  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.
