinking in the first half of the 19th century. Philosophical approaches became less relevant. Research concentrated on the biological, physiological and chemical foundations of life. Therefore, the creation of laboratories of experimental physiology, histology, toxicology and pathological anatomy was the result of the reorganization of the medicine faculty at Coimbra university between 1866 - 1872, according to the following paradigm replacement: The superficial look at disease was replaced by the study of the inner body, an attempt to understand the symptoms, giving rise to a new paradigm of medicine practice – evidence-based-medicine (EBM). However, in spite of the good conditions of space and light provided by the Colégio de Jesus in Coimbra to accommodate the laboratory of physiology and histology, an important “ingredient” was missing: the experimental instruments to design experimental works to provide - good teaching and research model for the Coimbra faculty of medicine. In peripheral countries, as Portugal, some professors played a central role in this development, bringing in new ideas, new instruments, and new techniques and producing scientific and didactic texts in native languages.