Abstract EN:

What shall we properly call mathematic? and what is properly meant in greek by the words mathesis or mathemata? rene descartes raised nearly the same questions as he asked himself about the true mathematic (la veritable mathematique) in his regulae ad directionem ingenii. The main interest of this question is the following : while descartes claims that the true mathematic is obvious (obvious enough to be considered as an all-embracing knowledge), he is soon led to speak about it as a secret (le secret de l'art), as if it was impossible to point out the obviousness of this veritable mathematiquue. But if descartes failed to tell us what is truly meant by "mathematic", this failure was not fruitless, and generally speaking we see this failure as characterising the proper meaning of this greek word : while asking these questions, we not only encounter the impossibility to answer it, but above all the strange fact is that this failure leads us to do something without being able to tell clearly what we are thus doing - or better undergoing. We call this tragic experience, to enter the secret of learning. This means to go through learning which is not knowing a learning that we don't control and that makes us change. To undergo such a change is to undergo what aristotle calls in his physics the "move of all" (kinesis tou holou), a kind of total change which is deep enough to remove any landmark, including the own identity of who undergoes this change. Aristole says again that this "move of all" is the ancient meaning of time (chronos). Accordingly, there is a deep relationship between learning conceived as uncontrolled and the fact of undergoing time, i. E. Change. This link between time and mathematic allows us to understand the latter.