Skip to main content
SpringerLink
Log in

Mathematics Ho! Which Modern Mathematics Was Modernist?

  • Viewpoint
  • Published:
The Mathematical Intelligencer Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Bibliography

  • Astroh, M. and Read, S. 1999. (Eds.), Special issue on Hugh MacColl, Nordic journal for philosophical logic, 2, nos. 1–2.

  • Beall, J.L. and Restall, G. 2005. Logical pluralism, Oxford: Oxford University Press.

    Google Scholar 

  • Biermann, K.-R. 1988. Die Mathematik und ihre Dozenten an der Berliner Universität 1810–1933, Berlin, DDR: Akademie Verlag.

    MATH  Google Scholar 

  • Brady, G. 2004. From Peirce to Skolem, Amsterdam: Elsevier.

    Google Scholar 

  • Brigaglia, A. and Masotto, G. 1982. Il Circolo Matematico di Palermo, Bari: Dedalo.

    MATH  Google Scholar 

  • Butler, C. 1994. Early modernism. Literature, music and poetry in Europe 1900–1916, Oxford: Oxford University Press.

    Google Scholar 

  • Coffa, J.A. 1979. ‘The humble origins of Russell’s paradox’, Russell, no. 33, 31–38.

    Google Scholar 

  • Coffa, J.A. 1991. The semantic tradition from Kant to Carnap, Cambridge: Cambridge University Press.

    Google Scholar 

  • Coray, D., Furinghetti, F., Gispert, H., Hodgson, B.R., and Schubring, G. 2003. (Eds.), One hundred years of L’enseignement mathématique, Geneva: L’Enseignement mathématique.

  • de Morgan, A. 1839. First notions of logic (preparatory to the study of geometry), 1st ed., London: Taylor and Walton. [2nd ed. 1840; repr. as Formal logic, London: Walton and Maberly, 1847, chap. 1.].

    Google Scholar 

  • Dugas, R. 1940. Essai sur l’incompréhension mathématique, Paris: Vuibert. [Most of pp. 6–34, 38–43 reprinted in Thalès, 4 (1937–1939: published 1940), 168–183].

  • Ferreirós, J. and Gray, J.J. 2006. (Eds.), The architecture of modern mathematics, Oxford: Oxford University Press.

    MATH  Google Scholar 

  • Feuer, L.S. 1971. ‘The social roots of Einstein’s theory of relativity’, Annals of science, 27, 277–298, 313–344.

    Google Scholar 

  • Friedman, M. and Nordmann, A. 2006. (Eds.), The Kantian legacy in nineteenth-century science, Cambridge, MA. and London: The MIT Press.

    MATH  Google Scholar 

  • Garber, E. 1999. The language of physics. The calculus and the development of theoretical physics in Europe, 1750–1914, Basel: Birkhäuser.

    MATH  Google Scholar 

  • Giacardi, L. 2006. (Ed.), Da Casati a Gentile. Momenti di storia dell’insegnamento secondario della matematica in Italia, Lugano: Agorà Publishing.

    Google Scholar 

  • Grattan-Guinness, I. 1970. The development of the foundations of mathematical analysis from Euler to Riemann, Cambridge, Mass.: M.I.T. Press.

    MATH  Google Scholar 

  • Grattan-Guinness, I. 1972. ‘A mathematical union: William Henry and Grace Chisholm Young’, Annals of science, 29, 105–186.

    Article  Google Scholar 

  • Grattan-Guinness, I. 1977. Dear Russell—dear Jourdain, London, Duckworth; New York: Columbia University Press.

    MATH  Google Scholar 

  • Grattan-Guinness, I. 1978. ‘How Bertrand Russell discovered his paradox’, Historia mathematica, 5, 127–137.

    Article  MATH  MathSciNet  Google Scholar 

  • Grattan-Guinness, I. 1988. ‘Living together and living apart: on the interactions between mathematics and logics from the French Revolution to the First World War’, South African journal of philosophy, 7, no. 2, 73–82.

  • Grattan-Guinness, I. 1990. Convolutions in French mathematics, 1800–1840, 3 vols. Basel, Birkhäuser; Berlin: Deutscher Verlag der Wissenschaften.

    MATH  Google Scholar 

  • Grattan-Guinness, I. 1992. ‘Structure-similarity as a cornerstone of the philosophy of mathematics’, in J. Echeverria, A. Ibarra and T. Mormann (eds.), The space of mathematics, Berlin and New York: de Gruyter, 91-111.

    Google Scholar 

  • Grattan-Guinness, I. 1996. ‘Numbers, magnitudes, ratios and proportions in Euclid’s Elements : how did he handle them?’, Historia mathematica, 23, 355-375. [Printing correction: 24 (1997), 213. Repr. in [2009c], ch. 13].

  • Grattan-Guinness, I. 2000a. The search for mathematical roots, 1870-1940, Princeton: Princeton University Press.

    MATH  Google Scholar 

  • Grattan-Guinness, I. 2000b. ‘A sideways look at Hilbert’s twenty-three problems of 1900’, Notices of the American Mathematical Society, 42, 752-757.

    MathSciNet  Google Scholar 

  • Grattan-Guinness, I. 2002a. ‘Re-interpreting “λ“: Kempe on multisets and Peirce on graphs, 1886-1905’, Transactions of the C.S. Peirce Society, 38, 327-350.

    MathSciNet  Google Scholar 

  • Grattan-Guinness, I. 2002b. ‘Victoria, Lady Welby’s papers at York University, Toronto’, Russell, new ser. 22, 57-58.

    Google Scholar 

  • Grattan-Guinness, I. 2004a. ‘The mathematical turns in logic’, in D. Gabbay and J. Woods (eds.), The rise of modern logic from Leibniz to Frege, Amsterdam: Elsevier, 545-556.

    Chapter  Google Scholar 

  • Grattan-Guinness, I. 2004b. ‘The mathematics of the past. Distinguishing its history from our heritage’. Historia mathematica, 31, 163-185 [Repr. in [2009c], ch. 2].

    Article  MATH  MathSciNet  Google Scholar 

  • Grattan-Guinness, I. 2005. (Ed.), Landmark writings in Western mathematics 1640-1940, Amsterdam: Elsevier.

    MATH  Google Scholar 

  • Grattan-Guinness, I. 2006. ‘Classical mechanics as a formal(ised) science’, in B. Loewe, V. Peckhaus and T. Räsch (ed.), The history of the concept of the formal sciences, London: College Publications King’s College, 51-68.

    Google Scholar 

  • Grattan-Guinness, I. 2008a. ‘Solving Wigner’s mystery: the reasonable (though perhaps limited) effectiveness of mathematics in the natural sciences’, The mathematical intelligencer 30, no. 3, 7-17.

  • Grattan-Guinness, I. 2008b. ‘Differential equations and linearity in the 19th and early 20th centuries’, Archives internationales d’histoire des sciences, 58, 343-351.

    Google Scholar 

  • Grattan-Guinness, I. 2009a. ‘How influential was Frege on Russell and Carnap?’ in G. Löffladt (Ed.), Mathematik – Logik – Philosophie und ihre historischen Wechselwirkungen, Frankfurt/Main: Deutsch, to appear.

  • Grattan-Guinness, I. 2009b. ‘The reception of Gödel’s 1931 incompletability theorems by mathematicians, and some logicians, up to the early 1960s’, in M. Baaz (ed.), Horizons of truth, New York: Cambridge University Press, to appear.

  • Grattan-Guinness, I. 2009c. Routes of learning. Selected articles, Baltimore: Johns Hopkins University Press, to appear.

    Google Scholar 

  • Grattan-Guinness, I. 2009d. ‘Instruction in the calculus and differential equations in Britain, 1820s–1900s’, in: R.J. Wilson (Ed.). Victorian mathematics, Oxford: Oxford University Press, to appear.

    Google Scholar 

  • Gray, J.J. 2008. Plato’s ghost. The modernist transformation of mathematics, Oxford: Princeton University Press.

    MATH  Google Scholar 

  • Hamel, G. 1909. ‘Über die Grundlagen der Mechanik’, Mathematische Annalen, 66, 350-397.

    Article  MathSciNet  Google Scholar 

  • Henderson, H. 1993. Catalyst for controversy. Paul Carus of Open Court, Carbondale, IL: Southern Illinois University Press.

    Google Scholar 

  • Hilbert, D. 1901. ‘Mathematische Probleme’, Archiv der Mathematik und Physik, (3)1, 44-63, 213-237. [Varius reprints, translations].

  • Kreiser, L. 1979. ‘W. Wundts Auffassung der Mathematik — Briefe von G. Cantor an W. Wundt’, Wissenschaftliche Zeitschrift der Karl-Marx Unive̠rsität, Geschichtliche und Sprachwissenschaftliche Reihe, 28, 197-206.

  • Lambert, C. 1934. Music Ho! A study of music in decline, London: Faber & Faber. [Edition cited: Harmondsworth: Pelican, 1948].

    Google Scholar 

  • Lecat, M. 1935. Erreurs de mathématiciens des origines à nos jours, Brussels: Librairie Castaigne.

    Google Scholar 

  • Maddux, R. 1991. ‘The origin of relation algebras in the development and axiomatization of the calculus of relations’, Studia logica, 50, 421-455.

    Article  MATH  MathSciNet  Google Scholar 

  • McCoy, R.E. 1987. Open Court. A centennial bibliography 1887-1987, La Salle, IL: Open Court.

    Google Scholar 

  • Mehrtens. H. 1990. Moderne Sprache Mathematik, Frankfurt/Main: Suhrkamp.

    MATH  Google Scholar 

  • Menghini, M., Furinghetti, F., Giacardi, L. and Arzarello, F. 2008. (Eds.), The first century of the International Commission on Mathematical Instruction, Rome: Istituto della Enciclopedia Italiana.

  • Müller, H.F. 1905. ‘Karl Schellbach. Rückblick auf sein wissenschaftliches Leben’, Abhandlungen zur Geschichte der Math- ematik, 20, 1-86.

    Google Scholar 

  • Parry, W.T. 1968. ‘The logic of C.I. Lewis’, in P.A. Schilpp (Ed.), The philosophy of C.I. Lewis, La Salle, IL: Open Court, 15-54.

    Google Scholar 

  • Peckhaus, V. 1991. ‘Ernst Schröder und die “Pasigraphischen Systeme” von Peano und Peirce’, Modern logic, 1, 174-205.

    MATH  MathSciNet  Google Scholar 

  • Pólya, G. 1954. Mathematics and plausible reasoning, 2 vols., 1st ed., Princeton: Princeton University Press. [2nd ed. 1968].

    Google Scholar 

  • Price, M.H. 1994. Mathematics for the multitude? A history of the Mathematical Association, Leicester: Mathematical Association.

    Google Scholar 

  • Pulte, H. 2005. Axiomatik und Empirie. Eine wissenschaftstheoriegeschichtliche Untersuchung zur mathematischen Naturphilosophie von Newton bis Neu- mann, Darmstadt: Wissenschaftliche Buchgesellschaft.

    MATH  Google Scholar 

  • Roche, J.J. 1998. The mathematics of measurement. A critical history, London: Athlone Press.

    MATH  Google Scholar 

  • Rostand, F. 1960. Souci d’exactitude et scrupules des mathématiciens, Paris: Vrin.

    Google Scholar 

  • Rostand, F. 1962. Sur la clarté des démonstrations mathématiques, Paris: Vrin.

    Google Scholar 

  • Rougier, L.P.A. 1920. La Philosophie géométrique de Henri Poincaré, Paris: F. Alcan.

  • Schmid, A.-F. 2001. (Ed.), Bertrand Russell. Correspondance sur la philosophie, la logique et la politique avec … Louis Couturat (1879-1913), Paris: Kimé.

    Google Scholar 

  • Schwegler, A. 1879. Handbook of the history of philosophy (Transl. and ann. J.H. Stirling), 7th ed., Edinburgh: Oliver & Boyd; London: Simpkin, Marshall.

  • Stadler, F. 2001. The Vienna Circle, Vienna and New York: Springer.

    Google Scholar 

  • Stump, D. 1997. ‘Reconstructing the unity of mathematics circa 1900’, Perspectives on science, 5, 383-417.

    MathSciNet  Google Scholar 

  • Tucciarone, J. 1973. ‘The development of the theory of summable divergent series from 1880 to 1925’, Archive for history of exact sciences, 10, 1-40.

    Article  MATH  MathSciNet  Google Scholar 

  • van Heijenoort, J. 1967. [Ed.] From Frege to Gödel. A source book in mathematical logic, Cambridge, MA: Harvard University Press.

    MATH  Google Scholar 

  • Vercelloni, L. 1989. Filosofia delle strutture, Florence: La Nuova Italia.

    Google Scholar 

  • West, B.J. 1985. An essay on the importance of being nonlinear, Berlin: Springer.

    MATH  Google Scholar 

  • Wolenski, J. 1989. Logic and philosophy in the Lvov-Warsaw school, Dordrecht: Kluwer.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Middlesex University Business School, The Burroughs, Hendon, London, NW4 4BT, UK

    I. Grattan-Guinness

  2. Centre for Philosophy of Natural and Social Science, London School of Economics, Houghton Street, London, WC2A 2AE, UK

    I. Grattan-Guinness

Authors
  1. I. Grattan-Guinness
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. Grattan-Guinness.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Grattan-Guinness, I. Mathematics Ho! Which Modern Mathematics Was Modernist?. Math Intelligencer 31, 3–11 (2009). https://doi.org/10.1007/s00283-009-9076-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00283-009-9076-4

Keywords

Search

Navigation