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. Its interpretation presents a certain degree of difficulty because of the intertwined fields that play a role in it : philosophy, history and mathematics. But conversely, correctly understood, it provides clues on both 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, ends on an aporia, in accordance with the whole dialogue.