Abstract
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.
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- 1.
Pierre Hérigone (1580–1643) is a Frenchman from the Basque region who, starting from 1634, published a “Course in mathematics” in six volumes (bilingual Latin–French), invented the abbreviation used to express the orthogonality of two straight lines, and we have kept his layout for the so-called “Pascal’s” triangle which he explains by using expansions of the powers of a binomial such as \(a+b\).
- 2.
The French translation used is the one given by Bernard Vitrac (Les Éléments d’Euclide, 4 volumes, Paris, PUF, 1990–2001) which we are lucky to have in French and which wisely reviews the tradition of comments on this text, while remaining readable by someone trying to understand the mathematics at stake, and who does not want to get overwhelmed by philological remarks, but merely benefit from his understanding.
- 3.
The axiom of choice is a seemingly harmless axiom which states that, given a family of sets, it is always possible to choose an element from each of these sets, even if there are infinitely many sets, for as large an infinity as desired.
- 4.
Chinese mathematics book from the 2nd–1st century B.C.
- 5.
Olivier Keller, Aux origines de la géométrie, Le Paléolithique et le monde des chasseurs-cuilleurs, Paris, Vuibert 2004.
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Cartier, P., Dhombres, J., Heinzmann, G., Villani, C. (2016). On the Origins of Mathematics. In: Freedom in Mathematics. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2788-5_1
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DOI: https://doi.org/10.1007/978-81-322-2788-5_1
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