Theaetetus Theodorus Theaetetus incommensurables number systems Euclid's Elements Pappus arithmetic Euclid Plato irrational
Plato had a keen interest in mathematics, and distinguished clearly between arithmetic and calculation. (By arithmetic he meant, in part, theorising on number, rather than what arithmetic or number theory have come to mean.) It is through one of Plato's dialogues—namely, Theaetetus—that we know that Theodorus had proven that 





3


,


5


,
…
,


17




{\displaystyle {\sqrt {3}},{\sqrt {5}},\dots ,{\sqrt {17}}}

 are irrational. Theaetetus was, like Plato, a disciple of Theodorus's; he worked on distinguishing different kinds of incommensurables, and was thus arguably a pioneer in the study of number systems. (Book X of Euclid's Elements is described by Pappus as being largely based on Theaetetus's work.)
