Some Comments on Multiple Discovery in Mathematics
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Introduction
Copyrighted Material Introduction This book, unlike most books on mathematics, is about math- ematicians, their extraordinary passion for mathematics and their full complexity of being. We emphasize the social and emotional sides of mathematical life. In the great and famous works of Euclid and Newton, we find axioms and theorems. The mathematics seems to speak for itself. No first person speaks, no second person is addressed: “Here is Truth, here is Proof, no more need be said.” Going back to the reports of Plato and Descartes, mathematical think- ing has been seen as pure reason–a perfect and eternal faculty. The thoughts, feelings, and tribulations of the mathematician are not included. But it doesn’t take deep reflection to realize that this perfec- tion is a human creation. Mathematics is an artifact created by thinking creatures of flesh and blood. Indeed, this fact has al- ways been known to poets, novelists, and dramatists. Math- ematicians, like all people, think socially and emotionally in the categories of their time and place and culture. In any great en- deavor, such as the structuring of mathematical knowledge, we bring all of our humanity to the work. Along with reasoning, the work includes the joy of discovery, the struggle with uncer- tainty, and many other emotions. And it is shaped by social real- ities, including war, political oppression, sexism, and racism, as they have affected society and mathematicians in different eras. Today the connection between thought and emotion is a ma- jor active field of scientific research. Recently the neuroscientist Antonio Damasio and a collaborator wrote, “Modern biol- ogy reveals humans to be fundamentally emotional and social Copyrighted Material • intrODUCTION creatures. -
Contemporary Mathematics 78
CONTEMPORARY MATHEMATICS 78 Braids Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference on Artin's Braid Group held July 13-26. 1986 at the University of California, Santa Cruz, California Joan S. Birman Anatoly Libgober Editors http://dx.doi.org/10.1090/conm/078 Recent Titles in This Series 120 Robert S. Doran, Editor, Selfadjoint and nonselfadjoint operator algebras and operator theory, 1991 119 Robert A. Melter, Azriel Rosenfeld, and Prabir Bhattacharya, Editors, Vision geometry, 1991 118 Yan Shi-Jian, Wang Jiagang, and Yang Chung-chun, Editors, Probability theory and its applications in China, 1991 117 Morton Brown, Editor, Continuum theory and dynamical systems, 1991 116 Brian Harboume and Robert Speiser, Editors, Algebraic geometry: Sundance 1988, 1991 115 Nancy Flournoy an'il Robert K. Tsutakawa, Editors, Statistical multiple integration, 1991 114 Jeffrey C. Lagarias and Michael J. Todd, Editors, Mathematical developments arising from linear programming, 1990 113 Eric Grinberg and Eric Todd Quinto, Editors, Integral geometry and tomography, 1990 112 Philip J. Brown and Wayne A. Fuller, Editors, Statistical analysis of measurement error models and applications, 1990 Ill Earl S. Kramer and Spyros S. Magliveras, Editors, Finite geometries and combinatorial designs, I 990 II 0 Georgia Benkart and J. Marshall Osborn, Editors, Lie algebras and related topics, 1990 109 Benjamin Fine, Anthony Gaglione, and Francis C. Y. Tang, Editors, Combinatorial group theory, 1990 108 Melvyn S. Berger, Editor, Mathematics of nonlinear science, 1990 107 Mario Milman and Tomas Schonbek, Editors, Harmonic analysis and partial differential equations, 1990 I 06 Wilfried Sieg, Editor, Logic and computation, 1990 I 05 Jerome Kaminker, Editor, Geometric and topological invariants of elliptic operators, 1990 I 04 Michael Makkai and Robert Pare, Accessible categories: The foundations of categorical model theory, 1989 I 03 Steve Fisk, Coloring theories, 1989 I 02 Stephen McAdam, Primes associated to an ideal, 1989 101 S.-Y. -
Mathematical Genealogy of the Union College Department of Mathematics
Gemma (Jemme Reinerszoon) Frisius Mathematical Genealogy of the Union College Department of Mathematics Université Catholique de Louvain 1529, 1536 The Mathematics Genealogy Project is a service of North Dakota State University and the American Mathematical Society. Johannes (Jan van Ostaeyen) Stadius http://www.genealogy.math.ndsu.nodak.edu/ Université Paris IX - Dauphine / Université Catholique de Louvain Justus (Joost Lips) Lipsius Martinus Antonius del Rio Adam Haslmayr Université Catholique de Louvain 1569 Collège de France / Université Catholique de Louvain / Universidad de Salamanca 1572, 1574 Erycius (Henrick van den Putte) Puteanus Jean Baptiste Van Helmont Jacobus Stupaeus Primary Advisor Secondary Advisor Universität zu Köln / Université Catholique de Louvain 1595 Université Catholique de Louvain Erhard Weigel Arnold Geulincx Franciscus de le Boë Sylvius Universität Leipzig 1650 Université Catholique de Louvain / Universiteit Leiden 1646, 1658 Universität Basel 1637 Union College Faculty in Mathematics Otto Mencke Gottfried Wilhelm Leibniz Ehrenfried Walter von Tschirnhaus Key Universität Leipzig 1665, 1666 Universität Altdorf 1666 Universiteit Leiden 1669, 1674 Johann Christoph Wichmannshausen Jacob Bernoulli Christian M. von Wolff Universität Leipzig 1685 Universität Basel 1684 Universität Leipzig 1704 Christian August Hausen Johann Bernoulli Martin Knutzen Marcus Herz Martin-Luther-Universität Halle-Wittenberg 1713 Universität Basel 1694 Leonhard Euler Abraham Gotthelf Kästner Franz Josef Ritter von Gerstner Immanuel Kant -
Psychology of Aesthetics, Creativity, and the Arts
Psychology of Aesthetics, Creativity, and the Arts Foresight, Insight, Oversight, and Hindsight in Scientific Discovery: How Sighted Were Galileo's Telescopic Sightings? Dean Keith Simonton Online First Publication, January 30, 2012. doi: 10.1037/a0027058 CITATION Simonton, D. K. (2012, January 30). Foresight, Insight, Oversight, and Hindsight in Scientific Discovery: How Sighted Were Galileo's Telescopic Sightings?. Psychology of Aesthetics, Creativity, and the Arts. Advance online publication. doi: 10.1037/a0027058 Psychology of Aesthetics, Creativity, and the Arts © 2012 American Psychological Association 2012, Vol. ●●, No. ●, 000–000 1931-3896/12/$12.00 DOI: 10.1037/a0027058 Foresight, Insight, Oversight, and Hindsight in Scientific Discovery: How Sighted Were Galileo’s Telescopic Sightings? Dean Keith Simonton University of California, Davis Galileo Galilei’s celebrated contributions to astronomy are used as case studies in the psychology of scientific discovery. Particular attention was devoted to the involvement of foresight, insight, oversight, and hindsight. These four mental acts concern, in divergent ways, the relative degree of “sightedness” in Galileo’s discovery process and accordingly have implications for evaluating the blind-variation and selective-retention (BVSR) theory of creativity and discovery. Scrutiny of the biographical and historical details indicates that Galileo’s mental processes were far less sighted than often depicted in retrospective accounts. Hindsight biases clearly tend to underline his insights and foresights while ignoring his very frequent and substantial oversights. Of special importance was how Galileo was able to create a domain-specific expertise where no such expertise previously existed—in part by exploiting his extensive knowledge and skill in the visual arts. Galileo’s success as an astronomer was founded partly and “blindly” on his artistic avocations. -
The Theory of Multiple Simultaneous Discoveries
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Electronic archive of Tomsk Polytechnic University В целом видно, что студенты положительно оценивают наличие дисциплины «Творческий проект» в учебном плане и дают высокую оценку качеству ее проведения. Вывод: Кто такой инженер? И что такое творчество? Инженер от лат. «ingenium» означает способность, изобретательность. Инженер имеет дело с разработкой и внедрением инноваций и для этого ему необходим творческий как подход как основа будущей деятельности. Творчество – создание чего-то нового, которое непременно разрешает определенную проблему. Отсюда видно, что эти два понятия тесно связаны. Поэтому авторы считают, что дисциплина «Творческий про- ект» положительно влияет на процесс обучения студентов младших курсов и дает возможность получения глубоких практических знаний технических основ будущей профессии. ЛИТЕРАТУРА: 1. Всемирная инициатива CDIO. Стандарты: информ.-метод. изд. / пер. с англ. и ред. А. И. Чучалина, Т. С. Петровской, Е. С. Ку- люкиной; Том. политехн. ун-т. – Томск, 2011. 2. Рабочие программы по дисциплине «Творческий проект» [Элек- тронный ресурс] – URL: http://portal.tpu.ru/fond2 (дата обраще- ния: 13.09.15). Научный руководитель: В.С. Иванова, к.т.н., доцент, каф. ТП ИНК. THE THEORY OF MULTIPLE SIMULTANEOUS DISCOVERIES D.V. Isaeva National research Tomsk polytechnic university, Institute of non- destructive testing, Precise instrument making department, group 1B3V Since the beginning of time, people have been making different dis- coveries and inventions. They make great discoveries, which are based not only on the experience of previous generations, but on experiments and scientific analysis. However, what is the nature of discoveries? Theories of invention has been an ongoing discussion for more than a century. -
Mathematicians Fleeing from Nazi Germany
Mathematicians Fleeing from Nazi Germany Mathematicians Fleeing from Nazi Germany Individual Fates and Global Impact Reinhard Siegmund-Schultze princeton university press princeton and oxford Copyright 2009 © by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 6 Oxford Street, Woodstock, Oxfordshire OX20 1TW All Rights Reserved Library of Congress Cataloging-in-Publication Data Siegmund-Schultze, R. (Reinhard) Mathematicians fleeing from Nazi Germany: individual fates and global impact / Reinhard Siegmund-Schultze. p. cm. Includes bibliographical references and index. ISBN 978-0-691-12593-0 (cloth) — ISBN 978-0-691-14041-4 (pbk.) 1. Mathematicians—Germany—History—20th century. 2. Mathematicians— United States—History—20th century. 3. Mathematicians—Germany—Biography. 4. Mathematicians—United States—Biography. 5. World War, 1939–1945— Refuges—Germany. 6. Germany—Emigration and immigration—History—1933–1945. 7. Germans—United States—History—20th century. 8. Immigrants—United States—History—20th century. 9. Mathematics—Germany—History—20th century. 10. Mathematics—United States—History—20th century. I. Title. QA27.G4S53 2008 510.09'04—dc22 2008048855 British Library Cataloging-in-Publication Data is available This book has been composed in Sabon Printed on acid-free paper. ∞ press.princeton.edu Printed in the United States of America 10 987654321 Contents List of Figures and Tables xiii Preface xvii Chapter 1 The Terms “German-Speaking Mathematician,” “Forced,” and“Voluntary Emigration” 1 Chapter 2 The Notion of “Mathematician” Plus Quantitative Figures on Persecution 13 Chapter 3 Early Emigration 30 3.1. The Push-Factor 32 3.2. The Pull-Factor 36 3.D. -
Mathematical Genealogy of the Wellesley College Department Of
Nilos Kabasilas Mathematical Genealogy of the Wellesley College Department of Mathematics Elissaeus Judaeus Demetrios Kydones The Mathematics Genealogy Project is a service of North Dakota State University and the American Mathematical Society. http://www.genealogy.math.ndsu.nodak.edu/ Georgios Plethon Gemistos Manuel Chrysoloras 1380, 1393 Basilios Bessarion 1436 Mystras Johannes Argyropoulos Guarino da Verona 1444 Università di Padova 1408 Cristoforo Landino Marsilio Ficino Vittorino da Feltre 1462 Università di Firenze 1416 Università di Padova Angelo Poliziano Theodoros Gazes Ognibene (Omnibonus Leonicenus) Bonisoli da Lonigo 1477 Università di Firenze 1433 Constantinople / Università di Mantova Università di Mantova Leo Outers Moses Perez Scipione Fortiguerra Demetrios Chalcocondyles Jacob ben Jehiel Loans Thomas à Kempis Rudolf Agricola Alessandro Sermoneta Gaetano da Thiene Heinrich von Langenstein 1485 Université Catholique de Louvain 1493 Università di Firenze 1452 Mystras / Accademia Romana 1478 Università degli Studi di Ferrara 1363, 1375 Université de Paris Maarten (Martinus Dorpius) van Dorp Girolamo (Hieronymus Aleander) Aleandro François Dubois Jean Tagault Janus Lascaris Matthaeus Adrianus Pelope Johann (Johannes Kapnion) Reuchlin Jan Standonck Alexander Hegius Pietro Roccabonella Nicoletto Vernia Johannes von Gmunden 1504, 1515 Université Catholique de Louvain 1499, 1508 Università di Padova 1516 Université de Paris 1472 Università di Padova 1477, 1481 Universität Basel / Université de Poitiers 1474, 1490 Collège Sainte-Barbe -
Mathematics in the Austrian-Hungarian Empire
Mathematics in the Austrian-Hungarian Empire Christa Binder The appointment policy in the Austrian-Hungarian Empire In: Martina Bečvářová (author); Christa Binder (author): Mathematics in the Austrian-Hungarian Empire. Proceedings of a Symposium held in Budapest on August 1, 2009 during the XXIII ICHST. (English). Praha: Matfyzpress, 2010. pp. 43–54. Persistent URL: http://dml.cz/dmlcz/400817 Terms of use: © Bečvářová, Martina © Binder, Christa Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This document has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library http://dml.cz THE APPOINTMENT POLICY IN THE AUSTRIAN- -HUNGARIAN EMPIRE CHRISTA BINDER Abstract: Starting from a very low level in the mid oft the 19th century the teaching and research in mathematics reached world wide fame in the Austrian-Hungarian Empire before World War One. How this was complished is shown with three examples of careers of famous mathematicians. 1 Introduction This symposium is dedicated to the development of mathematics in the Austro- Hungarian monarchy in the time from 1850 to 1914. At the beginning of this period, in the middle of the 19th century the level of teaching and researching mathematics was very low – with a few exceptions – due to the influence of the jesuits in former centuries, and due to the reclusive period in the first half of the 19th century. But even in this time many efforts were taken to establish a higher education. -
MATH 801 — Braids Spring 2008 Prof
MATH 801 — Braids Spring 2008 Prof. Jean-Luc Thiffeault DESCRIPTION Everyone understands intuitively the concept of a braid as a collection of intertwined strands. However, there is a rigorous mathematical theory of braids, pioneered by Artin, which complements knot theory but is in many ways separate. Unlike knots, braids have a simple algebraic description in terms of a group, and can thus be manipulated more easily. This group structure also connects them to the mapping class groups of a surface: each element of this group describes a way of mapping a surface to itself. Braids thus provides insight into the structure of mappings of surfaces. We shall tie this to the powerful Thurston–Nielsen classification of surface diffeomorphisms. This opens the door to many applications in fluid dynamics, since fluid motion can be regarded as a re-ordering of the fluid material. Braids are also being used in computational robotics, where the motion of robotic agents subject to constraints has to be optimized. On the algebraic side, braids are potentially useful in cryptography, since there are sev- eral computationally ‘hard’ problems associated with factoring braids — especially the conjugacy problem. In this course I will present the basic theory of braids, assuming relatively few prerequi- sites. The approach will vary from semi-rigorous to rigorous, with some theorems proved and others merely motivated. The goal is to cover a lot of ground and not be slowed down by lengthy proofs. The course is aimed at both applied and pure students. A sample of topics to be covered, time permitting: • Physical braids and the algebraic description of braids • Configuration space • Braids on other surfaces; The Dirac string problem • Alexander’s and Markov’s theorem • Garside normal form and the word and conjugacy problems • The Burau representation and faithfulness • Mapping class groups • Thurston–Nielsen classification • Topological entropy • Robotics • Stirring with braids 1 PREREQUISITES Basic knowledge of group theory will help. -
Christopher J. Leininger
Christopher J. Leininger Department of Mathematics [email protected] University of Illinois at Urbana Champaign (217)-265-6763 273 Altegeld Hall, 1409 W. Green St. Urbana, IL 61802 U.S. Citizen, Born Dec. 5, 1973 EDUCATION • The University of Texas, Austin, TX Ph.D. in Mathematics, May 2002. Supervisor: Alan W. Reid • Ball State University, Muncie, IN B.S. in Mathematics, May 1997 ACADEMIC POSITIONS • University of Illinois, Urbana-Champaign, IL Associate Professor, Dept. of Math., Fall 2010{present • University of Illinois, Urbana-Champaign, IL Assistant Professor, Dept. of Math., Fall 2005{Summer 2010. • Columbia University/Barnard College, New York City, NY Assistant Professor/NSF Postdoctoral Fellow, Dept. of Math., Fall 2002{Spring 2005. VISITS • Centro di Ricerca Matematica Ennio De Giorgi, Pisa, Italy, June 2014. • Aix-Marseille Universite, July 2013. • Centre de Recerca Matem`aticaBarcelona, Spain, September/October 2012. • Park City Math Institute, Utah, July 2011, July 2012. • Oberwolfach, Germany, May 2011, June 2011, June 2015. • Hausdorff Research Institute for Mathematics, Bonn, Germany, May/June 2010. • Universit´ePaul C´ezanne, Marseille, France, Professeur Invit´e, June 2008. • Mathematical Sciences Research Institute Berkeley, CA, Member, Fall 2007. • Max-Planck-Institut f¨urMathematik, Bonn, Germany, July 2006. • University of Chicago, Chicago, IL, May/June, 2006. GRANTS & AWARDS • N.S.F. Grants D.M.S.-060388, 0905748, 1207184, 1510034: 5/2006{5/2018. • Lois M. Lackner Scholar, Dept. of Math., UIUC, 2011{2013. • Campus Research Board, UIUC, Summer 2010, spring 2007, Fall 2005. • Helen Corley Petit Scholar, College of LAS, UIUC, 2010{2011. • N. Tenney Peck Teaching Award in Mathematics, Dept. -
Telling Women's Stories: a Resource for College Mathematics Instructors
Journal of Humanistic Mathematics Volume 9 | Issue 2 July 2019 Telling Women's Stories: A Resource for College Mathematics Instructors Sarah Mayes-Tang University of Toronto Follow this and additional works at: https://scholarship.claremont.edu/jhm Part of the Arts and Humanities Commons, Curriculum and Instruction Commons, Gender Equity in Education Commons, Mathematics Commons, and the Science and Mathematics Education Commons Recommended Citation Mayes-Tang, S. "Telling Women's Stories: A Resource for College Mathematics Instructors," Journal of Humanistic Mathematics, Volume 9 Issue 2 (July 2019), pages 78-92. DOI: 10.5642/jhummath.201902.07 . Available at: https://scholarship.claremont.edu/jhm/vol9/iss2/7 ©2019 by the authors. This work is licensed under a Creative Commons License. JHM is an open access bi-annual journal sponsored by the Claremont Center for the Mathematical Sciences and published by the Claremont Colleges Library | ISSN 2159-8118 | http://scholarship.claremont.edu/jhm/ The editorial staff of JHM works hard to make sure the scholarship disseminated in JHM is accurate and upholds professional ethical guidelines. However the views and opinions expressed in each published manuscript belong exclusively to the individual contributor(s). The publisher and the editors do not endorse or accept responsibility for them. See https://scholarship.claremont.edu/jhm/policies.html for more information. Telling Women's Stories: A Resource for College Mathematics Instructors Cover Page Footnote I would like to thank the reviewer for -
OPEN SCIENCE' an Essay on Patronage, Reputation and Common Agency Contracting in the Scientific Revolution
This work is distributed as a Discussion Paper by the STANFORD INSTITUTE FOR ECONOMIC POLICY RESEARCH SIEPR Discussion Paper No. 06-38 THE HISTORICAL ORIGINS OF 'OPEN SCIENCE' An Essay on Patronage, Reputation and Common Agency Contracting in the Scientific Revolution By Paul A. David Stanford University & the University of Oxford December 2007 Stanford Institute for Economic Policy Research Stanford University Stanford, CA 94305 (650) 725-1874 The Stanford Institute for Economic Policy Research at Stanford University supports research bearing on economic and public policy issues. The SIEPR Discussion Paper Series reports on research and policy analysis conducted by researchers affiliated with the Institute. Working papers in this series reflect the views of the authors and not necessarily those of the Stanford Institute for Economic Policy Research or Stanford University. THE HISTORICAL ORIGINS OF ‘OPEN SCIENCE’ An Essay on Patronage, Reputation and Common Agency Contracting in the Scientific Revolution By Paul A. David Stanford University & the University of Oxford [email protected] or [email protected] First version: March 2000 Second version: August 2004 This version: December 2007 SUMMARY This essay examines the economics of patronage in the production of knowledge and its influence upon the historical formation of key elements in the ethos and organizational structure of publicly funded open science. The emergence during the late sixteenth and early seventeenth centuries of the idea and practice of “open science" was a distinctive and vital organizational aspect of the Scientific Revolution. It represented a break from the previously dominant ethos of secrecy in the pursuit of Nature’s Secrets, to a new set of norms, incentives, and organizational structures that reinforced scientific researchers' commitments to rapid disclosure of new knowledge.