TY - JOUR
TI - L’origine de la démonstration : essai d’épistémologie didactique
AU - Arsac, Gilbert
T2 - Recherches En Didactique Des Mathématiques
AB - Mathematical proof, which is a means for asserting the truth of a mathematical statement, gives mathematics a character distinct from that of the other sciences. In France, mathematical proof first appears in the curriculum of 13-years old pupils.
This paper studies the historical origins of mathematical proof, beginning in Greece in the 5th Century B.C., and it starts with the question : is the appearance of mathematical proof linked to a particular problem within mathematics or is it a consequence of the general course of Greek thought ?
We also try to show that certain concepts created in order to analyse didactical situations can shed light on historical origins as well.
This methodological choice and the choice of the questions we ask lead us to talk of a "didactical epistemology".
The essence of our argument is that :
- the encounter with the problem of irrationality lies at the origin of the transformation of mathematics from a pragmatic to a hypothetico-deductive science;
- this transformation, which involved the use of mathematical proof as well as of axiomatisation, leads to the resolution of the contradictions associated with the problem of irrationality. The choice of this particular solution, though, depends on the character of Greek thought.
DA - 1987///
PY - 1987
VL - 8
IS - 3
SP - 267
EP - 312
J2 - RDM
LA - FR
SN - 0246–9367
UR - https://revue-rdm.com/1987/l-origine-de-la-demonstration/
ER -