Both lectures focus on the first part of the so-called ‘mathematical part’ of Plato’s Theaetetus. In this passage, the young Theaetetus briefly recounts the mathematical lesson given by the geometer Theodorus. The first lecture delves into the figures drawn by Theodorus, while the second explores his methods of proof. Here, we present a new translation and a new interpretation of this passage. Both lectures are based on a collaborative work in progress with Luc Brisson.