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  1. added 2018-11-26
    The Invariant Twins.Michael Meo - 2008 - Metascience 17 (1):27-32.
    Two recently published scholarly biographies of leading nineteenth-century British mathematicians, pioneers in abstract algebra and personal friends, provide an informed comparison of their lives and work.
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  2. added 2018-09-28
    A Life in Science, Philosophy, and the Public Domain: Three Biographies of PoincaréJeremy J. Gray. Henri Poincaré: A Scientific Biography. Princeton, NJ: Princeton University Press, 2013. Pp. Xii+592. $35.00/£24.95 .Ferdinand Verhulst. Henri Poincaré: Impatient Genius. New York: Springer, 2012. Pp. Xi+260. $49.95 ; $39.95 .Jean-Marc Ginoux and Christian Gerini. 2012. Henri Poincaré: Une Biographie au Quotidien. Paris: Ellipses, 2012. Pp. Iv+298. €24.00 . [Henri Poincaré: A Biography Through the Daily Papers. Singapore: World Scientific, 2013. Pp. 260. $29.00 ; $22.00 .]. [REVIEW]David J. Stump - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (2):309-318.
  3. added 2018-09-20
    Exploring Predicativity.Laura Crosilla - 2018 - In Proof and Computation. pp. 83-108.
    Prominent constructive theories of sets as Martin-Löf type theory and Aczel and Myhill constructive set theory, feature a distinctive form of constructivity: predicativity. This may be phrased as a constructibility requirement for sets, which ought to be finitely specifiable in terms of some uncontroversial initial “objects” and simple operations over them. Predicativity emerged at the beginning of the 20th century as a fundamental component of an influential analysis of the paradoxes by Poincaré and Russell. According to this analysis the paradoxes (...)
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  4. added 2018-06-07
    Lautman on Problems as the Conditions of Existence of Solutions.Simon B. Duffy - 2018 - Angelaki 23 (2):79-93.
    Albert Lautman (b. 1908–1944) was a philosopher of mathematics whose views on mathematical reality and on the philosophy of mathematics parted with the dominant tendencies of mathematical epistemology of the time. Lautman considered the role of philosophy, and of the philosopher, in relation to mathematics to be quite specific. He writes that: ‘in the development of mathematics, a reality is asserted that mathematical philosophy has as a function to recognize and describe’ (Lautman 2011, 87). He goes on to characterize this (...)
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  5. added 2018-03-19
    On A.A. Markov’s Attitude Towards Brouwer’s Intuitionism.Ioannis M. Vandoulakis - 2015 - Philosophia Scientae 19:143-158.
    The paper examines Andrei A. Markov’s critical attitude towards L.E.J. Brouwer’s intuitionism, as is expressed in his endnotes to the Russian translation of Heyting’s Intuitionism, published in Moscow in 1965. It is argued that Markov’s algorithmic approach was shaped under the impact of the mathematical style and values prevailing in the Petersburg mathematical school, which is characterized by the proclaimed primacy of applications and the search for rigor and effective solutions.
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  6. added 2018-02-17
    Interpreting Gödel: Critical Essays.Juliette Kennedy (ed.) - 2014 - Cambridge: Cambridge University Press.
    The logician Kurt Gödel published a paper in 1931 formulating what have come to be known as his 'incompleteness theorems', which prove, among other things, that within any formal system with resources sufficient to code arithmetic, questions exist which are neither provable nor disprovable on the basis of the axioms which define the system. These are among the most celebrated results in logic today. In this volume, leading philosophers and mathematicians assess important aspects of Gödel's work on the foundations and (...)
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  7. added 2018-02-17
    "Mathesis of the Mind": A Study of Fichte’s Wissenschaftslehre and Geometry.David W. Wood - 2012 - New York/Amsterdam: Editions Rodopi (Brill Publishers). Fichte-Studien-Supplementa Vol. 29.
    This is an in-depth study of J.G. Fichte’s philosophy of mathematics and theory of geometry. It investigates both the external formal and internal cognitive parallels between the axioms, intuitions and constructions of geometry and the scientific methodology of the Fichtean system of philosophy. In contrast to “ordinary” Euclidean geometry, in his Erlanger Logik of 1805 Fichte posits a model of an “ursprüngliche” or original geometry – that is to say, a synthetic and constructivistic conception grounded in ideal archetypal elements that (...)
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  8. added 2018-01-16
    Wranglers and Physicists. Studies on Cambridge [Mathematical] Physics in the Nineteenth Century. [REVIEW]Frank James - 1987 - British Journal for the History of Science 20 (2):233-234.
  9. added 2018-01-08
    Discours de la methode pour bien conduire sa raison & chercher la verité dans les sciences. Plus La dioptrique. Les meteores. Et La geometrie. Qui sont des essais de cete methode.René Descartes - 1637 - Leiden: Jan Maire.
  10. added 2017-09-15
    Paul Erickson, The World the Game Theorists Made. [REVIEW]Philip Mirowski - 2017 - Hopos: The Journal of the International Society for the History of Philosophy of Science 7 (1):160-163.
  11. added 2017-07-07
    Whitehead and Pythagoras.Arran Gare - 2006 - Concrescence 7:3 - 19.
    While the appeal of scientific materialism has been weakened by developments in theoretical physics, chemistry and biology, Pythagoreanism still attracts the allegiance of leading scientists and mathematicians. It is this doctrine that process philosophers must confront if they are to successfully defend their metaphysics. Peirce, Bergson and Whitehead were acutely aware of the challenge of Pythagoreanism, and attempted to circumvent it. The problem addressed by each of these thinkers was how to account for the success of mathematical physics if the (...)
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  12. added 2017-03-16
    Die Entstehung des Tensorkalkuls: Von den Anfangen in der Elastizitatstheorie Bis Zur Verwendung in der BaustatikDieter Herbert. [REVIEW]Renatus Ziegler - 1994 - Isis 85 (1):178-179.
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  13. added 2017-03-06
    Forms of Mathematization (14th-17th Centuries).Sophie Roux - 2010 - Early Science and Medicine 15 (4):319-337.
    According to a grand narrative that long ago ceased to be told, there was a seventeenth century Scientific Revolution, during which a few heroes conquered nature thanks to mathematics. This grand narrative began with the exhibition of quantitative laws that these heroes, Galileo and Newton for example, had disclosed: the law of falling bodies, according to which the speed of a falling body is proportional to the square of the time that has elapsed since the beginning of its fall; the (...)
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  14. added 2017-02-17
    The Interplay Between Mathematical Practices and Results.Mélissa Arneton, Amirouche Moktefi & Catherine Allamel-Raffin - 2014 - In Léna Soler, Sjoerd Zwart, Michael Lynch & Vincent Israel-Jost (eds.), Science after the Practice Turn in the Philosophy, History, and Social Studies of Science. New York - London: Routledge. pp. 269-276.
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  15. added 2017-02-17
    La Logique Symbolique En Débat À Oxford À la Fin du XIXe Siècle : Les Disputes Logiques de Lewis Carroll Et John Cook Wilson.Mathieu Marion & Amirouche Moktefi - 2014 - Revue D’Histoire des Sciences 67 (2):185-205.
    The development of symbolic logic is often presented in terms of a cumulative story of consecutive innovations that led to what is known as modern logic. This narrative hides the difficulties that this new logic faced at first, which shaped its history. Indeed, negative reactions to the emergence of the new logic in the second half of the nineteenth century were numerous and we study here one case, namely logic at Oxford, where one finds Lewis Carroll, a mathematical teacher who (...)
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  16. added 2017-02-15
    Review of Gabriele Lolli, Numeri. La creazione continua della matematica. [REVIEW]Longa Gianluca - 2016 - Lo Sguardo. Rivista di Filosofia 21 (II):377-380.
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  17. added 2017-02-15
    The Teacher as Mathematician: Problem Solving for Today's Social Context.Holly Brewster - unknown
    A current trend in social justice oriented education research is the promotion of certain intellectual virtues that support epistemic responsibility, or differently put, the dispositions necessary to be a good knower. On the surface, the proposition of epistemically responsible teaching, or teaching students to be responsible knowers is innocuous, even banal. In the mathematics classroom, however, it is patently at odds with current practice and with the stated goals of mathematics education. This dissertation begins by detailing the extant paradigm in (...)
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  18. added 2017-02-15
    Second-Order Models of Students' Mathematics: Delving Into Possibilities.T. Dooley - 2014 - Constructivist Foundations 9 (3):346-348.
    Open peer commentary on the article “Constructivist Model Building: Empirical Examples From Mathematics Education” by Catherine Ulrich, Erik S. Tillema, Amy J. Hackenberg & Anderson Norton. Upshot: I look at the different possibilities offered by the trajectory of second-order models in mathematics education. It seems to me that although possibilities are extended as models become more elaborate, this is only the case if teacher/researchers remain cognisant of a radical constructivist perspective. I also suggest that broad-ranging research on the models affords (...)
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  19. added 2017-02-15
    Postmodern Mathematics Education: Script For Animated Movie Discussion.Paul Ernest & Allan Tarp - 2013 - Philosophy of Mathematics Education Journal 27.
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  20. added 2017-02-15
    The Scope and Limits of Critical Mathematics Education.Paul Ernest - 2010 - Philosophy of Mathematics Education Journal 25.
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  21. added 2017-02-15
    A Well-Grounded Education: The Role of Perception in Science and Mathematics.Robert Goldstone, David Landy & Son & Y. Ji - 2008 - In Manuel de Vega, Arthur Glenberg & Arthur Graesser (eds.), Symbols and Embodiment: Debates on Meaning and Cognition. Oxford University Press.
  22. added 2017-02-15
    Deconstructing the Scholarly Literature on Gender Differentials in Mathematics Education: Implications for Research on Girls Learning Mathematics in Botswana.Alakanani Nkhwalume - 2007 - Philosophy of Mathematics Education Journal 20.
  23. added 2017-02-15
    What has Power Got to Do with Mathematics Education?Paola Valero - 2007 - Philosophy of Mathematics Education Journal 21.
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  24. added 2017-02-15
    Supporting a Discourse About Incommensurable Theoretical Perspectives in Mathematics Education.Paul Cobb - 2006 - Philosophy of Mathematics Education Journal 19.
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  25. added 2017-02-15
    Early Mathematics Education.Stephen Campbell - 2002 - Philosophy of Mathematics Education Journal 15.
  26. added 2017-02-15
    The Question of Knowing Others: Doing Research in Mathematics Education.Margaret Walshaw - 2001 - Philosophy of Mathematics Education Journal 14.
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  27. added 2017-02-15
    Towards a Philosophy of Critical Mathematics Education. [REVIEW]Paul Ernest - 1996 - Philosophy of Mathematics Education Journal 9.
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  28. added 2017-02-15
    Is 'the Discipline Of Noticing' A New Paradigm For Research In Mathematics Education?Paul Ernest - 1995 - Philosophy of Mathematics Education Journal 8.
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  29. added 2017-02-15
    Saussurian Linguistics Revisited: Can It Inform Our Understanding of Mathematics Education.O. McNamara - 1995 - Science & Education 4:253-266.
  30. added 2017-02-15
    The Principle Of Economy In The Learning And Teaching Of Mathematics, By David P. Hewitt. [REVIEW]Paul Ernest - 1995 - Philosophy of Mathematics Education Journal 8.
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  31. added 2017-02-15
    Chinese Mathematics. A Concise History. [REVIEW]Karine Chemla - 1990 - British Journal for the History of Science 23 (4):493-495.
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  32. added 2017-02-14
    Can History of Mathematics and Mathematics Education Coexist.M. Fried - 2001 - Science & Education 10 (4):391-408.
  33. added 2017-02-14
    Can Mathematics Education and History of Mathematics Coexist?Michael N. Fried - 2001 - Science & Education 10 (4):391-408.
  34. added 2017-02-14
    An Objectivist Critique of Relativism in Mathematics Education.Stuart Rowlands, Ted Graham & John Berry - 2001 - Science & Education 10 (3):215-241.
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  35. added 2017-02-14
    Fallibilism and the Use of History in Mathematics Education.Eduard Glas - 1998 - Science & Education 7 (4):361-379.
  36. added 2017-02-14
    Prolegomena Mathematica: From Apollonius of Perga to the Late Neoplatonism. With an Appendix on Pappus and the History of Platonism.Jaap Mansfeld - 1998 - Brill.
    This is the first study to deal with Greek mathematics from the viewpoint of cultural history. Mathematics, and especially the teaching of mathematics, did not proceed in isolation, but developed along lines parallel to the development of general literate culture.
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  37. added 2017-02-11
    Mathematics, Explanation and Reductionism: Exposing the Roots of the Egyptianism of European Civilization.Arran Gare - 2005 - Cosmos and History 1 (1):54-89.
    We have reached the peculiar situation where the advance of mainstream science has required us to dismiss as unreal our own existence as free, creative agents, the very condition of there being science at all. Efforts to free science from this dead-end and to give a place to creative becoming in the world have been hampered by unexamined assumptions about what science should be, assumptions which presuppose that if creative becoming is explained, it will be explained away as an illusion. (...)
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  38. added 2017-02-10
    The History of the History of Mathematics.Benjamin Wardhaugh (ed.) - 2012 - Peter Lang.
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  39. added 2017-02-08
    The Place of Mathematics in Education.Paul Carus - 1905 - The Monist 15 (2):295-300.
  40. added 2017-01-31
    Poincaré on the Foundations of Arithmetic and Geometry. Part 1: Against “Dependence-Hierarchy” Interpretations.Katherine Dunlop - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (2):274-308.
    The main goal of part 1 is to challenge the widely held view that Poincaré orders the sciences in a hierarchy of dependence, such that all others presuppose arithmetic. Commentators have suggested that the intuition that grounds the use of induction in arithmetic also underlies the conception of a continuum, that the consistency of geometrical axioms must be proved through arithmetical induction, and that arithmetical induction licenses the supposition that certain operations form a group. I criticize each of these readings. (...)
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  41. added 2017-01-27
    Snezana Lawrence and Mark McCartney, Eds., Mathematicians and Their Gods: Interactions Between Mathematics and Religious Beliefs. [REVIEW]Madeline Muntersbjorn - 2016 - Hopos: The Journal of the International Society for the History of Philosophy of Science 6 (2):333-336.
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  42. added 2017-01-27
    Mathematical Heritage of India: Some Remedial Issues: Mathematics History in Teaching.Vinod Mishra - 2011 - Philosophy of Mathematics Education Journal 26.
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  43. added 2017-01-21
    Der Aufbruch Zum „Funktionalen Denken“: Geschichte des Mathematikunterrichts Im Kaiserreich.Gert Schubring - 2007 - NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 15 (1):1-17.
    By the end of the 19th century, mathematics teaching underwent a crisis of similar proportion in several European countries. Constrained by the values of classical Antiquity, which dominated in secondary education, mathematics was taught as a formal discipline enhancing elementary geometry and intended as some gymnastics of the mind. Moreover, a specific feature in Germany was that the country was split up into numerous independent states each having a separated educational system of its own. Many of these conferred an only (...)
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  44. added 2017-01-21
    The Research Group of History of Mathematics at the Federal University of Paraná.Clóvis Pereira da Silva - 1993 - NTM Zeitschrift für Geschichte der Wissenschaften, Technik und Medizin 1 (1):184-185.
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  45. added 2017-01-16
    Athār-I-Bāqiya, a History of Arabic MathematicsṢāliḥ Zekī.A. Adnan - 1933 - Isis 19 (3):506-515.
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  46. added 2017-01-14
    Purpose and Education: The Case of Mathematics.Houman Harouni - unknown
    Why do schools teach mathematics, and why do they teach the mathematics that they do? In this three-part dissertation, I argue that the justifications offered by national education systems are not convincing, and that students are tested on content whose purpose neither they nor their teachers clearly understand. In the first part of the dissertation, I propose a theoretical framework for understanding the content and pedagogy of school mathematics as a set of practices reflecting socio-political values, particularly in relation to (...)
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  47. added 2016-12-08
    Scientific Heritage.Zbigniew Król - 2012 - Dialogue and Universalism 22 (4):41-65.
    This paper presents sources pertinent to the transmission of Euclid’s Elements in Western medieval civilization. Some important observations follow from the pure description of the sources concerning the development of mathematics, e.g., the text of the Elements was supplemented with new axioms, proofs and theorems as if an “a priori skeleton” lost in Dark Ages was reconstructed and rediscovered during the late Middle Ages. Such historical facts indicate the aprioricity of mathematics.
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  48. added 2016-12-08
    Das Mathematische Denken der Antike. [REVIEW]S. B. R. - 1959 - Review of Metaphysics 12 (4):662-662.
  49. added 2016-10-03
    Leopold Kronecker's Conception of the Foundations of Mathematics.Jacqueline Boniface - 2005 - Philosophia Scientiae 9 (S2):143-156.
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  50. added 2016-10-03
    Das Fotoalbum Fur Weierstrass. A Photo Album for Weierstrass.R. Bolling & I. Grattan-Guinness - 1995 - Annals of Science 52 (5):527-527.
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1 — 50 / 181