Life Theodorus of Cyrene (Θεόδωρος ὁ Κυρηναῖος) was a Greek mathematician active in the late 5th century BCE. He is known primarily from Plato’s dialogue Theaetetus, which depicts him in Athens engaging with Socrates and his student Theaetetus [1][2]. Socrates credits Theodorus with instructing him in geometry, astronomy, arithmetic, and music [1].

Works No written works by Theodorus survive. His contributions are recorded indirectly in Plato’s Theaetetus (147d-148b), where Theaetetus describes a lesson in which Theodorus proves the irrationality of the square roots of the non-square integers from 3 up to 17, demonstrating each case individually [1][2][3].

Significance Theodorus holds a significant place in the history of mathematics for his early work on irrational numbers. His proofs extended the discovery of irrationality beyond √2. He directly influenced Socrates and, crucially, his student Theaetetus, who generalized these results into a theory foundational for Book X of Euclid’s Elements [1][2].

Sources 1. Stanford Encyclopedia of Philosophy (Plato's Theaetetus): https://plato.stanford.edu/entries/plato-theaetetus/ 2. Internet Encyclopedia of Philosophy (Irrational Numbers): https://iep.utm.edu/irrational-numbers/ 3. Encyclopædia Britannica (Theodorus of Cyrene): https://www.britannica.com/biography/Theodorus-of-Cyrene