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6 - Mathematical Schools, Communities, and Networks

from Part II - Discipline Building in the Sciences: Places, Instruments, Communication

Published online by Cambridge University Press:  28 March 2008

By
David Rowe
Edited by
Mary Jo Nye
Mary Jo Nye
Affiliation:
Oregon State University
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Summary

Mathematical knowledge has long been regarded as essentially stable and, hence, rooted in a world of ideas only superficially affected by historical forces. This general viewpoint has profoundly influenced the historiography of mathematics, which until recently has focused primarily on internal developments and related epistemological issues. Standard historical accounts have concentrated heavily on the end products of mathematical research: theorems, solutions to problems, and the technical difficulties that had to be mastered before a well-posed question could be answered. This kind of approach inevitably suggests a cumulative picture of mathematical knowledge that tells us little about how such knowledge was gained, refined, codified, or transmitted. Moreover, the purported permanence and stability of mathematical knowledge begs some obvious questions with regard to accessibility – known to whom and by what means? Issues of this kind have seldom been addressed in historical studies of mathematics, which often treat priority disputes among mathematicians as merely a matter of “who got there first.” By implication, such studies suggest that mathematical truths reside in a Platonic realm independent of human activity, and that mathematical findings, once discovered and set down in print, can later be retrieved at will.

If this fairly pervasive view of the epistemological status of mathematical assertions were substantially correct, then presumably mathematical knowledge and the activities that lead to its acquisition ought to be sharply distinguished from their counterparts in the natural sciences. Recent research, however, has begun to undercut this once-unquestioned canon of scholarship in the history of mathematics. At the same time, mathematicians and philosophers alike have come increasingly to appreciate that, far from being immune to the vicissitudes of historical change, mathematical knowledge depends on numerous contextual factors that have dramatically affected the meanings and significance attached to it.

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Chapter
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The Cambridge History of Science , pp. 111 - 132
Publisher: Cambridge University Press
Print publication year: 2002

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References

Biermann, Kurt-R., Die Mathematik und ihre Dozenten an der Berliner Universität, 1810–1933 (Berlin: Akademie Verlag, 1988).Google Scholar
Corry, Leo, Modern Algebra and the Rise of Mathematical Structures (Science Networks, 16) (Boston: Birkhäuser, 1996).Google Scholar
Crowe, Michael J., A History of Vector Analysis (Notre Dame, Ind.: University of Notre Dame Press, 1967).Google Scholar
Dalen, Dirk, Mystic, Geometer, and Intuitionist: The Life of L. E. J. Brouwer, vol. 1 (Oxford: Clarendon Press, 1999).Google Scholar
Dalmedico, Amy Dahan, “Mathematics in the Twentieth Century,” in Science in the Twentieth Century, ed. Krige, John and Pestre, Dominique (Paris: Harwood Academic Publishers, 1997).Google Scholar
Dauben, Joseph W., “Conceptual Revolutions and the History of Mathematics: Two Studies in the Growth of Knowledge,” in Revolutions in Mathematics, ed. Gillies, Donald (Oxford: Clarendon Press, 1992).Google Scholar
Epple, Moritz, Die Entstehung der Knotentheorie: Kontexte und Konstruktionen einer modernen mathematischen Theorie (Braunschweig: Vieweg, 1999).CrossRefGoogle Scholar
Fox, Robert, “The Rise and Fall of Laplacian Physics,” Historical Studies in the Physical Sciences, 4 (1974).CrossRefGoogle Scholar
Geison, Gerald L. and Holmes, Frederic L. ed., Research Schools: Historical Reappraisals, Osiris, 8 (1993).Google Scholar
Grabiner, Judith V., “Is Mathematical Truth Time-Dependent?” in New Directions in the Philosophy of Mathematics, ed. Tymoczko, Thomas (Boston: Birkhäuser, 1985).Google Scholar
Graham, Loren, Science in Russia and the Soviet Union (Cambridge: Cambridge University Press, 1993).Google Scholar
Grattan-Guinness, Ivor, Convolutions in French Mathematics, 1800–1840 (Science Networks, vols. 2–4) (Basel: Birkhäuser, 1990).Google Scholar
Harman, P. M., ed., Wranglers and Physicists (Manchester: Manchester University Press, 1985).Google Scholar
Heims, Steve J., John von Neumann and Norbert Wiener (Cambridge, Mass.: MIT Press, 1980).Google Scholar
Lakatos, Imre, Proofs and Refutations, ed. Worrall, John and Zahar, Elie (Cambridge: Cambridge University Press, 1976).CrossRefGoogle Scholar
Lüptzen, Jesper, Joseph Liouville, 1809–1882 (Studies in the History of Mathematics and Physical Sciences, 15) (NewYork: Springer-Verlag, 1990).CrossRefGoogle Scholar
Mehrtens, Herbert, Moderne-Sprache-Mathematik (Frankfurt: Suhrkamp, 1990).Google Scholar
Parshall, Karen H. and Rowe, David E., The Emergence of the American Mathematical Research Community, 1876–1900: J. J. Sylvester, Felix Klein, and E. H. Moore (Providence, R.I.: American Mathematical Society, 1994).CrossRefGoogle Scholar
Pyenson, Lewis, Neohumanism and the Persistence of Pure Mathematics in Wilhelmian Germany (Philadelphia: American Philosophical Society, 1983).Google Scholar
Reich, Karin, Die Entwicklung des Tensorkalküls: Vom absoluten Differentialkalkül zur Relativitätstheorie (Science Networks, vol. 11) (Basel: Birkhäuser, 1992).Google Scholar
Richards, Joan L., “The History of Mathematics and ‘L’esprit humain’: A Critical Reappraisal,” in Constructing Knowledge in the History of Science, ed. Thackray, Arnold, Osiris, 10 (1995).CrossRefGoogle Scholar
Richards, Joan L., Mathematical Visions: The Pursuit of Geometry in Victorian England (Boston: Academic Press, 1988).Google Scholar
Rowe, David E., “Klein, Hilbert, and the Göttingen Mathematical Tradition,” in Science in Germany: The Intersection ofInstitutional and Intellectual Issues, ed. Olesko, Kathryn M., Osiris, 5 (1989).CrossRefGoogle Scholar
Servos, John, “Research Schools and their Histories,” Research Schools: Historical Reappraisals, ed. Geison, Gerald L. and Holmes, Frederic L., Osiris, 8 (1993).Google ScholarPubMed
Siegmund-Schultze, Reinhard, Mathematiker auf der Flucht vor Hitler (Dokumente zur Geschichte der Mathematik, Band 10) (Braunschweig: Vieweg 1998).Google Scholar
Sieno, Simonetta et al., eds., La Matematica Italiana dopo L’Unita (Milan: Marcos y Marcos, 1998).Google Scholar
Turner, R. Steven, “The Prussian Universities and the Concept of Research,” Internationales Archiv für Sozialgeschichte der deutschen Literatur, 5 (1980).CrossRefGoogle Scholar

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