Learning mathematical certainties in the age of social networks and AI

Abstract

This is a philosophical-educational reflection on the acquisition of mathematical certainties in basic education, inspired by the philosophical ideas of the second phase of Ludwig Wittgenstein's thought. I begin by revisiting some of his reflections on the nature of mathematical knowledge and its relations with the empirical world, aiming to transpose them to the current context of the greater complexity of generative AI models (which generate texts through probability calculations), in order to problematize the use of these devices in the formation of mathematical thinking and the learning of its most fundamental concepts in the school context, from the earliest levels of education. We conclude that the philosopher's critique of the Platonic conception of mathematical knowledge, based on a referential model of language, remains extremely relevant today for clarifying classroom confusions arising from a use, in my view, quite misguided, of AI chatbots, such as the GPT chat, used in the school context by students and teachers, especially as an oracle for the immediate completion of various tasks. This deprives students, in particular, of fundamental steps both for understanding the meaning of mathematical language and for acquiring its different modes of thought; thus hindering the development of the ability to apply this knowledge in the empirical world with discernment and ethics.