Theon of Smyrna

Theon of Smyrna (Greek: Θέων ὁ Σμυρναῖος, gen. Θέωνος; fl. 100 CE) was a Greek philosopher and mathematician, whose works were strongly influenced by the Pythagorean school of thought. His surviving On Mathematics Useful for the Understanding of Plato is an introductory survey of Greek mathematics.

Little is known about the life of Theon of Smyrna. A bust created at his death, and dedicated by his son, was discovered at Smyrna, and art historians date it to around 135 CE. Ptolemy refers several times in his Almagest to a Theon who made observations at Alexandria, but it is uncertain whether he is referring to Theon of Smyrna. The lunar impact crater Theon Senior is named for him.

Theon wrote several commentaries on the works of mathematicians and philosophers of the time, including works on the philosophy of Plato. Most of these works are lost. The one major survivor is his On Mathematics Useful for the Understanding of Plato. A second work concerning the order in which to study Plato's works has recently been discovered in an Arabic translation.

His On Mathematics Useful for the Understanding of Plato is not a commentary on Plato's writings but rather a general handbook for a student of mathematics. It is not so much a groundbreaking work as a reference work of ideas already known at the time. Its status as a compilation of already-established knowledge and its thorough citation of earlier sources is part of what makes it valuable.

The first part of this work is divided into two parts, the first covering the subjects of numbers and the second dealing with music and harmony. The first section, on mathematics, is most focused on what today is most commonly known as number theory: odd numbers, even numbers, prime numbers, perfect numbers, abundant numbers, and other such properties. It contains an account of 'side and diameter numbers', the Pythagorean method for a sequence of best rational approximations to the square root of 2, the denominators of which are Pell numbers. It is also one of the sources of our knowledge of the origins of the classical problem of Doubling the cube.

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