Biographies of the Authors, Who Published in The
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Guido Fubini-Ghiron
Intellectuals Displaced from Fascist Italy Firenze University Press 2019- Guido Fubini-Ghiron Go to personal file When he was almost 60, he was expelled from the Polytechnic University of Link to other connected Lives on the move: Turin because he was Jewish. Known as one of the sharpest and most intelligent Italian analysts, he decided to continue his brilliant work on Fubini Mario Fubini Ghiron Eugenio 1 differential geometry abroad, hoping for a better future for him and his family . (Eugene) Fubini Ghiron Gino He immediately left for Paris, and soon found himself welcomed to Princeton. His two sons, expelled in Italy at the beginning of their academic career, also found their way to the USA and stayed there. Formative years in Paris He was born in Venice on 19 January 1879 to Lazzaro Fubini, a mathematics teacher at the machinist school, and to Zoraide Torre. At only nine years old, he was enrolled at Foscarini High School in Venice, achieving, in his eight years of ginnasio and liceo [junior high school and high school], perfect grades (all 10s) in mathematics2. In 1896, at seventeen years old, he enrolled in the Facoltà di Matematica [School of Mathematics] at the Scuola normale superiore of Pisa, «where many scholars became passionate about research in geometry»3. A student of Ulisse Dini, Eugenio Bertini and, above all, Luigi Bianchi, he graduated with honors in 1900 with a thesis titled «Il parallelismo di Clifford negli spazi ellittici» [Clifford’s parallelism in elliptical spaces]4. 1 Letter of 30 October 1938 from Tullio Levi-Civita to Oswald Veblen from the Institute for Advanced Study at Princeton University, translated and reported on the Università Bocconi’s website, section Rubriche <http://matematica-old.unibocconi.it> (accessed 2 February 2019). -
Chapter 5 Product Measures
Chapter 5 Product Measures Lebesgue measure on R generalizes the notion of the length of an interval. In this chapter, we see how two-dimensional Lebesgue measure on R2 generalizes the notion of the area of a rectangle. More generally, we construct new measures that are the products of two measures. Once these new measures have been constructed, the question arises of how to compute integrals with respect to these new measures. Beautiful theorems proved in the first decade of the twentieth century allow us to compute integrals with respect to product measures as iterated integrals involving the two measures that produced the product. Furthermore, we will see that under reasonable conditions we can switch the order of an iterated integral. Main building of Scuola Normale Superiore di Pisa, the university in Pisa, Italy, where Guido Fubini (1879–1943) received his PhD in 1900. In 1907 Fubini proved that under reasonable conditions, an integral with respect to a product measure can be computed as an iterated integral and that the order of integration can be switched. Leonida Tonelli (1885–1943) also taught for many years in Pisa; he also proved a crucial theorem about interchanging the order of integration in an iterated integral. CC-BY-SA Lucarelli © Sheldon Axler 2020 S. Axler, Measure, Integration & Real Analysis, Graduate Texts 116 in Mathematics 282, https://doi.org/10.1007/978-3-030-33143-6_5 Section 5A Products of Measure Spaces 117 5A Products of Measure Spaces Products of s-Algebras Our first step in constructing product measures is to construct the product of two s-algebras. -
Definitions and Nondefinability in Geometry 475 2
Definitions and Nondefinability in Geometry1 James T. Smith Abstract. Around 1900 some noted mathematicians published works developing geometry from its very beginning. They wanted to supplant approaches, based on Euclid’s, which han- dled some basic concepts awkwardly and imprecisely. They would introduce precision re- quired for generalization and application to new, delicate problems in higher mathematics. Their work was controversial: they departed from tradition, criticized standards of rigor, and addressed fundamental questions in philosophy. This paper follows the problem, Which geo- metric concepts are most elementary? It describes a false start, some successful solutions, and an argument that one of those is optimal. It’s about axioms, definitions, and definability, and emphasizes contributions of Mario Pieri (1860–1913) and Alfred Tarski (1901–1983). By fol- lowing this thread of ideas and personalities to the present, the author hopes to kindle interest in a fascinating research area and an exciting era in the history of mathematics. 1. INTRODUCTION. Around 1900 several noted mathematicians published major works on a subject familiar to us from school: developing geometry from the very beginning. They wanted to supplant the established approaches, which were based on Euclid’s, but which handled awkwardly and imprecisely some concepts that Euclid did not treat fully. They would present geometry with the precision required for general- ization and applications to new, delicate problems in higher mathematics—precision beyond the norm for most elementary classes. Work in this area was controversial: these mathematicians departed from tradition, criticized previous standards of rigor, and addressed fundamental questions in logic and philosophy of mathematics.2 After establishing background, this paper tells a story about research into the ques- tion, Which geometric concepts are most elementary? It describes a false start, some successful solutions, and a demonstration that one of those is in a sense optimal. -
Toward a Scientific and Personal Biography of Tullio Levi-Civita (1873-1941) Pietro Nastasi, Rossana Tazzioli
Toward a scientific and personal biography of Tullio Levi-Civita (1873-1941) Pietro Nastasi, Rossana Tazzioli To cite this version: Pietro Nastasi, Rossana Tazzioli. Toward a scientific and personal biography of Tullio Levi-Civita (1873-1941). Historia Mathematica, Elsevier, 2005, 32 (2), pp.203-236. 10.1016/j.hm.2004.03.003. hal-01459031 HAL Id: hal-01459031 https://hal.archives-ouvertes.fr/hal-01459031 Submitted on 7 Feb 2017 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Towards a Scientific and Personal Biography of Tullio Levi-Civita (1873-1941) Pietro Nastasi, Dipartimento di Matematica e Applicazioni, Università di Palermo Rossana Tazzioli, Dipartimento di Matematica e Informatica, Università di Catania Abstract Tullio Levi-Civita was one of the most important Italian mathematicians in the early 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. -
Archivio Istituzionale Open Access Dell'università Di Torino Original
AperTO - Archivio Istituzionale Open Access dell'Università di Torino From Emancipation to Persecution: Aspects and Moments of the Jewish Mathematical Milieu in Turin (1848-1938) This is the author's manuscript Original Citation: Availability: This version is available http://hdl.handle.net/2318/1677679 since 2019-01-02T09:39:53Z Published version: DOI:10.19272/201809201005 Terms of use: Open Access Anyone can freely access the full text of works made available as "Open Access". Works made available under a Creative Commons license can be used according to the terms and conditions of said license. Use of all other works requires consent of the right holder (author or publisher) if not exempted from copyright protection by the applicable law. (Article begins on next page) 28 September 2021 BOLLETTINO DI STORIA DELLE SCIENZE MATEMATICHE Anno XXXVIII · Numero 1 · Giugno 2018 PISA · ROMA FABRIZIO SERRA EDITORE MMXVIII Autorizzazione del Tribunale di Pisa n. 13 del 17.07.2001. Direttore responsabile: Lucia Corsi * Amministrazione e abbonamenti Fabrizio Serra editore® Casella postale n. 1, succursale n. 8, I 56123 Pisa Uffici di Pisa: Via Santa Bibbiana 28, I 56127 Pisa, tel. +39 050542332, fax +39 050574888, [email protected] Uffici di Roma: Via Carlo Emanuele I, I 00185 Roma, tel. +39 0670493456, fax +39 0670476605, [email protected] I prezzi ufficiali di abbonamento cartaceo e Online sono consultabili presso il sito Internet della casa editrice www.libraweb.net. Print and Online official subscription rates are available at Publisher’s website www.libraweb.net. I pagamenti possono essere effettuati tramite versamento su c.c.p. -
The Case of Sicily, 1880–1920 Rossana Tazzioli
Interplay between local and international journals: The case of Sicily, 1880–1920 Rossana Tazzioli To cite this version: Rossana Tazzioli. Interplay between local and international journals: The case of Sicily, 1880–1920. Historia Mathematica, Elsevier, 2018, 45 (4), pp.334-353. 10.1016/j.hm.2018.10.006. hal-02265916 HAL Id: hal-02265916 https://hal.archives-ouvertes.fr/hal-02265916 Submitted on 12 Aug 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Interplay between local and international journals: The case of Sicily, 1880–1920 Rossana Tazzioli To cite this version: Rossana Tazzioli. Interplay between local and international journals: The case of Sicily, 1880–1920. Historia Mathematica, Elsevier, 2018, 45 (4), pp.334-353. 10.1016/j.hm.2018.10.006. hal-02265916 HAL Id: hal-02265916 https://hal.archives-ouvertes.fr/hal-02265916 Submitted on 12 Aug 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. -
LONG-TERM HISTORY and EPHEMERAL CONFIGURATIONS Catherine Goldstein
LONG-TERM HISTORY AND EPHEMERAL CONFIGURATIONS Catherine Goldstein To cite this version: Catherine Goldstein. LONG-TERM HISTORY AND EPHEMERAL CONFIGURATIONS. Interna- tional Congress of Mathematicians, Aug 2018, Rio de Janeiro, Brazil. pp.487-522. hal-02334505 HAL Id: hal-02334505 https://hal.archives-ouvertes.fr/hal-02334505 Submitted on 29 Oct 2019 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. LONG-TERM HISTORY AND EPHEMERAL CONFIGURATIONS CATHERINE GOLDSTEIN Abstract. Mathematical concepts and results have often been given a long history, stretching far back in time. Yet recent work in the history of mathe- matics has tended to focus on local topics, over a short term-scale, and on the study of ephemeral configurations of mathematicians, theorems or practices. The first part of the paper explains why this change has taken place: a renewed interest in the connections between mathematics and society, an increased at- tention to the variety of components and aspects of mathematical work, and a critical outlook on historiography itself. The problems of a long-term history are illustrated and tested using a number of episodes in the nineteenth-century history of Hermitian forms, and finally, some open questions are proposed. -
TOWARDS a HISTORY of the GEOMETRIC FOUNDATIONS of MATHEMATICS LATE Xixth CENTURY*
ARTICLES TOWARDS A HISTORY OF THE GEOMETRIC FOUNDATIONS OF MATHEMATICS LATE XIXth CENTURY* Rossana TAZZIOLI RÉSUMÉ : Beaucoup de « géomètres » du XIXe siècle – Bernhard Riemann, Hermann von Helmholtz, Felix Klein, Riccardo De Paolis, Mario Pieri, Henri Poincaré, Federigo Enriques, et autres – ont joué un rôle important dans la discussion sur les fondements des mathématiques. Mais, contrairement aux idées d’Euclide, ils n’ont pas identifié « l’espace physique » avec « l’espace de nos sens ». Partant de notre expérience dans l’espace, ils ont cherché à identifier les propriétés les plus importantes de l’espace et les ont posées à la base de la géométrie. C’est sur la connaissance active de l’espace que les axiomes de la géométrie ont été élaborés ; ils ne pouvaient donc pas être a priori comme ils le sont dans la philosophie kantienne. En outre, pendant la dernière décade du siècle, certains mathématiciens italiens – De Paolis, Gino Fano, Pieri, et autres – ont fondé le concept de nombre sur la géométrie, en employant des résultats de la géométrie projective. Ainsi, on fondait l’arithmétique sur la géométrie et non l’inverse, comme David Hilbert a cherché à faire quelques années après, sans succès. MOTS-CLÉS : Riemann, Helmholtz, fondements des mathématiques, géométrie, espace. ABSTRACT : Many XIXth century « geometers » – such as Bernhard Riemann, Hermann von Helmholtz, Felix Klein, Riccardo De Paolis, Mario Pieri, Henri Poincaré, Federigo Enriques, and others – played an important role in the discussion about the founda- tions of mathematics. But in contrast to Euclid’s ideas, they did not simply identify « physical space » with the « space of the senses ». -
Notices of the American Mathematical Society ABCD Springer.Com
ISSN 0002-9920 Notices of the American Mathematical Society ABCD springer.com Highlights in Springer’s eBook Collection of the American Mathematical Society August 2009 Volume 56, Number 7 Guido Castelnuovo and Francesco Severi: NEW NEW NEW Two Personalities, Two The objective of this textbook is the Blackjack is among the most popular This second edition of Alexander Soifer’s Letters construction, analysis, and interpreta- casino table games, one where astute How Does One Cut a Triangle? tion of mathematical models to help us choices of playing strategy can create demonstrates how different areas of page 800 understand the world we live in. an advantage for the player. Risk and mathematics can be juxtaposed in the Students and researchers interested in Reward analyzes the game in depth, solution of a given problem. The author mathematical modelling in math- pinpointing not just its optimal employs geometry, algebra, trigono- ematics, physics, engineering and the strategies but also its financial metry, linear algebra, and rings to The Dixmier–Douady applied sciences will find this text useful. performance, in terms of both expected develop a miniature model of cash flow and associated risk. mathematical research. Invariant for Dummies 2009. Approx. 480 p. (Texts in Applied Mathematics, Vol. 56) Hardcover 2009. Approx. 140 p. 23 illus. Hardcover 2nd ed. 2009. XXX, 174 p. 80 illus. Softcover page 809 ISBN 978-0-387-87749-5 7 $69.95 ISBN 978-1-4419-0252-8 7 $49.95 ISBN 978-0-387-74650-0 7 approx. $24.95 For access check with your librarian Waco Meeting page 879 A Primer on Scientific Data Mining in Agriculture Explorations in Monte Programming with Python A. -
Jewish Intellectual Diaspora and the Circulation of Mathematics: Alessandro Terracini in Argentina (1939-1948)
AperTO - Archivio Istituzionale Open Access dell'Università di Torino Jewish intellectual diaspora and the circulation of mathematics: Alessandro Terracini in Argentina (1939-1948) This is the author's manuscript Original Citation: Availability: This version is available http://hdl.handle.net/2318/1741839 since 2020-06-19T10:09:29Z Publisher: Birkuser-Springer Terms of use: Open Access Anyone can freely access the full text of works made available as "Open Access". Works made available under a Creative Commons license can be used according to the terms and conditions of said license. Use of all other works requires consent of the right holder (author or publisher) if not exempted from copyright protection by the applicable law. (Article begins on next page) 26 September 2021 � UN1 Prof. Maria Teresa Borgato [email protected] � ..-\ Università Dipartimento UJ .,,. Università degli Studi di Ferrara u.. "'. degli Studi di Matematica Dipartimento di Matematica e Informatica ., Via Machiavelli 30 • 44121 Ferrara di Ferrara e Informatica lei. 0532 974040 FiE f dmi.unife.it June 16, 2020 To whom it may concern I certify that the work of Erika Luciano, entitled: Jewish intellectua/ diaspora and the circulation of mathematics: Alessandro Terracini in Argentina (1939-1948) has been accepted for publication in the volume: In Foreign Lands: The Migrations of Scientists for Politica/ or Economie Reasons of the Birkauser-Springer series Trends in the History of Science (ISSN: 2297-2951). of the Springer Publishing House (https://www.springer.com/series/11668) In faith Maria Teresa Borgata Prof. Maria Teresa Borgata University of Ferrara Department of Mathematics and Computer Science Corresponding Editor of the Volume: In Foreign Lands: The Migrations of Scientists tor politica/ or Economie Reasons. -
Einstein and Besso: from Zürich to Milano
1 Einstein and Besso: From Zürich to Milano. Christian BRACCO Syrte, CNRS-Observatoire de Paris, 61, avenue de l’observatoire, 75014 Paris CRHI, EA 4318, Université de Nice-Sophia Antipolis, UFR LASH, BP 3209, 98 Bd Hériot, 06204 Nice Cedex 3. E-mail : [email protected] Presented at the Istituto Lombardo, Accademia di Scienze e Lettere, Milan, Italy. Session of Thursday 18th December 2014. To be published in the Rendiconti for year 2014. Abstract: The 1896-1901 Milanese period is a key one to understand Einstein’s training background. When he was a student at the ETH in Zürich (the Swiss Federal Polytechnic in Zürich) from 1896 to 1900, he would make regular trips back to Milan to stay with his family who was involved in the development of the electricity industry in northern Italy. Between 1899 and 1901, he would meet his faithful friend and collaborator, Michele Besso in Milan on a regular basis. Given their relationship, the 1899-1901 Milanese period therefore foreshadowed the Bern period later in 1904. In order to specify the circumstances under which Einstein and Besso got the chance to meet, we will show that their respective families did have interconnected social networks, especially through the electricity sector and the polytechnic engineering Universities of Zürich and Milan. The branch of the Cantoni family, on Michele’s mother’s side, rather ignored by now, played a crucial role: with Vittorio Cantoni, a renowned electrical engineer who had not been previously identified as being Michele’s uncle, and Giuseppe Jung, professor at the Milan Politecnico. We will also show that when staying in Milan, Einstein, who lived in a well-known Milanese palace in the heart of the city, worked in the nearby rich library of the Istituto Lombardo, Accademia di Scienze e Lettere in Brera. -
Introduction to Transcendental Dynamics Christopher J. Bishop
Introduction to Transcendental Dynamics Christopher J. Bishop Department of Mathematics Stony Brook University Intentions Despite many previous opportunities and a brush with conformal dynamics in the form of Kleinian groups, I had never worked on the iteration of holomorphic functions until April 2011 when I met Misha Lyubich on the stairwell of the Stony Brook math building he told me that Alex Eremenko had a question for me. Alex was visiting for a few days and his question was the following: given any compact, connected, planar set K and an ǫ > 0, is there a polynomial p(z) with only two critical values, whose critical points approximate K to within ǫ in the Hausdorff metric? 1 It turns out that we can assume the critical values are 1 and then T = p− ([ 1, 1]) ± − is a finite tree in the plane and Alex’s question is equivalent to asking if such trees are dense in all compact sets. Such a tree is conformally balanced in the sense that every edge gets equal harmonic measure from and every subset of an edge gets ∞ equal harmonic measure from either side. This makes the existence of such trees seem unlikely, or at least requiring very special geometry, but I was able to show that Alex’s conjecture was correct by building an approximating tree that is balanced in a quasiconformal sense and then “fixing” it with the measurable Riemann mapping theorem. When I asked for the motivation behind the question, Alex explained that entire functions with a finite number of critical points play an important role in transcen- dental dynamics because they mimic certain properties of polynomials, e.g., Dennis Sullivan’s “no wandering domains” theorem can be extended to such functions.