ABSTRACT
Plato’s dialogue, the Theatetus, contains a nested sequence of accountsinterpretations of interpretations-that lead back to a purported discussion on the nature of knowledge between Socrates and two mathematicians, Theodorus and his young student Theatetus. This discussion is of interest to historians of mathematics because, in passing, it describes Theodorus as having established the irrationality of square roots of non-square numbers up to 17-‘where for some reason he got stuck’—and it indicates that Theatetus may have generalized the result. It is not clear why Theodorus stopped at 17 and many plausible and implausible interpretations have been proposed. But what is more important in the context of the Platonic dialogue is that Theatetus invokes the binary classification of numbers in terms of rationality as a possible metaphor for what he imagines are two sorts of knowledge, namely the sciences on the one hand as opposed to something else on the other, that he does not yet quite understand, but which is implicit in Socrates’ method of inquiry.
