- “Mathematics”? What do you mean? - Don’t play the fool; everybody knows it.

Abstract

We criticize the polysemy of the signifier “mathematics”. Its commonsense meaning should not be considered enough to ground mathematics education. We describe a formof speech emerging in Ancient Greece, originated from the social necessity to avoid intra-family clashes by means of precise agreements, written laws, and democratic dialog in a singular historical situation. This formof speech emerged together with coinage, was made numerically precise with the Pythagorean movement, and logically precise after the crisis unleashed by Russell’s paradoxin the beginning of the last century. We show how this formof speech has developed in history together with communities that came to be known as “exact sciences”, among which is Mathematics, a distinguished community of speech. We end the paper suggesting a political agenda for mathematics education.