, Volume 26, Issue 1, pp 131–135 | Cite as

The changing practices of proof in mathematics

Gilles Dowek: Computation, proof, machine. Cambridge: Cambridge University Press, 2015. Translation of Les Métamorphoses du calcul, Paris: Le Pommier, 2007. Translation from the French by Pierre Guillot and Marion Roman, $124.00HB, $40.99PB
  • Andrew Arana
Book Review

When deciding how many tiles we need in order to cover our kitchen floor, we calculate as: compute the total area of the kitchen and the area of the tiles, and divide as needed. One could use this particular practical problem to raise a more abstract problem concerning the partition of arbitrary finite polygon configurations in the plane. The interest of this abstract problem might be to generalize the given particular problem so as to optimize our problem-solving and resolve a family of such particular problems with one solution, or it may simply be interesting in its own right. This second abstract problem will not be readily resolved by calculations of the type familiar from home renovation, though. Instead, the problem calls for reasoning: for instance, an analysis, to break it into smaller, more manageable problems.

Gilles Dowek’s fascinating book begins with this cleavage between computation and reasoning, illustrated by the transition from the algorithmic solutions to accounting...


  1. Arana, A. 2016. On the alleged simplicity of impure proof. In Simplicity: Ideals of Practice in Mathematics and the Arts, ed. R. Kossak, and P. Ording. Berlin: Springer.Google Scholar
  2. Detlefsen, M., and A. Arana. 2011. Purity of methods. Philosophers’ Imprint 11: 2.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Department of Philosophy, Institute for History and Philosophy of Science and Technology (IHPST)University of Paris 1 Panthéon-SorbonneParisFrance

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