Comprendre les math\'ematiques pour comprendre Platon - th\'e\'et\`ete (147d-148b)

TL;DR

This paper analyzes Plato's Theaetetus to explore the historical and philosophical significance of Greek mathematical concepts like irrationality, offering a new interpretation that critiques ancient mathematical thinking and its influence on Plato's philosophy.

Contribution

It provides a novel interdisciplinary interpretation of the mathematical part of Plato's Theaetetus, emphasizing its philosophical critique and historical context.

Findings

Reveals the text's critique of ancient Greek mathematical methods

Connects mathematical concepts to Plato's philosophical ideas

Offers a new historical interpretation of the origins of irrationals

Abstract

In this paper, we study the so-called 'Mathematical part' of Plato's Theaetetus. Its subject concerns the incommensurability of certain magnitudes, in modern terms the question of the rationality or irrationality of the square roots of integers. As the most ancient text on the subject, and on Greek mathematics and mathematicians as well, its historical importance is enormous. The difficulty to understand it lies in the close intertwining of different fields we found in it: philosophy, history and mathematics. But conversely, correctly understood, it gives some evidences both about the question of the origins of the irrationals in Greek mathematics and some points concerning Plato's thought. Taking into account the historical context and the philosophical background generally forgotten in mathematical analyses, we get a new interpretation of this text, which far from being a tribute to some mathematicians, is a radical criticism of their ways of thinking. And the mathematical lesson, far from being a tribute to some future mathematical achievements, is ending on an aporia, in accordance with the whole dialogue.