**Theaetetus of Athens** was a Greek mathematician who made very important contributions to the theory of irrationals. His work is described in the Euclid's Elements.

- It is clear that Plato held Theaetetus in the highest regard and he wrote two dialogues which had Theaetetus as the principal character, one of the dialogues being Theaetetus while the other is the Sophist.
- In Theaetetus a discussion between Socrates, Theaetetus and his teacher Theodorus of Cyrene is recorded.
- This conversation took place in 399 BC and Theaetetus is described as a youth at the time.
- This allows us to give a fairly accurate date for Theaetetus's birth (although some have claimed that the Greek word could describe a man of up to 21 years old).
- However, the money was squandered by the trustees of the will but despite this Theaetetus was generous to all around him.
- In appearance Theaetetus had a snub nose and protruding eyes but he is described by Plato as having a beautiful mind and he is also described as being the perfect gentleman.
- There are two references to a 'Theaetetus' in the Suda Lexicon (a work of a 10th century Greek lexicographer).
- The Peloponnesian War was fought between Athens and Sparta from 431 BC to 404 BC so the dates here are consistent since Theaetetus would be 13 years old when the War ended so saying the he 'lived after the Peloponnesian war' is reasonable.
- Theaetetus took part in the battle between Athens and Corinth in 369 BC.
- As a result of the wounds that he received in the battle, Theaetetus contracted dysentery and died in Athens.
- Theaetetus made very important contributions to mathematics and despite none of his writing having survived we do know a great deal about his contribution.
- This means that it was Theaetetus's work on irrational lengths which is described in the Book X, thought by many to be the finest work of the Elements.
- This science has its origin in the school of Pythagoras, but underwent an important development in the hands of the Athenian, Theaetetus, who is justly admired for his natural aptitude in this as in other branches of mathematics.
- Pappus tells us, therefore, that Theaetetus was inspired by the work of Theodorus to work on incommensurables and that he made major contributions to the theory.
- was considerably developed by Theaetetus the Athenian, who gave proof, in this part of mathematics as in others, of ability which has been justly admired.
- For Theaetetus had distinguished square roots commensurable in length from those which are incommensurable, and who divided the more generally known irrational lines according to the different means, assigning the medial line to geometry, the binomial to arithmetic and the apotome to harmony, as stated by Eudemus...
- Hence the entire book is the work of Theaetetus.
- Bulmer-Thomas prefers the conjecture that although Book X is based on Theaetetus's work there is much due to Euclid presented there too.
- If his arguments are valid then, of course, Theaetetus would not be the first to prove the general result.
- Theaetetus is also thought to be the author of the theory of proportion which appears in Eudoxus's work.
- the five so-called Platonic figures which, however, do not belong to Plato, three of the five being due to the Pythagoreans, namely the cube, the pyramid, and the dodecahedron, while the octahedron and the icosahedron are due to Theaetetus.
- We quoted from Pappus above where he described Theaetetus's work on the medial, the binomial, and the apotome.

Born about 417 BC, Athens, Greece. Died about 369 BC, Athens, Greece.

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Ancient Greek, Astronomy, Origin Greece

**O’Connor, John J; Robertson, Edmund F**: MacTutor History of Mathematics Archive