Results for 'Mathematics History'

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  1.  28
    Mathematics, a Concise History and Philosophy.W. S. Anglin - 1996 - Springer.
    This is a concise introductory textbook for a one semester course in the history and philosophy of mathematics. It is written for mathematics majors, philosophy students, history of science students and secondary school mathematics teachers. The only prerequisite is a solid command of pre-calculus mathematics. It is shorter than the standard textbooks in that area and thus more accessible to students who have trouble coping with vast amounts of reading. Furthermore, there are many detailed (...)
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  2.  32
    The Architecture of Modern Mathematics: Essays in History and Philosophy.José Ferreirós Domínguez & Jeremy Gray (eds.) - 2006 - Oxford University Press.
    This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research and how a number of historical accounts can be deepened by embracing philosophical questions.
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  3. Essays in the Philosophy and History of Logic and Mathematics.Roman Murawski (ed.) - 2010 - Rodopi.
    The book is a collection of the author’s selected works in the philosophy and history of logic and mathematics. Papers in Part I include both general surveys of contemporary philosophy of mathematics as well as studies devoted to specialized topics, like Cantor's philosophy of set theory, the Church thesis and its epistemological status, the history of the philosophical background of the concept of number, the structuralist epistemology of mathematics and the phenomenological philosophy of mathematics. (...)
     
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  4.  11
    History of Mathematics in Mathematics Education.Michael N. Fried - 2014 - In Michael R. Matthews (ed.), International Handbook of Research in History, Philosophy and Science Teaching. Springer. pp. 669-703.
    This paper surveys central justifications and approaches adopted by educators interested in incorporating history of mathematics into mathematics teaching and learning. This interest itself has historical roots and different historical manifestations; these roots are examined as well in the paper. The paper also asks what it means for history of mathematics to be treated as genuine historical knowledge rather than a tool for teaching other kinds of mathematical knowledge. If, however, history of mathematics (...)
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  5.  61
    What Can the Philosophy of Mathematics Learn From the History of Mathematics?Brendan Larvor - 2008 - Erkenntnis 68 (3):393-407.
    This article canvasses five senses in which one might introduce an historical element into the philosophy of mathematics: 1. The temporal dimension of logic; 2. Explanatory Appeal to Context rather than to General Principles; 3. Heraclitean Flux; 4. All history is the History of Thought; and 5. History is Non-Judgmental. It concludes by adapting Bernard Williams’ distinction between ‘history of philosophy’ and ‘history of ideas’ to argue that the philosophy of mathematics is unavoidably (...)
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  6.  22
    New Perspectives on Mathematical Practices: Essays in Philosophy and History of Mathematics[REVIEW]Bart Van Kerkhove (ed.) - 2009 - World Scientific.
    This volume focuses on the importance of historical enquiry for the appreciation of philosophical problems concerning mathematics.
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  7. The History of Mathematics.Anne Rooney - 2013 - Rosen.
     
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  8.  24
    Ideas and Processes in Mathematics: A Course on History and Philosophy of Mathematics.Charalampos Toumasis - 1993 - Studies in Philosophy and Education 12 (2-4):245-256.
  9. Logos and Máthēma: Studies in the Philosophy of Mathematics and History of Logic.Roman Murawski - 2011 - Peter Lang.
  10. Analysis and Synthesis in Mathematics History and Philosophy.Michael Otte & Marco Panza - 1997
     
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  11.  94
    Diagrams in Mathematics: History and Philosophy.John Mumma & Marco Panza - 2012 - Synthese 186 (1):1-5.
    Diagrams are ubiquitous in mathematics. From the most elementary class to the most advanced seminar, in both introductory textbooks and professional journals, diagrams are present, to introduce concepts, increase understanding, and prove results. They thus fulfill a variety of important roles in mathematical practice. Long overlooked by philosophers focused on foundational and ontological issues, these roles have come to receive attention in the past two decades, a trend in line with the growing philosophical interest in actual mathematical practice.
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  12.  43
    Deleuze and the History of Mathematics: In Defense of the New.Simon B. Duffy - 2013 - Bloomsbury Academic.
    Gilles Deleuze’s engagements with mathematics, replete in his work, rely upon the construction of alternative lineages in the history of mathematics, which challenge some of the self imposed limits that regulate the canonical concepts of the discipline. For Deleuze, these challenges provide an opportunity to reconfigure particular philosophical problems – for example, the problem of individuation – and to develop new concepts in response to them. The highly original research presented in this book explores the mathematical construction (...)
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  13.  1
    Jiri Hudecek, Reviving Ancient Chinese Mathematics: Mathematics, History and Politics in the Work of Wu Wen-Tsun. New York: Routledge, 2014. Pp. Xii + 210. ISBN 978-0-4157-0296-6. £90.00. [REVIEW]Ubiratan D'Ambrosio - 2016 - British Journal for the History of Science 49 (1):143-144.
  14. A Short History of Greek Mathematics.James Gow - 1923 - Cambridge University Press.
    James Gow's A Short History of Greek Mathematics provided the first full account of the subject available in English, and it today remains a clear and thorough guide to early arithmetic and geometry. Beginning with the origins of the numerical system and proceeding through the theorems of Pythagoras, Euclid, Archimedes and many others, the Short History offers in-depth analysis and useful translations of individual texts as well as a broad historical overview of the development of mathematics. (...)
     
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  15.  54
    Review of Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics[REVIEW]Chris Smeenk - 2005 - Studies in History and Philosophy of Science Part B 36 (1):194-199.
    Book Review for Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics, La Salle, IL: Open Court, 2002. Edited by David Malament. This volume includes thirteen original essays by Howard Stein, spanning a range of topics that Stein has written about with characteristic passion and insight. This review focuses on the essays devoted to history and philosophy of physics.
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  16.  1
    Goldfarb Warren. Poincaré Against the Logicists. History and Philosophy of Modern Mathematics, Edited by Aspray William and Kitcher Philip, Minnesota Studies in the Philosophy of Science, Vol. 11, University of Minnesota Press, Minneapolis 1988, Pp. 61–81.Friedman Michael. Logical Truth and Analyticity in Carnap's “Logical Syntax of Language.” History and Philosophy of Modern Mathematics, Edited by Aspray William and Kitcher Philip, Minnesota Studies in the Philosophy of Science, Vol. 11, University of Minnesota Press, Minneapolis 1988, Pp. 82–94.Moore Gregory H.. The Emergence of First-Order Logic. History and Philosophy of Modern Mathematics, Edited by Aspray William and Kitcher Philip, Minnesota Studies in the Philosophy of Science, Vol. 11, University of Minnesota Press, Minneapolis 1988, Pp. 95–135.Dauben Joseph W.. Abraham Robinson and Nonstandard Analysis: History, Philosophy, and Foundations of Mathematics. History and Philosophy of Modern Mathematics, Edited by Aspray William. [REVIEW]Michael Hallett - 1990 - Journal of Symbolic Logic 55 (3):1315-1319.
  17.  2
    Review: E. R. Kiely, Mathematics, History Of. [REVIEW]Alonzo Church - 1975 - Journal of Symbolic Logic 40 (4):597-598.
  18. Jiri Hudecek. Reviving Ancient Chinese Mathematics: Mathematics, History, and Politics in the Work of Wu Wen-Tsun. Xii + 210 Pp., Figs., Tables, Bibl., Index. Abingdon, Oxfordshire: Routledge, 2014. $155. [REVIEW]Karine Chemla - 2016 - Isis 107 (4):894-896.
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  19. Kiely E. R.. Mathematics, History Of. New Catholic Encyclopedia, Prepared by an Editorial Staff at the Catholic University of America, McGraw-Hill Book Company, New York Etc. 1967, Vol. 9, Pp. 447–456. [REVIEW]Alonzo Church - 1975 - Journal of Symbolic Logic 40 (4):597-598.
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  20. Analysis and Synthesis in Mathematics: History and Philosophy. Michael Otte, Marco Panza.Antoni Malet - 2000 - Isis 91 (1):135-136.
  21. Reviews: Mathematics and Logic-Analysis and Synthesis in Mathematics. History and Philosophy. [REVIEW]Michael Otte, Marco Panza & I. Grattan-Guinness - 1998 - Annals of Science 55 (4):436-437.
     
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  22.  25
    Árpád Szabó and Imre Lakatos, or the Relation Between History and Philosophy of Mathematics.András Máté - 2006 - Perspectives on Science 14 (3):282-301.
    The thirty year long friendship between Imre Lakatos and the classic scholar and historian of mathematics Árpád Szabó had a considerable influence on the ideas, scholarly career and personal life of both scholars. After recalling some relevant facts from their lives, this paper will investigate Szabó's works about the history of pre-Euclidean mathematics and its philosophy. We can find many similarities with Lakatos' philosophy of mathematics and science, both in the self-interpretation of early axiomatic Greek (...) as Szabó reconstructs it, and in the general overview Szabó provides us about the turn from the intuitive methods of Greek mathematicians to the strict axiomatic method of Euclid's Elements. As a conclusion, I will argue that the correct explanation of these similarities is that in their main works they developed ideas they had in common from the period of intimate intellectual contact in Hungarian academic life in the mid-twentieth century. In closing, I will recall some relevant features of this background that deserve further research. (shrink)
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  23.  43
    The History of Applied Mathematics and the History of Society.Michael Stolz - 2002 - Synthese 133 (1-2):43 - 57.
    Choosing the history of statistics and operations research as a casestudy, several ways of setting the development of 20th century applied mathematics into a social context are discussed. It is shown that there is ample common ground between these contextualizations and several recent research programs in general contemporary history. It is argued that a closer cooperation between general historians and historians of mathematics might further the integration of the internalist and externalist approaches within the historiography of (...)
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  24. A History of Mathematics: From Mesopotamia to Modernity.Luke Hodgkin - 2005 - Oxford University Press UK.
    A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as (...)
     
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  25.  53
    C.K. Raju. Cultural Foundations of Mathematics: The Nature of Mathematical Proof and the Transmission of the Calculus From India to Europe in the 16th C. Ce. History of Science, Philosophy and Culture in Indian Civilization. [REVIEW]José Ferreirós - 2009 - Philosophia Mathematica 17 (3):nkn028.
    This book is part of a major project undertaken by the Centre for Studies in Civilizations , being one of a total of ninety-six planned volumes. The author is a statistician and computer scientist by training, who has concentrated on historical matters for the last ten years or so. The book has very ambitious aims, proposing an alternative philosophy of mathematics and a deviant history of the calculus. Throughout, there is an emphasis on the need to combine (...) and philosophy of mathematics, especially in order to evaluate properly the history of mathematics in India, in particular the history of the calculus.The pivotal goals of the book are to oppose the Eurocentric account of the history of science in general and mathematics in particular; to avoid the usual philosophical idea of the centrality of proof for mathematical knowledge, in favour of the traditional Indian notion of pramāṇa [validation] encompassing empirical elements and emphasizing calculation; to analyze the thousand-year-long development of infinite series in India, starting in the fifth century; and to show ‘how and why the calculus was imported into Europe’ from about 1500. The result is a picture in which inputs from the Indian subcontinent and epistemology are the driving forces of the history of mathematics, as people in the European subcontinent struggle to adopt new calculation techniques from the East in spite of Western philosophico-religious biases . Thus, a ‘first math war’ involved the algorismus de numero indorum, adopted for practical reasons, which forced Europeans to modify their epistemology of number and quantities. A ‘second math war’ revolved around infinite series and the calculus, since the background of Western epistemology created ‘spurious difficulties’ about infinities and infinitesimals, partially resolved with theories of real numbers. And a ‘third math war’ is …. (shrink)
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  26.  50
    William Tait. The Provenance of Pure Reason. Essays on the Philosophy of Mathematics and on its History.Charles Parsons - 2009 - Philosophia Mathematica 17 (2):220-247.
    William Tait's standing in the philosophy of mathematics hardly needs to be argued for; for this reason the appearance of this collection is especially welcome. As noted in his Preface, the essays in this book ‘span the years 1981–2002’. The years given are evidently those of publication. One essay was not previously published in its present form, but it is a reworking of papers published during that period. The Introduction, one appendix, and some notes are new. Many of the (...)
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  27.  41
    Rigorous Proof and the History of Mathematics: Comments on Crowe.Douglas Jesseph - 1990 - Synthese 83 (3):449 - 453.
    Duhem's portrayal of the history of mathematics as manifesting calm and regular development is traced to his conception of mathematical rigor as an essentially static concept. This account is undermined by citing controversies over rigorous demonstration from the eighteenth and twentieth centuries.
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  28.  2
    Physics and Astronomy: Aristotle's Physics II.2.193b22–194a12this Paper Was Prepared as the Basis of a Presentation at a Conference Entitled “Writing and Rewriting the History of Science, 1900–2000,” Les treilLes, France, September, 2003, Organized by Karine Chemla and Roshdi Rashed. I Have Compared Aristotle's and Ptolemy's Views of the Relationship Between Astronomy and Physics in a Paper Called “Astrologogeômetria and Astrophysikê in Aristotle and Ptolemy,” Presented at a Conference Entitled “Physics and Mathematics in Antiquity,” Leiden, the Netherlands, June, 2004, Organized by Keimpe Algra and Frans de Haas. For a Discussion of Hellenistic Views of This Relationship See Ian Mueller, “Remarks on Physics and Mathematical Astronomy and Optics in Epicurus, Sextus Empiricus, and Some Stoics,” in Philippa Lang , Re-Inventions: Essays on Hellenistic and Early Roman Science, Apeiron 37, 4 : 57–87. I Would Like to Thank Two Anonymous Readers of This Essay for Meticulous Corrections and Th. [REVIEW]Ian Mueller - 2006 - Arabic Sciences and Philosophy 16 (2):175-206.
    In the first part of chapter 2 of book II of the Physics Aristotle addresses the issue of the difference between mathematics and physics. In the course of his discussion he says some things about astronomy and the ‘ ‘ more physical branches of mathematics”. In this paper I discuss historical issues concerning the text, translation, and interpretation of the passage, focusing on two cruxes, the first reference to astronomy at 193b25–26 and the reference to the more physical branches at (...)
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  29.  3
    Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics.Ricardo Karam - 2015 - Science and Education 24 (5 - 6):543-559.
    In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a (...)
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  30.  3
    Book Reviews: Geraldine Brady, "From Peirce to Skolem. A Neglected Chapter in the History of Logic", Studies in the History and Philosophy of Mathematics, Vol. 4, Elsevier , 2000, ISBN-13: 978-0444503343, ISBN-10: 0-444-50334-X. [REVIEW]Davide Bondoni - 2009 - Logic and Logical Philosophy 17 (4):353-357.
    Geraldine Brady, "From Peirce to Skolem. A Neglected Chapter in the History of Logic", Studies in the History and Philosophy of Mathematics, vol. 4, Elsevier, 2000, ISBN-13: 978-0444503343, ISBN-10: 0-444-50334-X, 625~pp.
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  31. The Architecture of Modern Mathematics: Essays in History and Philosophy.J. Ferreiros & J. J. Gray (eds.) - 2006 - Oxford University Press UK.
    This edited volume, aimed at both students and researchers in philosophy, mathematics and history of science, highlights leading developments in the overlapping areas of philosophy and the history of modern mathematics. It is a coherent, wide ranging account of how a number of topics in the philosophy of mathematics must be reconsidered in the light of the latest historical research, and how a number of historical accounts can be deepened by embracing philosophical questions.
     
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  32.  12
    History & Mathematics: Processes and Models of Global Dynamics.Leonid Grinin, Peter Herrmann, Andrey Korotayev & Arno Tausch (eds.) - 2010
    A more and more important role is played by new directions in historical research that study long-term dynamic processes and quantitative changes. This kind of history can hardly develop without the application of mathematical methods. The history is studied more and more as a system of various processes, within which one can detect waves and cycles of different lengths – from a few years to several centuries, or even millennia. This issue is the third collective monograph in the (...)
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  33. A History of Mathematics: From Mesopotamia to Modernity.Luke Hodgkin - 2013 - Oxford University Press UK.
    A History of Mathematics: From Mesopotamia to Modernity covers the evolution of mathematics through time and across the major Eastern and Western civilizations. It begins in Babylon, then describes the trials and tribulations of the Greek mathematicians. The important, and often neglected, influence of both Chinese and Islamic mathematics is covered in detail, placing the description of early Western mathematics in a global context. The book concludes with modern mathematics, covering recent developments such as (...)
     
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  34. Routledge History of Philosophy Volume Ix: Philosophy of the English-Speaking World in the Twentieth Century 1: Science, Logic and Mathematics.S. G. Shanker (ed.) - 2003 - Routledge.
    Volume 9 of the Routledge History of Philosophy surveys ten key topics in the philosophy of science, logic and mathematics in the twentieth century. Each of the essays is written by one of the world's leading experts in that field. Among the topics covered are the philosophy of logic, of mathematics and of Gottlob Frege; Ludwig Wittgenstein's Tractatus ; a survey of logical positivism; the philosophy of physics and of science; probability theory, cybernetics and an essay on (...)
     
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  35. Routledge History of Philosophy Volume Ix: Philosophy of the English-Speaking World in the Twentieth Century 1: Science, Logic and Mathematics.S. G. Shanker (ed.) - 1996 - Routledge.
    Volume 9 of the _Routledge History of Philosophy_ surveys ten key topics in the philosophy of science, logic and mathematics in the twentieth century. Each of the essays is written by one of the world's leading experts in that field. Among the topics covered are the philosophy of logic, of mathematics and of Gottlob Frege; Ludwig Wittgenstein's _Tractatus_; a survey of logical positivism; the philosophy of physics and of science; probability theory, cybernetics and an essay on the (...)
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  36. Mathematics and Necessity Essays in the History of Philosophy.T. J. Smiley & British Academy - 2000
    Notes on Contributors Timothy Smiley, Preface M F Burnyeat, Plato on Why Mathematics is Good for the Soul Ian Hacking, What Mathematics Has Done to Some and Only Some Philosophers Jonathan Bennett, Infallibility and Modal Knowledge in Some Early Modern Philosophers.
     
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  37.  8
    History and Philosophy of Modern Mathematics.William Aspray & Philip Kitcher - 1988
  38.  41
    Testing the Philosophy of Mathematics in the History of Mathematics.Eduard Glas - 1989 - Studies in History and Philosophy of Science Part A 20 (1):115-131.
    Recent philosophical accounts of mathematics increasingly focus on the quasi-Empirical rather than the formal aspects of the field, The praxis of how mathematics is done rather than the idealized logical structure and foundations of the theory. The ultimate test of any philosophy of mathematics, However idealized, Is its ability to account adequately for the factual development of the subject in real time. As a text case, The works and views of felix klein (1849-1925) were studied. Major advances (...)
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  39.  33
    Testing the Philosophy of Mathematics in the History of Mathematics.Eduard Glas - 1989 - Studies in History and Philosophy of Science Part A 20 (2):157-174.
    Recent philosophical accounts of mathematics increasingly focus on the quasi-Empirical rather than the formal aspects of the field, The praxis of how mathematics is done rather than the idealized logical structure and foundations of the theory. The ultimate test of any philosophy of mathematics, However idealized, Is its ability to account adequately for the factual development of the subject in real time. As a text case, The works and views of felix klein (1849-1925) were studied. Major advances (...)
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  40.  7
    Literature Survey: Recent Publications in the History and Philosophy of Mathematics From the Renaissance to Berkeley. [REVIEW]Paolo Mancosu - 1999 - Metascience 8 (1):102-124.
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  41.  2
    On the Role of Equality and Inequality in the History of Mathematics.R. C. H. Tanner - 1962 - British Journal for the History of Science 1 (2):159-169.
    The following essay is adapted from one with the same title read to the British Society for the History of Science on 20 October 1958—the anniversary, by a striking coincidence, of the birth of W. H. Young . To his memory I dedicated the talk, and now rededicate its publication, not only because I am his daughter and of all that means, but because he invented a method, the method of monotone sequences, which shows the powerfulness of inequalities as (...)
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  42.  15
    Reading Natural Philosophy: Essays in the History and Philosophy of Science and Mathematics.David B. Malament (ed.) - 2002 - Open Court.
    In this book, 13 leading philosophers of science focus on the work of Professor Howard Stein, best known for his study of the intimate connection between ...
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  43.  17
    The Provenance of Pure Reason: Essays in the Philosophy of Mathematics and its History.William Tait - 2005 - Oup Usa.
    William Tait is one of the most distinguished philosophers of mathematics of the last fifty years. This volume collects his most important published philosophical papers from the 1980's to the present. The articles cover a wide range of issues in the foundations and philosophy of mathematics, including some on historical figures ranging from Plato to Gdel.
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  44.  27
    Into the 'Regions of Physical and Metaphysical Chaos': Maxwell's Scientific Metaphysics and Natural Philosophy of Action (Agency, Determinacy and Necessity From Theology, Moral Philosophy and History to Mathematics, Theory and Experiment).Jordi Cat - 2012 - Studies in History and Philosophy of Science Part A 43 (1):91-104.
  45.  4
    A Humanist History of Mathematics? Regiomontanus's Padua Oration in Context.James Steven Byrne - 2006 - Journal of the History of Ideas 67 (1):41-61.
  46.  38
    Duhem and History and Philosophy of Mathematics.Michael J. Crowe - 1990 - Synthese 83 (3):431 - 447.
    The first part of this paper consists of an exposition of the views expressed by Pierre Duhem in his Aim and Structure of Physical Theory concerning the philosophy and historiography of mathematics. The second part provides a critique of these views, pointing to the conclusion that they are in need of reformulation. In the concluding third part, it is suggested that a number of the most important claims made by Duhem concerning physical theory, e.g., those relating to the Newtonian (...)
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  47.  1
    Does the History of Science Treat of History of Science? The Case of Mathematics.Ivor Grattan-Guinness - 1990 - History of Science 28 (80):149-173.
  48.  1
    Augustus De Morgan, the History of Mathematics, and the Foundations of Algebra.Joan Richards - 1987 - Isis: A Journal of the History of Science 78:6-30.
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  49.  41
    Kuhnian Issues, Scientific Revolutions and the History of Mathematics.Leo Corry - 1993 - Studies in History and Philosophy of Science Part A 24 (1):95-117.
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  50.  3
    Christopher Hollings, Mathematics Across the Iron Curtain: A History of the Algebraic Theory of Semigroups. Providence, RI: American Mathematical Society, 2014. Pp. Xi + 441. ISBN 978-1-4704-1493-1. £79.95. [REVIEW]Michael J. Barany - 2016 - British Journal for the History of Science 49 (1):140-141.
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