DOCSLIB.ORG

E. H. Moore's Early Twentieth-Century Program for Reform in Mathematics Education David Lindsay Roberts

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
E. H. Moore's Early Twentieth-Century Program for Reform in Mathematics Education David Lindsay Roberts E. H. Moore's Early Twentieth-Century Program for Reform in Mathematics Education David Lindsay Roberts 1. INTRODUCTION. The purposeof this articleis to examinebriefly the natureand consequencesof an early twentieth-centuryprogram to reorientthe Americanmath- ematicalcurriculum, led by mathematicianEliakim Hastings Moore (1862-1932) of the Universityof Chicago.Moore's efforts, I conclude,were not ultimatelyvery suc- cessful, and the reasonsfor this failureare worthpondering. Like WilliamMueller's recentarticle [16], which drawsattention to the spiriteddebates regarding American mathematicseducation at the end of the nineteenthcentury, the presentarticle may re- mind some readersof morerecent educational controversies. I don't discouragesuch thinking,but cautionthat the lessons of historyare not likely to be simpleones. E. H. Mooreis especiallyintriguing as a pedagogicalpromoter because of his high placein the historyof Americanmathematics. He is a centralsource for muchof twen- tiethcentury American mathematical research activity. As a grossmeasure of Moore's influencewe may note the remarkablefact thatmore than twice as manyPh.D. mathe- maticianswere produced by his Universityof Chicagomathematics department during his tenurethan were producedby any othersingle institutionin the UnitedStates. In- deed, the Universityof Chicagoproduced nearly 20% of all Americanmathematics Ph.D.s duringthe period[22, p. 366]. Moreover,among Moore's doctoral students at Chicagowere suchluminaries as GeorgeDavid Birkhoff (1884-1944), OswaldVeblen (1880-1960), LeonardEugene Dickson (1874-1954), and RobertLee Moore (1882- 1974). This quartet,each one of whom became a presidentof the AmericanMathe- maticalSociety (AMS) as well as a memberof the NationalAcademy of Sciences, was especiallyfruitful in producingadditional distinguished researchers, at Harvard, Princeton,the Universityof Chicago, and the Universityof Texas, respectively.For details of the researchaccomplishments of Moore and his progenythe readermay consultthe excellentbook by KarenParshall and David Rowe on the formationof the Americanmathematical research community [18, pp. 323-426]. It is also clearthat Moore was a formidableacademic politician. Especially striking testimonyon this point was providedby OskarBolza (1857-1942), a Germanmath- ematicianwho came to the United States seeking academicopportunities, and who joined Moore'sdepartment when the Universityof Chicagoopened its doorsin 1892. Moorewas only thirty,five yearsBolza's junior, and Bolza was dubiousat firstabout this untriedperson as departmenthead. But Bolza foundhimself witnessingnot only the emergenceof a powerfulmathematics department at Chicagobut of a newly vig- orous Americanmathematical community as a whole. In his autobiography,written manyyears later after his returnto Germany,Bolza had no doubtwho was responsible for these developments.It was "E. H. Moore mit seinem aggressivenEnthusiasmus und seinem Organisationstalent"[3, p. 32], a characterizationthat readily leaps the languagebarrier. Remarkably,amidst his vigorous activities on behalf of the research commu- nity, Moore found time to engage with educationalreform in both the colleges and the secondaryschools. His most notable pedagogical statementcame in his retir- ing addressas presidentof the AMS in December 1902, publishedin March 1903 October2001] E. H. MOORE'S REFORM PROGRAM 689 [14, pp. 401-416]. This addresscreated much comment initially, and has contin- ued to stir interestin the years since. The NationalCouncil of Teachersof Math- ematics (NCTM) reprintedMoore's talk in its very first yearbook, published in 1926 [24, pp. 32-57]. A more recent referenceto Moore's addresscan be found in this MONTHLYfor December1997 [9, p. 955]. But whatexactly did Moorestand for andwhat became of his ideas? 2. CONTEXT OF MOORE'S EDUCATIONAL PROPOSALS. E. H. Moore shouldfirst of all be situatedwithin the contextof the declineof the so-calledclassical curriculumof Greek,Latin, and mathematics at the end of the nineteenthcentury. This curriculum,which had dominatedthe colleges and many of the secondaryschools, was frequentlyjustified in termsof "mentaldiscipline" and "faculty psychology". The mind was held to be composedof variousfaculties, such as the powers of memory, reasoning,observation, and will. These faculties could be strengthenedby mental exercise,much as muscles could be strengthenedby physicalexercise. Mathematics, it was claimed,was crucialfor promotingcertain key mentalfaculties [27, pp. 22-23], [2, pp. 78-85]. Thus we find an educatorin 1893 opining on the virtue of studying arithmetic: It is refreshingto know that there is one subject which [the student]must masterfor himself slowly, sometimes painfully, and always with much labor. If arithmeticstands in the way of drawingor music, of Germanor Latin, of book-keeping or civics, let us be thankfulthat it is an obstacle which will develop the sound mental muscle that is needed for the work further on [8, p. 135]. Moreadvanced mathematics was also valuedas a mentaldiscipline. This is epitomized in a statementmade by A. LawrenceLowell (1856-1943), who claimedto remember with specialfondness his undergraduatestudies at Harvardwith mathematicianBen- jamin Peirce (1809-1880) in the 1870s, beforeLowell moved on to become a lawyer andeventually president of Harvard: To those of us who have not pursuedthe study of mathematicssince college days the substance of what he taughtus has faded away, but the methods of thought,the attitudeof mind and the mode of approachhave remainedprecious possessions [29, pp. 40-41]. Pleasingas suchsentiments may have been to manymathematicians in the late nine- teenthcentury, there were some who were growingskeptical. They recognized that the mentaldiscipline thesis could be a barrierto introducingmore advanced topics into the school curriculum.Why shouldstudents study algebra when they could exercisetheir mentalmuscles simply by grindingaway at arithmeticyear afteryear? Furthermore, a numberof mathematiciansbegan to join othereducators in assertingthat true mental disciplinecould come only in a subjectin which the studentwas genuinelyinterested. Thusthe MathematicsConference of the celebratedCommittee of Tenof 1893,chaired by Simon Newcomb (1835-1909) and includingHenry Burchard Fine (1858-1928) andFlorian Cajori (1859-1930), madethe following statement: The opinion is widely prevalentthat even if the subjectsare totally forgotten,a valuablemental discipline is acquiredby the efforts made to masterthem. While the Conference admits that, consideredin itself this discipline has a certainvalue, it feels that such a discipline is greatly inferior to that which may be gained by a different class of exercises, and bears the same relation to a really improving discipline that lifting exercises in an ill-ventilated room bear to games in the open air. The movements of a race horse afford a better model of improving exercise than those of the ox in a tread-mill[2, pp. 133-34]. 690 ?nTHE MATHEMATICALASSOCIATION OF AMERICA [Monthly 108 But by emphasizingsuch distinctionsof disciplinaryvalue, mathematicianswere openingan avenuefor fundamentalattacks on theirown subject.If algebrawas better disciplinethan arithmetic,perhaps physics or biology, for example,would be better still. Indeed,a steadybuildup of argumentsfor the superiordisciplinary value of the naturalsciences had been going on since mid-centuryin both Britainand America, with mathematicsoften subjectto some degree of attackin the process. Some sci- entists saw mathematicsas characterizedby numbingdrill, in starkcontrast to the invigorationof scientific study,wherein the studentstood face to face with nature, in the field or in the laboratory.David StarrJordan (1851-1931), biologist and first presidentof StanfordUniversity, described students coming to science "by escape from Latinand calculuswith the eagernessof colts broughtfrom the barnto a spring pasture."[7, p. 358] 3. MOORE'S 1902 ADDRESS. It was into this environmentthat E. H. Mooreven- turedin his 1902 addressas retiringpresident of the AMS, andit is thusnot surprising to find him proposingto capitalizeon the rising prestigeof science and engineering by tying mathematicalinstruction closely to those endeavors,both in the secondary schools and in the early college courses.Moore had come to the conclusionthat the trainingof futurescientists and engineers had become a crucialjustification for teach- ing mathematics,and that it was destinedto becomemore so in the future.He champi- oned the ideas of Englishengineering educator John Perry (1850-1920), who strongly urgedthat the rigorousaxiomatic development of mathematicsbe de-emphasizedin favor of teachingit as an inductivescience. For example,beginning geometry stu- dents shouldtest propositionsfrom Euclidby carefulmeasurements using graphpa- per.Perry's influence can be foundin Moore'sinsistence that mathematical rigor was a relativerather than an absoluteconcept: "Sufficientunto the day is the precision thereof",declared Moore. Both Mooreand Perry sought to bringstudents very rapidly to the employmentof powerfulmathematical concepts, without insisting that all sup- portingtechnical details be mastered[14, p. 41 1]. Moore decriedvarious "chasms" he observedin Americanmathematical activity: *betweenpure and appliedmathematics; between research mathematicians and school teachers;between the public's foggy perceptionof mathematicsand "the very high positionin generalesteem and appreciativeinterest which it assuredlydeserves." [14,
Load more

Recommended publications
  • Locally Compact Groups: Traditions and Trends Karl Heinrich Hofmann Technische Universitat Darmstadt, [email protected]
    University of Dayton eCommons Summer Conference on Topology and Its Department of Mathematics Applications 6-2017 Locally Compact Groups: Traditions and Trends Karl Heinrich Hofmann Technische Universitat Darmstadt, [email protected] Wolfgang Herfort Francesco G. Russo Follow this and additional works at: http://ecommons.udayton.edu/topology_conf Part of the Geometry and Topology Commons, and the Special Functions Commons eCommons Citation Hofmann, Karl Heinrich; Herfort, Wolfgang; and Russo, Francesco G., "Locally Compact Groups: Traditions and Trends" (2017). Summer Conference on Topology and Its Applications. 47. http://ecommons.udayton.edu/topology_conf/47 This Plenary Lecture is brought to you for free and open access by the Department of Mathematics at eCommons. It has been accepted for inclusion in Summer Conference on Topology and Its Applications by an authorized administrator of eCommons. For more information, please contact [email protected], [email protected]. Some Background Notes Some \new" tools Near abelian groups Applications Alexander Doniphan Wallace (1905{1985) Gordon Thomas Whyburn Robert Lee Moore Some Background Notes Some \new" tools Near abelian groups Applications \The best mathematics is the most mixed-up mathematics, those disciplines in which analysis, algebra and topology all play a vital role." Gordon Thomas Whyburn Robert Lee Moore Some Background Notes Some \new" tools Near abelian groups Applications \The best mathematics is the most mixed-up mathematics, those disciplines in which
    [Show full text]
  • Boyer Is the Martin A
    II “WE ARE ALL ISLANDERS TO BEGIN WITH”: THE UNIVERSITY OF CHICAGO AND THE WORLD IN THE LATE NINETEENTH AND TWENTIETH CENTURIES J OHN W. B OYER OCCASIONAL PAPERS ON HIGHER XVIIEDUCATION XVII THE COLLEGE OF THE UNIVERSITY OF CHICAGO Hermann von Holst, oil portrait by Karl Marr, 1903 I I “WE ARE ALL ISLANDERS TO BEGIN WITH”: The University of Chicago and the World in the Late Nineteenth and Twentieth Centuries INTRODUCTION he academic year 2007–08 has begun much like last year: our first-year class is once again the largest in T our history, with over 1,380 new students, and as a result we have the highest Autumn Quarter enroll- ment in our history at approximately 4,900. We can be proud of the achievements and the competitiveness of our entering class, and I have no doubt that their admirable test scores, class ranks, and high school grade point averages will show their real meaning for us in the energy, intelligence, and dedication with which our new students approach their academic work and their community lives in the College. I have already received many reports from colleagues teaching first-year humanities general education sections about how bright, dedicated, and energetic our newest students are. To the extent that we can continue to recruit these kinds of superb students, the longer-term future of the College is bright indeed. We can also be very proud of our most recent graduating class. The Class of 2007 won a record number of Fulbright grants — a fact that I will return to in a few moments — but members of the class were rec- ognized in other ways as well, including seven Medical Scientist Training This essay was originally presented as the Annual Report to the Faculty of the College on October 30, 2007.
    [Show full text]
  • Janko's Sporadic Simple Groups
    Janko’s Sporadic Simple Groups: a bit of history Algebra, Geometry and Computation CARMA, Workshop on Mathematics and Computation Terry Gagen and Don Taylor The University of Sydney 20 June 2015 Fifty years ago: the discovery In January 1965, a surprising announcement was communicated to the international mathematical community. Zvonimir Janko, working as a Research Fellow at the Institute of Advanced Study within the Australian National University had constructed a new sporadic simple group. Before 1965 only five sporadic simple groups were known. They had been discovered almost exactly one hundred years prior (1861 and 1873) by Émile Mathieu but the proof of their simplicity was only obtained in 1900 by G. A. Miller. Finite simple groups: earliest examples É The cyclic groups Zp of prime order and the alternating groups Alt(n) of even permutations of n 5 items were the earliest simple groups to be studied (Gauss,≥ Euler, Abel, etc.) É Evariste Galois knew about PSL(2,p) and wrote about them in his letter to Chevalier in 1832 on the night before the duel. É Camille Jordan (Traité des substitutions et des équations algébriques,1870) wrote about linear groups defined over finite fields of prime order and determined their composition factors. The ‘groupes abéliens’ of Jordan are now called symplectic groups and his ‘groupes hypoabéliens’ are orthogonal groups in characteristic 2. É Émile Mathieu introduced the five groups M11, M12, M22, M23 and M24 in 1861 and 1873. The classical groups, G2 and E6 É In his PhD thesis Leonard Eugene Dickson extended Jordan’s work to linear groups over all finite fields and included the unitary groups.
    [Show full text]
  • Oswald Veblen
    NATIONAL ACADEMY OF SCIENCES O S W A L D V E B LEN 1880—1960 A Biographical Memoir by S A U N D E R S M A C L ANE Any opinions expressed in this memoir are those of the author(s) and do not necessarily reflect the views of the National Academy of Sciences. Biographical Memoir COPYRIGHT 1964 NATIONAL ACADEMY OF SCIENCES WASHINGTON D.C. OSWALD VEBLEN June 24,1880—August 10, i960 BY SAUNDERS MAC LANE SWALD VEBLEN, geometer and mathematical statesman, spanned O in his career the full range of twentieth-century Mathematics in the United States; his leadership in transmitting ideas and in de- veloping young men has had a substantial effect on the present mathematical scene. At the turn of the century he studied at Chi- cago, at the period when that University was first starting the doc- toral training of young Mathematicians in this country. He then continued at Princeton University, where his own work and that of his students played a leading role in the development of an outstand- ing department of Mathematics in Fine Hall. Later, when the In- stitute for Advanced Study was founded, Veblen became one of its first professors, and had a vital part in the development of this In- stitute as a world center for mathematical research. Veblen's background was Norwegian. His grandfather, Thomas Anderson Veblen, (1818-1906) came from Odegaard, Homan Con- gregation, Vester Slidre Parish, Valdris. After work as a cabinet- maker and as a Norwegian soldier, he was anxious to come to the United States.
    [Show full text]
  • Luther Pfahler Eisenhart
    NATIONAL ACADEMY OF SCIENCES L UTHER PFAHLER E ISENHART 1876—1965 A Biographical Memoir by S O L O M O N L EFSCHETZ Any opinions expressed in this memoir are those of the author(s) and do not necessarily reflect the views of the National Academy of Sciences. Biographical Memoir COPYRIGHT 1969 NATIONAL ACADEMY OF SCIENCES WASHINGTON D.C. LUTHER PFAHLER EISENHART January 13, 1876-October 28,1965 BY SOLOMON LEFSCHETZ UTHER PFAHLER EISENHART was born in York, Pennsylvania, L to an old York family. He entered Gettysburg College in 1892. In his mid-junior and senior years he was the only student in mathematics, so his professor replaced classroom work by individual study of books plus reports. He graduated in 1896 and taught one year in the preparatory school of the college. He entered the Johns Hopkins Graduate School in 1897 and ob- tained his doctorate in 1900. In the fall of the latter year he began his career at Princeton as instructor in mathematics, re- maining at Princeton up to his retirement in 1945. In 1905 he was appointed by Woodrow Wilson (no doubt on Dean Henry B. Fine's suggestion) as one of the distinguished preceptors with the rank of assistant professor. This was in accordance with the preceptorial plan which Wilson introduced to raise the educational tempo of Princeton. There followed a full pro- fessorship in 1909 and deanship of the Faculty in 1925, which was combined with the chairmanship of the Department of Math- ematics as successor to Dean Fine in January 1930. In 1933 Eisenhart took over the deanship of the Graduate School.
    [Show full text]
  • 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.
    [Show full text]
  • Perspective the PNAS Way Back Then
    Proc. Natl. Acad. Sci. USA Vol. 94, pp. 5983–5985, June 1997 Perspective The PNAS way back then Saunders Mac Lane, Chairman Proceedings Editorial Board, 1960–1968 Department of Mathematics, University of Chicago, Chicago, IL 60637 Contributed by Saunders Mac Lane, March 27, 1997 This essay is to describe my experience with the Proceedings of ings. Bronk knew that the Proceedings then carried lots of math. the National Academy of Sciences up until 1970. Mathemati- The Council met. Detlev was not a man to put off till to cians and other scientists who were National Academy of tomorrow what might be done today. So he looked about the Science (NAS) members encouraged younger colleagues by table in that splendid Board Room, spotted the only mathe- communicating their research announcements to the Proceed- matician there, and proposed to the Council that I be made ings. For example, I can perhaps cite my own experiences. S. Chairman of the Editorial Board. Then and now the Council Eilenberg and I benefited as follows (communicated, I think, did not often disagree with the President. Probably nobody by M. H. Stone): ‘‘Natural isomorphisms in group theory’’ then knew that I had been on the editorial board of the (1942) Proc. Natl. Acad. Sci. USA 28, 537–543; and “Relations Transactions, then the flagship journal of the American Math- between homology and homotopy groups” (1943) Proc. Natl. ematical Society. Acad. Sci. USA 29, 155–158. Soon after this, the Treasurer of the Academy, concerned The second of these papers was the first introduction of a about costs, requested the introduction of page charges for geometrical object topologists now call an “Eilenberg–Mac papers published in the Proceedings.
    [Show full text]
  • Curriculum Vitae
    Curriculum Vitae Assaf Naor Address: Princeton University Department of Mathematics Fine Hall 1005 Washington Road Princeton, NJ 08544-1000 USA Telephone number: +1 609-258-4198 Fax number: +1 609-258-1367 Electronic mail: [email protected] Web site: http://web.math.princeton.edu/~naor/ Personal Data: Date of Birth: May 7, 1975. Citizenship: USA, Israel, Czech Republic. Employment: • 2002{2004: Post-doctoral Researcher, Theory Group, Microsoft Research. • 2004{2007: Permanent Member, Theory Group, Microsoft Research. • 2005{2007: Affiliate Assistant Professor of Mathematics, University of Washington. • 2006{2009: Associate Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University (on leave Fall 2006). • 2008{2015: Associated faculty member in computer science, Courant Institute of Mathematical Sciences, New York University (on leave in the academic year 2014{2015). • 2009{2015: Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University (on leave in the academic year 2014{2015). • 2014{present: Professor of Mathematics, Princeton University. • 2014{present: Associated Faculty, The Program in Applied and Computational Mathematics (PACM), Princeton University. • 2016 Fall semester: Henry Burchard Fine Professor of Mathematics, Princeton University. • 2017{2018: Member, Institute for Advanced Study. • 2020 Spring semester: Henry Burchard Fine Professor of Mathematics, Princeton University. 1 Education: • 1993{1996: Studies for a B.Sc. degree in Mathematics at the Hebrew University in Jerusalem. Graduated Summa Cum Laude in 1996. • 1996{1998: Studies for an M.Sc. degree in Mathematics at the Hebrew University in Jerusalem. M.Sc. thesis: \Geometric Problems in Non-Linear Functional Analysis," prepared under the supervision of Joram Lindenstrauss. Graduated Summa Cum Laude in 1998.
    [Show full text]
  • 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.
    [Show full text]
  • Academic Genealogy of the Oakland University Department Of
    Basilios Bessarion Mystras 1436 Guarino da Verona Johannes Argyropoulos 1408 Università di Padova 1444 Academic Genealogy of the Oakland University Vittorino da Feltre Marsilio Ficino Cristoforo Landino Università di Padova 1416 Università di Firenze 1462 Theodoros Gazes Ognibene (Omnibonus Leonicenus) Bonisoli da Lonigo Angelo Poliziano Florens Florentius Radwyn Radewyns Geert Gerardus Magnus Groote Università di Mantova 1433 Università di Mantova Università di Firenze 1477 Constantinople 1433 DepartmentThe Mathematics Genealogy Project of is a serviceMathematics of North Dakota State University and and the American Statistics Mathematical Society. Demetrios Chalcocondyles http://www.mathgenealogy.org/ Heinrich von Langenstein Gaetano da Thiene Sigismondo Polcastro Leo Outers Moses Perez Scipione Fortiguerra Rudolf Agricola Thomas von Kempen à Kempis Jacob ben Jehiel Loans Accademia Romana 1452 Université de Paris 1363, 1375 Université Catholique de Louvain 1485 Università di Firenze 1493 Università degli Studi di Ferrara 1478 Mystras 1452 Jan Standonck Johann (Johannes Kapnion) Reuchlin Johannes von Gmunden Nicoletto Vernia Pietro Roccabonella Pelope Maarten (Martinus Dorpius) van Dorp Jean Tagault François Dubois Janus Lascaris Girolamo (Hieronymus Aleander) Aleandro Matthaeus Adrianus Alexander Hegius Johannes Stöffler Collège Sainte-Barbe 1474 Universität Basel 1477 Universität Wien 1406 Università di Padova Università di Padova Université Catholique de Louvain 1504, 1515 Université de Paris 1516 Università di Padova 1472 Università
    [Show full text]
  • A History of Mathematics in America Before 1900.Pdf
    THE BOOK WAS DRENCHED 00 S< OU_1 60514 > CD CO THE CARUS MATHEMATICAL MONOGRAPHS Published by THE MATHEMATICAL ASSOCIATION OF AMERICA Publication Committee GILBERT AMES BLISS DAVID RAYMOND CURTISS AUBREY JOHN KEMPNER HERBERT ELLSWORTH SLAUGHT CARUS MATHEMATICAL MONOGRAPHS are an expression of THEthe desire of Mrs. Mary Hegeler Carus, and of her son, Dr. Edward H. Carus, to contribute to the dissemination of mathe- matical knowledge by making accessible at nominal cost a series of expository presenta- tions of the best thoughts and keenest re- searches in pure and applied mathematics. The publication of these monographs was made possible by a notable gift to the Mathematical Association of America by Mrs. Carus as sole trustee of the Edward C. Hegeler Trust Fund. The expositions of mathematical subjects which the monographs will contain are to be set forth in a manner comprehensible not only to teach- ers and students specializing in mathematics, but also to scientific workers in other fields, and especially to the wide circle of thoughtful people who, having a moderate acquaintance with elementary mathematics, wish to extend their knowledge without prolonged and critical study of the mathematical journals and trea- tises. The scope of this series includes also historical and biographical monographs. The Carus Mathematical Monographs NUMBER FIVE A HISTORY OF MATHEMATICS IN AMERICA BEFORE 1900 By DAVID EUGENE SMITH Professor Emeritus of Mathematics Teacliers College, Columbia University and JEKUTHIEL GINSBURG Professor of Mathematics in Yeshiva College New York and Editor of "Scripta Mathematica" Published by THE MATHEMATICAL ASSOCIATION OF AMERICA with the cooperation of THE OPEN COURT PUBLISHING COMPANY CHICAGO, ILLINOIS THE OPEN COURT COMPANY Copyright 1934 by THE MATHEMATICAL ASSOCIATION OF AMKRICA Published March, 1934 Composed, Printed and Bound by tClfe QlolUgUt* $Jrr George Banta Publishing Company Menasha, Wisconsin, U.
    [Show full text]
  • Blaschke, Osgood, Wiener, Hadamard and the Early Development Of
    Blaschke, Osgood, Wiener, Hadamard and the Early Development of Modern Mathematics in China Chuanming Zong Abstract. In ancient times, China made great contributions to world civi- lization and in particular to mathematics. However, modern sciences includ- ing mathematics came to China rather too late. The first Chinese university was founded in 1895. The first mathematics department in China was for- mally opened at the university only in 1913. At the beginning of the twenti- eth century, some Chinese went to Europe, the United States of America and Japan for higher education in modern mathematics and returned to China as the pioneer generation. They created mathematics departments at the Chinese universities and sowed the seeds of modern mathematics in China. In 1930s, when a dozen of Chinese universities already had mathematics departments, several leading mathematicians from Europe and USA visited China, including Wilhelm Blaschke, George D. Birkhoff, William F. Osgood, Norbert Wiener and Jacques Hadamard. Their visits not only had profound impact on the mathematical development in China, but also became social events sometimes. This paper tells the history of their visits. 2020 Mathematics Subject Classification: 01A25, 01A60. 1. Introduction and Background In 1895, Peiyang University was founded in Tianjin as a result of the westernization movement. In 1898, Peking University was founded in Beijing. They are the earliest universities in China. On May 28, 1900, Britain, USA, France, Germany, Russia, Japan, Italy and Austria invaded China to suppress the Boxer Rebellion1 which was an organized movement against foreign missionaries and their followers. On August 14, 1900, more than 20,000 soldiers of the allied force occupied the Chinese capital Beijing and the emperor’s family with some high ranking officials and servants escaped to Xi’an.
    [Show full text]