─ “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 form of 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 form of speech emerged together with coinage, was made numerically precise with the Pythagorean movement, and logically precise after the crisis unleashed by Russell’s paradox in the beginning of the last century. We show how this form of 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.

Difficulties in telling the truth: The composition of a philosophical activity and its unfolding into rigors-events

“…The relations of knowledge production and, consequently, Mathematics, with productivity and hegemony of intellectual work has been a theme in many studies in Mathematics Education, highlighting(Baldino, 1998;Cabral; Baldino, 2022;Roque, 2021;Giraldo, 2022;Souza;Flores, 2022).2 The Parts In Quotation Marks That Compose The (Multi)(Di)Alogue Were Extracted Literally From Twilight of the Idols, by Friedrich Nietzsche, more specifically from the aphorisms 1-12 that compose The Problem of Socrates(Nietzsche, 1998, p. 11-15). Italics by the author.…”

“…However, thinking historically, it is possible to note that "precision, accuracy, rigor or objectivity are notions whose meaning changed with time"(Roque, 2022, p. 60). Thus, the separation between hard sciences and humanity sciences considers the supremacy of hard sciences, but also misses a primordial factor: without language, nothing would have happened(Cabral; Baldino, 2022). According to the aforementioned author, "this sedimentation of the hard sciences is tied to the teaching institutions and to the production of knowledge created in France after the revolution"(Roque, 2022, p. 62).…”