History and Didactics of Mathematics: a Problematic Relation
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Guido Castelnuovo and Francesco Severi: Two Personalities, Two Letters Donald Babbitt and Judith Goodstein
Guido Castelnuovo and Francesco Severi: Two Personalities, Two Letters Donald Babbitt and Judith Goodstein he Italian school of algebraic geometry letters reflect remarkably the enormous personal- flourished from the latter part of the ity differences between these two giants of Italian nineteenth century through the early mathematics. part of the twentieth century. Some of Guido Castelnuovo (1865–1952) was born and Tthe main contributors were Luigi Cre- raised in Venice, the son of Enrico Castelnuovo, mona, Eugenio Bertini, Giuseppe Veronese, Cor- director of the Scuola Superiore di Commercio and rado Segre, Guido Castelnuovo, Federigo Enriques, a popular nineteenth-century author of novels and and Francesco Severi. There were, of course, other short stories. He completed his doctor’s degree at important schools of algebraic geometry in other the University of Padua in 1886 under the direc- countries, but the Italian school stood out because tion of Giuseppe Veronese, one of the leading of its unique mathematical style, especially its algebraic geometers of that period. On the advice strong appeal to geometric intuition. Between of Veronese, Castelnuovo spent the following year 1896 and 1900 two members of this school, Guido in Rome on a postgraduate scholarship and then Castelnuovo and Federigo Enriques, developed the spent three years as assistant to geometer Enrico classification of algebraic surfaces, one of the great D’Ovidio at the University of Turin. In 1890, Castel- achievements of algebraic geometry.1 A few years nuovo won a concorso, or national competition, for later (1904–1908), together with Francesco Severi, a new chair of analytical and projective geometry at they significantly deepened that understanding the University of Rome—an award that was subse- of surfaces. -
The Geometrical Foundation of Federigo Enriques' Gnoseology
Advances in Historical Studies, 2015, 4, 118-145 Published Online April 2015 in SciRes. http://www.scirp.org/journal/ahs http://dx.doi.org/10.4236/ahs.2015.42012 The Geometrical Foundation of Federigo Enriques’ Gnoseology and Epistemology Paolo Bussotti1, Raffaele Pisano2 1Alexander von Humboldt Foundation, Berlin, Germany 2Department of Physics, Lille 1 University, Lille, France Email: [email protected], [email protected] Received 17 March 2015; accepted 6 April 2015; published 7 May 2015 Copyright © 2015 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract The purpose of this paper is to valuate the role of geometry inside Enriques’ theory of knowledge and epistemology. Our thesis is that such a role is prominent. We offer a particular interpretation of Enriques’ gnoseology, according to which geometry is the cornerstone to fully catch also the way in which he framed his conception of the history of science, of the origin of philosophy and of mathematics’ foundations. Our argumentation is divided into three sections: in the first one, we provide the reader with Enriques’ ideas on the physiological and conceptual bases of geometry. We distinguish between the primary and the secondary intuitions and expound the role Enriques ascribes to history inside the construction of human mind. In the second section, Enriques’ idea that philosophy was born as a rational geometry is expounded. In the third section we see what foundations of mathematics means in Enriques’ speculation. The reader will be in front of a thinker, whose theories are not separated one from the other, rather they are strictly connected. -
Bachelard, Enriques and Weyl: Comparing Some of Their Ideas
Bachelard, Enriques and Weyl: comparing some of their ideas Giuseppe Iurato Department of Physics, University of Palermo, IT E-mail: [email protected] Abstract. Some aspects of Federigo Enriques mathematical philosophy thought are taken as central reference points for a critical historic-epistemological comparison between it and some of the main aspects of the philosophical thought of other his contemporary thinkers like, Gaston Bachelard and Hermann Weyl. From what will be exposed, it will be also possible to make out possible educational implications of the historic-epistemological approach. 1. Introduction Even in modern textbooks and treatises on History of Philosophy and Philosophy of Science, both Italian1 and foreign, there exist neither a whole chapter nor few sections, devoted to the fundamental epistemological work of Federigo Enriques, whose philosophical thought is dismissed in few lines amongst the subjects related to the modern Italian Philosophy between the end of the 19th-Century and the beginning of the 20th- one. An exception is made by both some prefaces to the various anastatic reprints of Federigo Enriques works and some remarkable collective and proceeding works mainly edited by the Centro Studi Federigo Enriques in Livorno (IT). All that is quite unfair respect to the wide cleverness and acuteness of the forerunner Enriques’ thought: he has been remembered only for his high and celebrated contributions to Algebraic Geometry, and only recently a certain further attention has appeared towards this author2. An almost identical or similar fate has been undergone by Giovanni Vailati, almost to witness that absurd but real (and still effective) kind of reciprocal dislike that there exist, by both sides, between philosophers and scientists, which embed its historical roots into the secular dispute between Geisteswissenschaften on the one hand, and the Naturwissenschaften on the other hand3. -
Federigo Enriques (1871—1946) and History of Science in Italy in the Pre-War Years
\ ORGANON 22/23:1986/1987 META-HISTORY OF SCIENCE AT THE BERKELEY CONGRESS Salvo D'Agostino (Italy) FEDERIGO ENRIQUES (1871—1946) AND HISTORY OF SCIENCE IN ITALY IN THE PRE-WAR YEARS A panoramic view of Italian culture and society in the prewar years is a pre-requisite for an appraisal of Federigo Enriques' life and work. The Italian cultural scenery from 1900 to the thirties has been recently analysed from different angles,1 and various reasons have been found for that sort of backwardness which seemed to characterize this scenery in comparison with the then other leading European countries. It is my opinion that, concerning Italian science and culture in that period, one of the key aspects of the Italian panorama was the absence of interdisciplinary cross-fertilization between sciences and technology, on one side, and science and philosophy, on the other. It is known2 that this double cross-fertilization had played a fruitful role primarily in Germany at the turn of the century, promoting researches through financial support and stimulating fresh approaches to scientific problems. In fact this aspect did not pass unnoticed among the more distinguished representatives of Italian science: Vita Volterra (1860—1940), one of the major Italian contributors to mathematical physics in the pre-Fascist period, intended to react to the situation, founding in 1907 the Societa Italiana per il Progresso della Scienza, with the aims both to improve collaboration among specialists and to encourage diffusion of science at large. Like Poincare, Volterra was not favourably inclined, until 1922, towards Einstein's Relativity, considered by him "a simple formal variation of Lorentz's theory". -
Bachelard, Enriques and Weyl: Comparing Some of Their Ideas
Bachelard, Enriques and Weyl: comparing some of their ideas Giuseppe Iurato Department of Physics, University of Palermo, IT E-mail: [email protected] Abstract. Some aspects of Federigo Enriques mathematical philosophy thought are taken as central reference points for a critical historic-epistemological comparison between it and some of the main aspects of the thought of other his contemporary thinkers like Gaston Bachelard and Hermann Weyl. From what will be exposed, it will be also possible descry eventual educational implications of the historic-epistemological approach. 1. Introduction Even in the modern textbooks and treatises on History of Philosophy and Philosophy of Science, both Italian1 and foreign, there exist neither a whole chapter nor few sections, devoted to the fundamental epistemological work of Federigo Enriques, whose philosophical thought is dismissed in few lines among the subjects related to the modern Italian Philosophy between the end of the 19th-Century and the beginning of the 20th- one. Make an exception both some prefaces to the various anastatic reprints of the Federigo Enriques works and some remarkable collective and proceeding works mainly edited by the Centro Studi Federigo Enriques in Livorno (IT). All that is quite unfair respect to the wide cleverness and acuteness of the forerunner Enriques’ thought: he has been remembered only for his high and celebrated contributions to Algebraic Geometry, and only recently a certain further attention has appeared towards this author2. An almost same fate has been undergone by Giovanni Vailati, almost to witness that absurd but real (and still effective) kind of reciprocal dislike, by both sides, between philosophers and scientists, which embed its historical roots into the secular dispute between Geisteswissenschaften on the one hand, and the Naturwissenschaften on the other hand3. -
Oscar Zariski 1899–1986
Oscar Zariski 1899–1986 A Biographical Memoir by David Mumford ©2013 National Academy of Sciences. Any opinions expressed in this memoir are those of the author and do not necessarily reflect the views of the National Academy of Sciences. OSCAR ZARISKI April 24, 1899–July 4, 1986 Elected to the NAS, 1944 Oscar Zariski was born in the town of Kobryn, which lies on the border between Poland and Russia. It was a part of Russia at the time of Zariski’s birth, a part of Poland between the two world wars, and is now in the Republic of Belarus. Zariski was the son of Bezalel and Chana Zaristky, and was given the name of Asher Zaristky, which he changed to Oscar Zariski when he later came to Italy. Kobryn was a small town where his mother ran a general store, his father having died when he was two. In 1918, Zariski went to the University of Kiev in the midst of the revolutionary struggle. He was seriously wounded in one leg1 when caught in a crowd that was fired upon by troops, but he recovered after two months in the hospital. As a By David Mumford student, he was attracted to algebra and number theory as well as to the revolutionary political ideas of the day. Zariski supported himself partly by writing for a local Communist paper. This is most surprising for those of us who only knew him much later, but it calls to mind the quip, “A man has no heart if he is not radical in his youth and no mind if he is not conservative in his mature years.” In 1921, Zariski went to Italy, largely because of the limited educational opportunities available to Jews in Russia at that time. -
Matemática E Matemáticos Na Universidade De São Paulo: Italianos, Brasileiros E Bourbakistas (1934-1958)
UNIVERSIDADE FEDERAL DA BAHIA UNIVERSIDADE ESTADUAL DE FEIRA DE SANTANA PROGRAMA DE PÓS-GRADUAÇÃO EM ENSINO, FILOSOFIA E HISTÓRIA DAS CIÊNCIAS ELIENE BARBOSA LIMA MATEMÁTICA E MATEMÁTICOS NA UNIVERSIDADE DE SÃO PAULO: ITALIANOS, BRASILEIROS E BOURBAKISTAS (1934-1958) Salvador - Ba 2012 ELIENE BARBOSA LIMA MATEMÁTICA E MATEMÁTICOS NA UNIVERSIDADE DE SÃO PAULO: ITALIANOS, BRASILEIROS E BOURBAKISTAS (1934-1958) Tese apresentada ao Programa de Pós-Graduação em Ensino, Filosofia e História das Ciências da Universidade Federal da Bahia, Universidade Estadual de Feira de Santana, como requisito parcial para a obtenção do grau de Doutora em Ensino, Filosofia e História das Ciências, na área de concentração de História e Filosofia das Ciências e implicações para o Ensino das Ciências. Orientador: Prof. Dr. André Luis Mattedi Dias Salvador – Ba 2012 Biblioteca Central Julieta Carteado – UEFS Lima, Eliene Barbosa L697m Matemática e matemáticos na Universidade de São Paulo: italianos, brasileiros e bourbakistas (1934-1958). / Eliene Barbosa Lima. – Salvador, BA, 2012. 260f. Orientador: André Luis Mattedi Dias Tese (doutorado) – Programa de Pós-Graduação em Ensino, Filosofia e História das Ciências, Universidades Federal da Bahia, Universidade Estadual de Feira de Santana, 2012. 1.Geometria algébrica – História. 2.Escola italiana. 3.Escola bourbakista. 4.Matemáticos brasileiros – História. 5.Abordagens geométrica e algébrica. I.Dias, André Luis Mattedi. II. Universidade Federal da Bahia. III.Universidade Estadual de Feira de Santana. IV. Título. CDU: 512.7(09) ELIENE BARBOSA LIMA MATEMÁTICA E MATEMÁTICOS NA UNIVERSIDADE DE SÃO PAULO: ITALIANOS, BRASILEIROS E BOURBAKISTAS (1934-1958) Tese apresentada como requisito parcial para obtenção do grau de Doutora em Ensino, Filosofia e História das Ciências, na área de concentração de História e Filosofia das Ciências e implicações para o Ensino das Ciências da Universidade Federal da Bahia, Universidade Estadual de Feira de Santana. -
Toward a Scientific and Personal Biography of Tullio Levi-Civita
Historia Mathematica 32 (2005) 203–236 www.elsevier.com/locate/hm Toward a scientific and personal biography of Tullio Levi-Civita (1873–1941) Pietro Nastasi a, Rossana Tazzioli b,∗ a Dipartimento di Matematica e Applicazioni, Università di Palermo, Palermo, Italy b Dipartimento di Matematica e Informatica, Università di Catania, Catania, Italy Available online 12 May 2004 Abstract Tullio Levi-Civita was one of the most important Italian mathematicians of the first part of the 20th century, contributing significantly to a number of research fields in mathematics and physics. In addition, he was involved in the social and political life of his time and suffered severe political and racial persecution during the period of Fascism. He tried repeatedly and in several cases successfully to help colleagues and students who were victims of anti-Semitism in Italy and Germany. His scientific and private life is well documented in the letters and documents contained in his Archive. The authors’ aim is to illustrate the events of his life by means of his large and remarkable correspondence. 2004 Elsevier Inc. All rights reserved. Sommario Tullio Levi-Civita fu uno dei più importanti matematici italiani della prima parte del ventesimo secolo e contribuì in modo significativo a numerose discipline in campo matematico e fisico. Inoltre, egli partecipò alla vita sociale e politica del suo tempo e fu vittima delle severe persecuzioni politiche e razziali del periodo fascista. Egli tentò in più occasioni, e talvolta con successo, di aiutare colleghi e studenti che erano vittime dell’anti-semitismo sia in Italia sia in Germania. La sua vita scientifica e personale è ben documentata nelle lettere e nei manoscritti contenuti nel suo Archivio. -
Italian Mathematics Between the Two World Wars
Science Networks · Historical Studies Founded by Erwin Hiebert and Hans Wußing Volume 29 Edited by Eberhard Knobloch and Erhard Scholz Editorial Board: K. Andersen, Aarhus R. Halleux, Liège D. Buchwald, Pasadena S. Hildebrandt, Bonn H.J.M. Bos, Utrecht Ch. Meinel, Regensburg U. Bottazzini, Roma J. Peiffer, Paris J.Z. Buchwald, Cambridge, Mass. W. Purkert, Leipzig K. Chemla, Paris D. Rowe, Mainz S.S. Demidov, Moskva A.I. Sabra, Cambridge, Mass. E.A. Fellmann, Basel Ch. Sasaki, Tokyo M. Folkerts, München R.H. Stuewer, Minneapolis P. Galison, Cambridge, Mass. H. Wußing, Leipzig I. Grattan-Guinness, London V.P. Vizgin, Moskva J. Gray, Milton Keynes Angelo Guerraggio Pietro Nastasi Italian Mathematics Between the Two World Wars Birkhäuser Verlag Basel · Boston · Berlin Authors’ addresses: Angelo Guerraggio Pietro Nastasi Centro PRISTEM-Eleusi Dipartimento di Matematica Università Bocconi Università di Palermo Viale Isonzo, 25 Via Archirafi , 34 20135 Milano 90123 Palermo Italy Italy email: [email protected] email: [email protected] 2000 Mathematics Subject Classifi cation: 01A60, 01A72 A CIP catalogue record for this book is available from the Library of Congress, Washington D.C., USA. Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbiografi e; detailed bibliographic data is available in the internet at http://dnb.ddb.de. ISBN 3-7643-6555-2 Birkhäuser Verlag, Basel – Boston – Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifi cally the rights of translation, reprin- ting, re-use of illustrations, broadcasting, reproduction on microfi lms or in other ways, and storage in data banks. -
Dig Where You Stand
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Institutional Research Information System University of Turin “Dig where you stand” 3 Proceedings of the Third International Conference on the History of Mathematics Education September 25–28, 2013, at Department of Education, Uppsala University, Sweden Editors: Kristín Bjarnadóttir Fulvia Furinghetti Johan Prytz Gert Schubring Uppsala University Department of Education “Dig where you stand” 3 Proceedings of the Third International Conference on the History of Mathematics Education September 25–28, 2013, at the Department of Education, Uppsala University, Sweden Editors: Kristín Bjarnadóttir University of Iceland, School of Education, Reykjavík, Iceland Fulvia Furinghetti Dipartimento di Matematica dell’Università di Genova, Italy Johan Prytz Uppsala University, Department of Education, Sweden Gert Schubring Universidade Federal do Rio de Janeiro, Instituto de Matemática, Brazil Institut für Didaktik der Mathematik, Universität Bielefeld, Germany Cover design: Graphic Services, Uppsala University Printed by: DanagårdLITHO AB, Ödeshög 2015 The production of this volume is funded by the Faculty of Education at Uppsala University, the Department of Education at Uppsala University and the Swedish Research Council. All rights reserved © 2015 Authors 1st edition, March 2015 ISBN 978-91-506-2444-1 Published by Uppsala University – Department of Education Uppsala Francesco Severi and mathematics teaching in secondary schools. Science, politics and schools in the first half of the twentieth century Livia Giacardi, Alice Tealdi Università di Torino, Dipartimento di Matematica, Italia Abstract Francesco Severi (1879 –1961) was, as is well known, a top-level mathematician who made very significant contributions in the field of algebraic geometry as well as in various other areas in mathematics. -
The Influence of Oscar Zariski on Algebraic Geometry 3
The influence of Oscar Zariski on algebraic geometry Piotr Blass Introduction Oscar Zariski was born in 1899 in Kobryn in the Ukraine (today Kobryn lies in Belarus) in a Jewish family. His first name, as he once told me, was sometimes pronounced Aszer in his childhood. He loved mathematics and original creative thinking about mathematics from a very early age. He recalled the exhilaration of doing mathematics as a boy. His father died when Oscar was very young; his mother was a business lady, as he used to say. She would sell various things in the Jewish Nalewki district in Warsaw. Oscar Zariski (1899-1986) (picture by George M. Bergman) In 1921, Oscar Zariski went to study in Rome. He had previously studied in Kiev and recalled that he was strongly interested in algebra and also in number theory. The latter subject was by tradition strongly cultivated in Russia. He went to Rome on a Polish passport. His stay in Rome must have been very exciting. It lasted from 1921 until 1927. He became a student at the University of Rome and he married a wonderful woman who was his unfailing companion and This paper was originally published in the Australian Mathematical Society Gazette vol. 16, No. 6 (December 1989). We thank the Australian Mathematical Publishing Association Inc. for permission to reprint an updated version of this paper. The updated version of the paper has been prepared by Piotr Pragacz; the typing and pictures are due to Maria Donten-Bury. 1 2 PIOTR BLASS soulmate for the next 65 years, Yole. -
The Italian School of Algebraic Geometry and the Teaching of Mathematics in Secondary Schools: Motivations, Assumptions and Strategies
Rend. Sem. Mat. Univ. Politec. Torino Vol. 71, 3–4 (2013), 421 – 461 L. Giacardi THE ITALIAN SCHOOL OF ALGEBRAIC GEOMETRY AND THE TEACHING OF MATHEMATICS IN SECONDARY SCHOOLS: MOTIVATIONS, ASSUMPTIONS AND STRATEGIES Abstract. In this paper I intend to illustrate the reasons which led some members of the Ital- ian School of algebraic geometry – in particular, Corrado Segre (1863-1924), Guido Castel- nuovo (1865-1952), Federigo Enriques (1871-1946) and Francesco Severi (1879-1961) – to become so concerned with problems pertaining to mathematics teaching; describe the epis- temological vision which inspired them; discuss the various ways in which this commitment manifested itself (school legislation, teacher training, textbooks, publishing initiatives, uni- versity lectures, etc.); make evident the influence of the reform movements abroad, particu- larly that of Klein; finally, show how, in this respect as well, Italian geometers projected an unquestionable image of a “School”. 1. Introduction IamverypleasedtotakepartinthisconferencededicatedtoAlberto Conte in celebration of his seventieth birthday. The reason I was invited to a such a strictly gath- ering of mathematicians is due to the fact that Alberto Conte,alongwithhisresearch work in the field of algebraic geometry, has always cultivatedaninterestinhistoryof mathematics, both that of his specific area of study and that more generally related to Turin’s rich scientific tradition. Further, with great sensitivity he has encouraged and supported initiatives aimed at bringing that tradition to