Theaetetus (mathematician) in the context of "Irrational number"

Euclid (/ˈjuːklɪd/; Ancient Greek: Εὐκλείδης; fl. 300 BC) was an ancient Greek mathematician active as a geometer and logician. Considered the "father of geometry", he is chiefly known for the Elements treatise, which established the foundations of geometry that largely dominated the field until the early 19th century. His system, now referred to as Euclidean geometry, involved innovations in combination with a synthesis of theories from earlier Greek mathematicians, including Eudoxus of Cnidus, Hippocrates of Chios, Thales and Theaetetus. With Archimedes and Apollonius of Perga, Euclid is generally considered among the greatest mathematicians of antiquity, and one of the most influential in the history of mathematics.

Very little is known of Euclid's life, and most information comes from the scholars Proclus and Pappus of Alexandria many centuries later. Medieval Islamic mathematicians invented a fanciful biography, and medieval Byzantine and early Renaissance scholars mistook him for the earlier philosopher Euclid of Megara. It is now generally accepted that he spent his career in Alexandria and lived around 300 BC, after Plato's students and before Archimedes. There is some speculation that Euclid studied at the Platonic Academy and later taught at the Musaeum; he is regarded as bridging the earlier Platonic tradition in Athens with the later tradition of Alexandria.

The Elements (Ancient Greek: Στοιχεῖα Stoikheîa) is a mathematical treatise written c. 300 BC by the Ancient Greek mathematician Euclid.

The Elements is the oldest extant large-scale deductive treatment of mathematics. Drawing on the works of earlier mathematicians such as Hippocrates of Chios, Eudoxus of Cnidus, and Theaetetus, the Elements is a collection in 13 books of definitions, postulates, geometric constructions, and theorems with their proofs that covers plane and solid Euclidean geometry, elementary number theory, and incommensurability. These include the Pythagorean theorem, Thales' theorem, the Euclidean algorithm for greatest common divisors, Euclid's theorem that there are infinitely many prime numbers, and the construction of regular polygons and polyhedra.

The Theaetetus (/ˌθiːɪˈtiːtəs/; Greek: Θεαίτητος Theaítētos, lat. Theaetetus) is a philosophical work written by Plato in the early-middle 4th century BCE that investigates the nature of knowledge, and is considered one of the founding works of epistemology. Like many of Plato's works, the Theaetetus is written in the form of a dialogue, in this case between Socrates and the young mathematician Theaetetus and his teacher Theodorus of Cyrene. In the dialogue, Socrates and Theaetetus attempt to come up with a definition of episteme, or knowledge, and discuss three definitions of knowledge: knowledge as nothing but perception, knowledge as true judgment, and, finally, knowledge as a true judgment with an account. Each of these definitions is shown to be unsatisfactory as the dialogue ends in aporia as Socrates leaves to face a hearing for his trial for impiety.

As one of the major works of Plato's theory of knowledge, the Theaetetus was influential on Platonism from at least the time of the Skeptical Academy of the 3rd century BCE through the Neoplatonism of the 6th century CE. It has also been the subject of increased attention in modern times as a result of its influence on Edmund Gettier, who challenged the existing definitions of knowledge as a "justified true belief" in a paper that investigated Plato's theory of knowledge as outlined in this work.