Theodorus of Cyrene

Theodorus of Cyrene (Ancient Greek: Θεόδωρος ὁ Κυρηναῖος, romanized: Theódōros ho Kyrēnaîos; fl.

The only first-hand accounts of him that survive are in three of Plato's dialogues: the Theaetetus, the Sophist, and the Statesman.

[1] He complains of old age in the Theaetetus, the dramatic date of 399 BC of which suggests his period of flourishing to have occurred in the mid-5th century.

The text also associates him with the sophist Protagoras, with whom he claims to have studied before turning to geometry.

[2] A dubious tradition repeated among ancient biographers like Diogenes Laërtius[3] held that Plato later studied with him in Cyrene, Libya.

[1] This eminent mathematician Theodorus was, along with Alcibiades and many other of Socrates' companions (many of whom would be associated with the Thirty Tyrants), accused of distributing the mysteries at a symposium, according to Plutarch, who himself was priest of the temple at Delphi.

Theodorus' work is known through a sole theorem, which is delivered in the literary context of the Theaetetus and has been argued alternately to be historically accurate or fictional.

That one cannot prove the irrationality the square root of 17 by considerations restricted to the arithmetic of the even and the odd has been shown in one system of the arithmetic of the even and the odd in [7] and,[8] but it is an open problem in a stronger natural axiom system for the arithmetic of the even and the odd [9] A possibility suggested earlier by Zeuthen[10] is that Theodorus applied the so-called Euclidean algorithm, formulated in Proposition X.2 of the Elements as a test for incommensurability.

In modern terms, the theorem is that a real number with an infinite continued fraction expansion is irrational.