On the Origins of Mathematics

  • Pierre Cartier
  • Jean Dhombres
  • Gerhard Heinzmann
  • Cédric Villani


Sylvestre Huet: Why and how did man start doing mathematics, in particular based on the most elementary mathematical objects such as the point, the line, or the surface? Issues about the relationship between mathematical objects and reality arise from the onset: why and how does one do mathematics, and what is the relationship between mathematical objects and real objects or natural sciences? The informed general public is usually aware that the most basic mathematical notions, including numbers, were difficult constructions: think about the time taken to invent zero or positional number systems, concepts that we now learn as early as primary level... Yet, the invention of the concepts required bright minds, the brightest of the time. The relationship between mathematics and reality, which may seem obvious, is not so at all. Jean Dhombres could expand upon that, in order to begin the discussion by its historical aspect.


Mathematical Object Pythagoras Theorem Platonic Conception Positional Number System Ancient Mathematic 
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Copyright information

© Springer India 2016

Authors and Affiliations

  • Pierre Cartier
    • 1
  • Jean Dhombres
    • 2
  • Gerhard Heinzmann
    • 3
  • Cédric Villani
    • 4
  1. 1.Institut des Hautes Études Scientifiques (IHÉS)Bures-sur-YvetteFrance
  2. 2.Centre Koyré, EHESSParisFrance
  3. 3.Maison des sciences de l’HommeUniversity of LorraineNancyFrance
  4. 4.Institut Henri Poincaré (IHP)ParisFrance

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