Book Review
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MathSciNet review:
3049877
Full text of review:
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Book Information:
Author:
Jeremy Gray
Title:
Plato’s ghost: the modernist transformation of mathematics
Additional book information:
Princeton University Press,
Princeton,
2008,
x+515 pp.,
ISBN 978-0-691-13610-3
Cajori, Florian, A History of Mathematics, 5th ed., Providence, R.I.; American Mathematical Society, 1991.
Leo Corry, Modern algebra and the rise of mathematical structures, Science Networks. Historical Studies, vol. 17, Birkhäuser Verlag, Basel, 1996. MR 1391720
D. van Dalen, The war of the frogs and the mice, or the crisis of the Mathematische Annalen, Math. Intelligencer 12 (1990), no. 4, 17–31. MR 1076531, DOI 10.1007/BF03024028
Dirk van Dalen, Mystic, geometer, and intuitionist, The Clarendon Press, Oxford University Press, New York, 1999. The life of L. E. J. Brouwer. Vol. 1; The dawning revolution. MR 1669279
Dirk van Dalen, Mystic, geometer, and intuitionist, The Clarendon Press, Oxford University Press, Oxford, 2005. The life of L. E. J. Brouwer, 1881–1966. Vol. 2; Hope and disillusion. MR 2171883
Davis, Phillip J. & Hersh, Reuben, The Mathematical Experience, Boston: Houghton Mifflin, 1981.
Moritz Epple, Die Entstehung der Knotentheorie, Friedr. Vieweg & Sohn, Braunschweig, 1999 (German, with German summary). Kontexte und Konstruktionen einer modernen mathematischen Theorie. [Contexts and constructions of a modern mathematical theory]. MR 1716305, DOI 10.1007/978-3-322-80295-8
José Ferreirós, Labyrinth of thought, Science Networks. Historical Studies, vol. 23, Birkhäuser Verlag, Basel, 1999. A history of set theory and its role in modern mathematics. MR 1726552, DOI 10.1007/978-3-0348-5049-0
Dennis E. Hesseling, Gnomes in the fog, Science Networks. Historical Studies, vol. 28, Birkhäuser Verlag, Basel, 2003. The reception of Brouwer’s intuitionism in the 1920s. MR 2023449, DOI 10.1007/978-3-0348-7989-7
Hilbert, David, “Mathematische Probleme. Vortrag, gehalten auf dem internationalen Mathematiker-Kongress zu Paris 1900,” Nachrichten von der königlichen Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-physikalische Klasse aus dem Jahre 1900, 253-97.
Hilbert, David, “The New Grounding of Mathematics: First Report,” (1922), trans. W. Ewald, in [Man 1998, 198-214].
McCormmach, Russell, Night Thoughts of a Classical Physicist, Cambridge, Mass.: Harvard University Press, 1982.
Mehrtens, Herbert, “Ludwig Bieberbach and ‘Deutsche Mathematik’ ”, in Phillips, E. R., ed., Studies in the History of Mathematics, MAA Studies in Mathematics, vol. 26, Washington, D.C., 1987.
Herbert Mehrtens, Moderne—Sprache—Mathematik, Suhrkamp Verlag, Frankfurt am Main, 1990 (German). Eine Geschichte des Streits um die Grundlagen der Disziplin und des Subjekts formaler Systeme. [A history of the controversy surrounding the foundations of the discipline and the subject of formal systems]. MR 1090540
Volker Peckhaus, Hilbertprogramm und Kritische Philosophie, Studien zur Wissenschafts-, Sozial- und Bildungsgeschichte der Mathematik [Studies on the Scientific, Social and Educational History of Mathematics], vol. 7, Vandenhoeck & Ruprecht, Göttingen, 1990 (German). Das Göttinger Modell interdisziplinärer Zusammenarbeit zwischen Mathematik und Philosophie. [The Göttingen model of interdisciplinary cooperation between mathematics and philosophy]. MR 1116994
Walter Purkert, The double life of Felix Hausdorff/Paul Mongré, Math. Intelligencer 30 (2008), no. 4, 36–50. MR 2501397, DOI 10.1007/BF03038095
David E. Rowe, Perspective on Hilbert, Perspect. Sci. 5 (1997), no. 4, 533–570 (1999). MR 1671564
David E. Rowe, Hermann Weyl, the reluctant revolutionary, Math. Intelligencer 25 (2003), no. 1, 61–70. MR 1962928, DOI 10.1007/BF02985642
Paolo Mancosu, From Brouwer to Hilbert, Oxford University Press, New York, 1998. The debate on the foundations of mathematics in the 1920s; With the collaboration of Walter P. van Stigt; Reproduced historical papers translated from the Dutch, French and German. MR 1685779
References
- Cajori, Florian, A History of Mathematics, 5th ed., Providence, R.I.; American Mathematical Society, 1991.
- Leo Corry, Modern algebra and the rise of mathematical structures, Science Networks. Historical Studies, vol. 17, Birkhäuser Verlag, Basel, 1996. MR 1391720 (97i:01023)
- D. van Dalen, The war of the frogs and the mice, or the crisis of the Mathematische Annalen, Math. Intelligencer 12 (1990), no. 4, 17–31. MR 1076531 (91i:01147), DOI 10.1007/BF03024028
- Dirk van Dalen, Mystic, geometer, and intuitionist, The Clarendon Press Oxford University Press, New York, 1999. The life of L. E. J. Brouwer. Vol. 1; The dawning revolution. MR 1669279 (2000g:01037)
- Dirk van Dalen, Mystic, geometer, and intuitionist, The Clarendon Press Oxford University Press, Oxford, 2005. The life of L. E. J. Brouwer, 1881–1966. Vol. 2; Hope and disillusion. MR 2171883 (2007i:01004)
- Davis, Phillip J. & Hersh, Reuben, The Mathematical Experience, Boston: Houghton Mifflin, 1981.
- Moritz Epple, Die Entstehung der Knotentheorie, Friedr. Vieweg & Sohn, Braunschweig, 1999 (German, with German summary). Kontexte und Konstruktionen einer modernen mathematischen Theorie. [Contexts and constructions of a modern mathematical theory]. MR 1716305 (2000i:01001), DOI 10.1007/978-3-322-80295-8
- José Ferreirós, Labyrinth of thought, Science Networks. Historical Studies, vol. 23, Birkhäuser Verlag, Basel, 1999. A history of set theory and its role in modern mathematics. MR 1726552 (2000m:03005)
- Dennis E. Hesseling, Gnomes in the fog, Science Networks. Historical Studies, vol. 28, Birkhäuser Verlag, Basel, 2003. The reception of Brouwer’s intuitionism in the 1920s. MR 2023449 (2005j:03002), DOI 10.1007/978-3-0348-7989-7
- Hilbert, David, “Mathematische Probleme. Vortrag, gehalten auf dem internationalen Mathematiker-Kongress zu Paris 1900,” Nachrichten von der königlichen Gesellschaft der Wissenschaften zu Göttingen. Mathematisch-physikalische Klasse aus dem Jahre 1900, 253-97.
- Hilbert, David, “The New Grounding of Mathematics: First Report,” (1922), trans. W. Ewald, in [Man 1998, 198-214].
- McCormmach, Russell, Night Thoughts of a Classical Physicist, Cambridge, Mass.: Harvard University Press, 1982.
- Mehrtens, Herbert, “Ludwig Bieberbach and ‘Deutsche Mathematik’ ”, in Phillips, E. R., ed., Studies in the History of Mathematics, MAA Studies in Mathematics, vol. 26, Washington, D.C., 1987.
- Herbert Mehrtens, Moderne—Sprache—Mathematik, Suhrkamp Verlag, Frankfurt am Main, 1990 (German). Eine Geschichte des Streits um die Grundlagen der Disziplin und des Subjekts formaler Systeme [A history of the controversy surrounding the foundations of the discipline and the subject of formal systems]. MR 1090540 (92g:01005)
- Volker Peckhaus, Hilbertprogramm und Kritische Philosophie, Studien zur Wissenschafts-, Sozial- und Bildungsgeschichte der Mathematik [Studies on the Scientific, Social and Educational History of Mathematics], vol. 7, Vandenhoeck & Ruprecht, Göttingen, 1990 (German). Das Göttinger Modell interdisziplinärer Zusammenarbeit zwischen Mathematik und Philosophie [The Göttingen model of interdisciplinary cooperation between mathematics and philosophy]. MR 1116994 (92g:01054)
- Walter Purkert, The double life of Felix Hausdorff/Paul Mongré, Math. Intelligencer 30 (2008), no. 4, 36–50. MR 2501397, DOI 10.1007/BF03038095
- David E. Rowe, Perspective on Hilbert, Perspect. Sci. 5 (1997), no. 4, 533–570 (1999). MR 1671564 (2000b:01022)
- David E. Rowe, Hermann Weyl, the reluctant revolutionary, Math. Intelligencer 25 (2003), no. 1, 61–70. MR 1962928 (2003k:01035), DOI 10.1007/BF02985642
- Weyl, Hermann, “On the New Foundational Crisis of Mathematics,” trans. B. Müller, in From Brouwer to Hilbert: the debate on the foundations of mathematics in the 1920s, Paolo Mancosu (ed.), with the collaboration of Walter P. van Stigt; reproduced historical papers translated from the Dutch, French and German, Oxford University Press, New York, 1998. MR 1685779 (2000j:01122)
Review Information:
Reviewer:
David E. Rowe
Affiliation:
Mainz University
Email:
rowe@mathematik.uni-mainz.de
Journal:
Bull. Amer. Math. Soc.
50 (2013), 513-521
DOI:
https://doi.org/10.1090/S0273-0979-2012-01403-9
Published electronically:
December 18, 2012
Review copyright:
© Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
