Arithmetization of Analysis and Algebra

  • Yvon Gauthier
Part of the Studies in Universal Logic book series (SUL)


Arithmetization of analysis evokes at once the names of Cauchy, Weierstrass, Cantor and Dedekind and to a lesser degree those of Dirichlet, Abel or Bolzano; the process of arithmetization illustrates the need to instill rigour in analysis through what Cauchy called algebraic analysis in order to overcome the intuitive limitations of the geometer’s method of proof. The story of arithmetization needs not to be retold here (see Grattan-Guinness 1970); it is not a one-sided history, for rigour had a different meaning then and the tools used for rigorization (e.g. quadratic forms or homogeneous polynomials) were partly available in the nineteenth century. The algebraic symbolism (Descartes, Fermat and Leibniz) was already invading geometry and number theory (Diophantine equations) from Fermat on was to become the queen of arithmetical sciences.


Diophantine Equation Irrational Number General Arithmetic Peano Arithmetic Primitive Polynomial 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Yvon Gauthier
    • 1
  1. 1.University of MontrealMontrealCanada

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