Hubert Kennedy Eight Mathematical Biographies
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Catholic Christian Christian
Religious Scientists (From the Vatican Observatory Website) https://www.vofoundation.org/faith-and-science/religious-scientists/ Many scientists are religious people—men and women of faith—believers in God. This section features some of the religious scientists who appear in different entries on these Faith and Science pages. Some of these scientists are well-known, others less so. Many are Catholic, many are not. Most are Christian, but some are not. Some of these scientists of faith have lived saintly lives. Many scientists who are faith-full tend to describe science as an effort to understand the works of God and thus to grow closer to God. Quite a few describe their work in science almost as a duty they have to seek to improve the lives of their fellow human beings through greater understanding of the world around them. But the people featured here are featured because they are scientists, not because they are saints (even when they are, in fact, saints). Scientists tend to be creative, independent-minded and confident of their ideas. We also maintain a longer listing of scientists of faith who may or may not be discussed on these Faith and Science pages—click here for that listing. Agnesi, Maria Gaetana (1718-1799) Catholic Christian A child prodigy who obtained education and acclaim for her abilities in math and physics, as well as support from Pope Benedict XIV, Agnesi would write an early calculus textbook. She later abandoned her work in mathematics and physics and chose a life of service to those in need. Click here for Vatican Observatory Faith and Science entries about Maria Gaetana Agnesi. -
Maria Gaetana Agnesi Melissa De La Cruz
Maria Gaetana Agnesi Melissa De La Cruz Maria Gaetana Agnesi's life Maria Gaetana Agnesi was born on May 16, 1718. She also died on January 9, 1799. She was an Italian mathematician, philosopher, theologian, and humanitarian. Her father, Pietro Agnesi, was either said to be a wealthy silk merchant or a mathematics professor. Regardless, he was well to do and lived a social climber. He married Anna Fortunata Brivio, but had a total of 21 children with 3 female relations. He used his kids to be known with the Milanese socialites of the time and Maria Gaetana Agnesi was his oldest. He hosted soires and used his kids as entertainment. Maria's sisters would perform the musical acts while she would present Latin debates and orations on questions of natural philosophy. The family was well to do and Pietro has to make sure his children were under the best training to entertain well at these parties. For Maria, that meant well-esteemed tutors would be given because her father discovered her great potential for an advanced intellect. Her education included the usual languages and arts; she spoke Italian and French at the age of 5 and but the age of 11, she also knew how to speak Greek, Hebrew, Spanish, German and Latin. Historians have given her the name of the Seven-Tongued Orator. With private tutoring, she was also taught topics such as mathematics and natural philosophy, which was unusual for women at that time. With the Agnesi family living in Milan, Italy, Maria's family practiced religion seriously. -
The In/Visible Woman: Mariangela Ardinghelli and the Circulation Of
The In/visible Woman: Mariangela Ardinghelli and the Circulation of Knowledge between Paris and Naples in the Eighteenth Century Author(s): Paola Bertucci Source: Isis, Vol. 104, No. 2 (June 2013), pp. 226-249 Published by: The University of Chicago Press on behalf of The History of Science Society Stable URL: http://www.jstor.org/stable/10.1086/670946 . Accessed: 29/06/2013 11:12 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp . JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The University of Chicago Press and The History of Science Society are collaborating with JSTOR to digitize, preserve and extend access to Isis. http://www.jstor.org This content downloaded from 130.132.173.211 on Sat, 29 Jun 2013 11:12:01 AM All use subject to JSTOR Terms and Conditions The In/visible Woman Mariangela Ardinghelli and the Circulation of Knowledge between Paris and Naples in the Eighteenth Century By Paola Bertucci* ABSTRACT Mariangela Ardinghelli (1730–1825) is remembered as the Italian translator of two texts by the Newtonian physiologist Stephen Hales, Haemastaticks and Vegetable Staticks. This essay shows that her role in the Republic of Letters was by no means limited to such work. -
Cavendish the Experimental Life
Cavendish The Experimental Life Revised Second Edition Max Planck Research Library for the History and Development of Knowledge Series Editors Ian T. Baldwin, Gerd Graßhoff, Jürgen Renn, Dagmar Schäfer, Robert Schlögl, Bernard F. Schutz Edition Open Access Development Team Lindy Divarci, Georg Pflanz, Klaus Thoden, Dirk Wintergrün. The Edition Open Access (EOA) platform was founded to bring together publi- cation initiatives seeking to disseminate the results of scholarly work in a format that combines traditional publications with the digital medium. It currently hosts the open-access publications of the “Max Planck Research Library for the History and Development of Knowledge” (MPRL) and “Edition Open Sources” (EOS). EOA is open to host other open access initiatives similar in conception and spirit, in accordance with the Berlin Declaration on Open Access to Knowledge in the sciences and humanities, which was launched by the Max Planck Society in 2003. By combining the advantages of traditional publications and the digital medium, the platform offers a new way of publishing research and of studying historical topics or current issues in relation to primary materials that are otherwise not easily available. The volumes are available both as printed books and as online open access publications. They are directed at scholars and students of various disciplines, and at a broader public interested in how science shapes our world. Cavendish The Experimental Life Revised Second Edition Christa Jungnickel and Russell McCormmach Studies 7 Studies 7 Communicated by Jed Z. Buchwald Editorial Team: Lindy Divarci, Georg Pflanz, Bendix Düker, Caroline Frank, Beatrice Hermann, Beatrice Hilke Image Processing: Digitization Group of the Max Planck Institute for the History of Science Cover Image: Chemical Laboratory. -
The Development of Mathematical Logic from Russell to Tarski: 1900–1935
The Development of Mathematical Logic from Russell to Tarski: 1900–1935 Paolo Mancosu Richard Zach Calixto Badesa The Development of Mathematical Logic from Russell to Tarski: 1900–1935 Paolo Mancosu (University of California, Berkeley) Richard Zach (University of Calgary) Calixto Badesa (Universitat de Barcelona) Final Draft—May 2004 To appear in: Leila Haaparanta, ed., The Development of Modern Logic. New York and Oxford: Oxford University Press, 2004 Contents Contents i Introduction 1 1 Itinerary I: Metatheoretical Properties of Axiomatic Systems 3 1.1 Introduction . 3 1.2 Peano’s school on the logical structure of theories . 4 1.3 Hilbert on axiomatization . 8 1.4 Completeness and categoricity in the work of Veblen and Huntington . 10 1.5 Truth in a structure . 12 2 Itinerary II: Bertrand Russell’s Mathematical Logic 15 2.1 From the Paris congress to the Principles of Mathematics 1900–1903 . 15 2.2 Russell and Poincar´e on predicativity . 19 2.3 On Denoting . 21 2.4 Russell’s ramified type theory . 22 2.5 The logic of Principia ......................... 25 2.6 Further developments . 26 3 Itinerary III: Zermelo’s Axiomatization of Set Theory and Re- lated Foundational Issues 29 3.1 The debate on the axiom of choice . 29 3.2 Zermelo’s axiomatization of set theory . 32 3.3 The discussion on the notion of “definit” . 35 3.4 Metatheoretical studies of Zermelo’s axiomatization . 38 4 Itinerary IV: The Theory of Relatives and Lowenheim’s¨ Theorem 41 4.1 Theory of relatives and model theory . 41 4.2 The logic of relatives . -
Logique Combinatoire Et Physique Quantique
Eigenlogic Zeno Toffano [email protected] CentraleSupélec, Gif-sur-Yvette, France Laboratoire des Signaux et Systèmes, UMR8506-CNRS Université Paris-Saclay, France Zeno Toffano : “Eigenlogic” 1 UNILOG 2018 (6th World Congress and School on Universal Logic), Workshop Logic & Physics, Vichy (F), June 22, 2018 statement facts in quantum physics Quantum Physics started in 1900 with the quantification of radiation (Planck’s constant ℎ = 6.63 10−34 J.s) It is the most successful theory in physics and explains: nuclear energy, semiconductors, magnetism, lasers, quantum gravity… The theory has an increasing influence outside physics: computer science, AI, communications, biology, cognition… Nowadays there is a great quantum revival (second quantum revolution) which addresses principally: quantum entanglement (Bell inequalites, teleportation…), quantum superposition (Schrödinger cat), decoherence non-locality, non- separability, non-contextuality, non-classicality, non-… A more basic aspect is quantification: a measurement can only give one of the (real) eigenvalues of an observable. The associated eigenvector is the resulting quantum state. Measurements on non-eigenstates are indeterminate, the outcome probability is given by the Born rule. The eigenvalues are the spectrum (e.g. energies for the Hamiltonian). In physics it is natural to “work” in different representation eignespaces (of the considered observable) e.g: semiconductors “make sense” in the reciprocal lattice (momentum space 푝 , spatial Fourier transform of coordinate -
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. -
Computable Functions A
http://dx.doi.org/10.1090/stml/019 STUDENT MATHEMATICAL LIBRARY Volume 19 Computable Functions A. Shen N. K. Vereshchagin Translated by V. N. Dubrovskii #AMS AMERICAN MATHEMATICAL SOCIETY Editorial Board Robert Devaney Carl Pomerance Daniel L. Goroff Hung-Hsi Wu David Bressoud, Chair H. K. BepemarHH, A. Illem* BMHHCJIHMME ^YHKUMM MIIHMO, 1999 Translated from the Russian by V. N. Dubrovskii 2000 Mathematics Subject Classification. Primary 03-01, 03Dxx. Library of Congress Cataloging-in-Publication Data Vereshchagin, Nikolai Konstantinovich, 1958- Computable functions / A. Shen, N.K. Vereshchagin ; translated by V.N. Dubrovskii. p. cm. — (Student mathematical library, ISSN 1520-9121 ; v. 19) Authors' names on t.p. of translation reversed from original. Includes bibliographical references and index. ISBN 0-8218-2732-4 (alk. paper) 1. Computable functions. I. Shen, A. (Alexander), 1958- II. Title. III. Se• ries. QA9.59 .V47 2003 511.3—dc21 2002038567 Copying and reprinting. Individual readers of this publication, and nonprofit libraries acting for them, are permitted to make fair use of the material, such as to copy a chapter for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publication is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Acquisitions Department, American Mathematical Society, 201 Charles Street, Providence, Rhode Island 02904- 2294, USA. Requests can also be made by e-mail to reprint-permissionQams.org. © 2003 by the American Mathematical Society. -
Models in Geometry and Logic: 1870-1920 ∗
Models in Geometry and Logic: 1870-1920 ∗ Patricia Blanchette University of Notre Dame 1 Abstract Questions concerning the consistency of theories, and of the independence of axioms and theorems one from another, have been at the heart of logical investigation since the beginning of logic. It is well known that our own contemporary methods for proving independence and consistency owe a good deal to developments in geometry in the middle of the nineteenth century, and especially to the role of models in estab- lishing the consistency of non-Euclidean geometries. What is less well understood, and is the topic of this essay, is the extent to which the concepts of consistency and of independence that we take for granted today, and for which we have clear techniques of proof, have been shaped in the intervening years by the gradual de- velopment of those techniques. It is argued here that this technical development has brought about significant conceptual change, and that the kinds of consistency- and independence-questions we can decisively answer today are not those that first motivated metatheoretical work. The purpose of this investigation is to help clarify what it is, and importantly what it is not, that we can claim to have shown with a modern demonstration of consistency or independence.1 ∗This is the nearly-final version of the paper whose official version appears in Logic, Methodology, and Philosophy of Science - proceedings of the 15th International Congress, edited by Niiniluoto, Sepp¨al¨a,Sober; College Publications 2017, pp 41-61 1Many thanks to the organizers of CLMPS 2015 in Helsinki, and also to audience members for helpful comments. -
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. -
Theory and Experiment in the Work of Alonzo Church and Emil Post
Theory and Experiment in the work of Alonzo Church and Emil Post Liesbeth De Mol Abstract While most mathematicians would probably agree that ‘experi- mentation’ together with an ‘empirical’ attitude – both understood in their most general sense – can be important methods of mathematical discovery, this is often obscured in the final presentation of the results for the sake of mathematical elegance. In this paper it will be shown how this “method” has played a significant role in the work of two ma- jor contributors to the rather abstract discipline called mathematical logic, namely Alonzo Church and Emil Post. 1 Introduction In this paper it will be investigated in what way ‘experiment’ and ‘em- pirical evidence’ played an important role in the work of two mathemati- cians/logicians – Alonzo Church and Emil Post. Both made significant con- tributions to computer science, although at the time they wrote down their results it didn’t even exist yet. In Sec. 2 it will be shown in what way Post 1 had to rely on the more ‘experimental’ work of testing out specific cases in order to get a grip on certain formal systems called tag systems and how this led him to the at that time innovating idea that the Entscheidungsproblem might not be solvable. In investigating Church’s work, it will be explained how the notion of ‘empirical evidence’ played a significant role in the de- velopment of his ideas leading to his seminal 1936 paper (Sec. 3). From this perspective it is interesting to confront what is here called Post’s second thesis with Church’s thesis. -
Giuseppe Peano and His School: Axiomatics, Symbolism and Rigor
Philosophia Scientiæ Travaux d'histoire et de philosophie des sciences 25-1 | 2021 The Peano School: Logic, Epistemology and Didactics Giuseppe Peano and his School: Axiomatics, Symbolism and Rigor Paola Cantù and Erika Luciano Electronic version URL: http://journals.openedition.org/philosophiascientiae/2788 DOI: 10.4000/philosophiascientiae.2788 ISSN: 1775-4283 Publisher Éditions Kimé Printed version Date of publication: 25 February 2021 Number of pages: 3-14 ISBN: 978-2-38072-000-6 ISSN: 1281-2463 Electronic reference Paola Cantù and Erika Luciano, “Giuseppe Peano and his School: Axiomatics, Symbolism and Rigor”, Philosophia Scientiæ [Online], 25-1 | 2021, Online since 01 March 2021, connection on 30 March 2021. URL: http://journals.openedition.org/philosophiascientiae/2788 ; DOI: https://doi.org/10.4000/ philosophiascientiae.2788 Tous droits réservés Giuseppe Peano and his School: Axiomatics, Symbolism and Rigor Paola Cantù Aix-Marseille Université, CNRS, Centre Gilles-Gaston-Granger, Aix-en-Provence (France) Erika Luciano Università degli Studi di Torino, Dipartimento di Matematica, Torino (Italy) Peano’s axioms for arithmetic, published in 1889, are ubiquitously cited in writings on modern axiomatics, and his Formulario is often quoted as the precursor of Russell’s Principia Mathematica. Yet, a comprehensive historical and philosophical evaluation of the contributions of the Peano School to mathematics, logic, and the foundation of mathematics remains to be made. In line with increased interest in the philosophy of mathematics for the investigation of mathematical practices, this thematic issue adds some contributions to a possible reconstruction of the philosophical views of the Peano School. These derive from logical, mathematical, linguistic, and educational works1, and also interactions with contemporary scholars in Italy and abroad (Cantor, Dedekind, Frege, Russell, Hilbert, Bernays, Wilson, Amaldi, Enriques, Veronese, Vivanti and Bettazzi).