Mathematics and Revolution from Lacroix to Cauchy

  • Herbert Mehrtens
  • Henk Bos
  • Ivo Schneider


This paper is the outline of a project arising out of more general work on mathematics in France in the period 1790–1830. The problem on which I shall focus can be stated quite simply. Cauchy’s 1821 Cours d’ analyse aimed explicitly at producing a ‘revolution’ in the language of analysis to supersede the erroneous earlier approach (which we could call ‘classical’). The passage from Cauchy’s introduction which is generally regarded as his manifesto reads:

I have sought to give to the methods all the rigour which is demanded in geometry, in such a way as never to refer to reasons drawn from the generality of algebra... They tend to cause an indefinite validity to be attributed to algebraic formulae, while in reality the majority of these formulae hold only under certain conditions, and for certain values of the variables which they contain. By determining these conditions and values, and by fixing precisely the meaning of the notations I shall make use of, I shall dispel all uncertainty. (Cours d’analyse, p.ii)


Mathematical Text Algebraic Formula Discursive Formation Implicit Instruction Modern Differential Geometry 
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Copyright information

© Springer Science+Business Media New York 1981

Authors and Affiliations

  • Herbert Mehrtens
    • 1
  • Henk Bos
    • 2
  • Ivo Schneider
    • 3
  1. 1.Technische Universität BerlinBerlin 10Federal Republic of Germany
  2. 2.Math. InstituutRijksuniversiteit UtrechtBudapestlaan 6The Netherlands
  3. 3.Institut für Geschichte der Naturwissenschaften, Deutsches MuseumUniversität MünchenMünchen 26Federal Republic of Germany

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