Theaetetus
Theaetetus

417 BC?-369 BC?

Most of what we know of Theaetetus's life comes from the writing of Plato. It is clear that Plato held Theaetetus in the highest regard and he wrote two dialogues which had Theaetetus as the principal character. He was sent to Athens to be educated at the Academy there under Plato. He died of wounds he received in the battle between Athens and Corinth around 369 BC.

Theaetetus made very important contributions to mathematics, despite none of his writing having survived. Books 10 and 13 of Euclid's Elements are almost certainly a description of Theaetetus's work. This means that it was Theaetetus's work on irrational lengths which is described in the Book 10, thought by many to be the finest work of the Elements. Theaetetus was no doubt inspired by the work of Theodorus to work on incommensurables, and that he made major contributions to the theory. Given two magnitudes a and b, then the medial is ab, the binomial is a+b, and the apotome is a-b. It was also Theaetetus who "assigned the medial line to geometry, the binomial to arithmetic and the apotome to harmony".

He was the first to generalize Theodorus's proof that 3, 5, ..., 17 were irrational to all non-square numbers, which he called oblong numbers. Theaetetus is also thought to be the author of the theory of proportion which appears in Eudoxus's work. Theaetetus was the first to study the octahedron and the icosahedron, the other 3 Platonic solids being studied by the Pythagoreans.