Abstract
During the past decades several attempts have been made to reconsider the development of mathematics or the growth of mathematical knowledge from some unifying perspectives. Lakatos’ notion of “research programs” represents one such attempt. He did not find followers to pursue the matter beyond the few, and rather narrow, case studies he himself considered. A more recent attempt, still under discussion, was provoked by Kuhn’s work and led to the Crowe-Dauben debate on revolutions in mathematics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bottazzini, U. (1992). Editor’s Introduction to reprint of A.-L. Cauchy,
Cauchy, A.-L. (1992). Cours d’analyse. Bologna: Ed. CLUEB.
Euler, L. (1980). Opera omnia. Series 4A, Vol. 5. Basel: Birkhäuser.
Euler, L. (1947). Opera omnia. Series 2, Vol. 10. Bern: Orell Füssli und Teubner.
Gillespie, C. C. and A. P. Youschkevitch. (1979). Lazare Carnot savant et sa contribution à la théorie de l’infini mathématique. Paris: Vrin.
Laugwitz, D. (1986). Zahlen und Kontinuum. Mannheim: Bibliographisches Institut.
Laugwitz, D. (1987). “Infinitely small quantities in Cauchy’s textbooks.” Historia mathematica. Vol. 14: 258–74.
Laugwitz, D. (1989). “Definite values of infinite sums: Aspects of the foundations of infinitesimal analysis around 1820.” Archive for History of Exact Sciences. Vol. 39: 195–245.
Laugwitz, D. (1996). Bernhard Riemann 1826–1866: Wendepunkte in der Auffassung der Mathematik. Basel: Birkhäuser. Translated by Abe Schenitzer (1998). Bernhard Riemann 1826–1866: Turning Points in the Conception of Mathematics. Boston.
Meschkowski, H. and W. Nilson (Eds.). (1991). Georg Cantor, Briefe. Berlin: Springer Verlag.
Peiffer-Reuter, R. “L’infini relatif chez Veronese et Natorp.” in H. Barreau, J. Harthong (Eds.). (1989). La mathématique nonstandard. Pages 117–42. Paris: Editions du CNRS.
Youschkevitch, A. P. and R. Taton (1980). “Preface” (Euler 1980, Ser. 4A, Vol. V: 15–9).
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Laugwitz, D. (2000). Controversies about Numbers and Functions. In: Grosholz, E., Breger, H. (eds) The Growth of Mathematical Knowledge. Synthese Library, vol 289. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9558-2_13
Download citation
DOI: https://doi.org/10.1007/978-94-015-9558-2_13
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5391-6
Online ISBN: 978-94-015-9558-2
eBook Packages: Springer Book Archive