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Theon of Smyrna (ca. 70–ca. 135) was a Greek philosopher and mathematician, whose works were strongly influenced by the Pythagorean school of thought. Little is known about the early life of Theon of Smyrna; Ptolemy cites work of his on several occasions between 127 and 132, but there are few other dates that are known for certain. His death can only be dated to within ten years, based on the style of his bust created at his death; 135 is often given as a midpoint guess between the possible dates of 130 and 140 CE.

Theon wrote several commentaries on the works of mathematicians and philosophers of the time; he authored three works on the philosophy of Plato, of which two are lost. The only one which survives is On Mathematics Useful for the Understanding of Plato. Theon's aim was not to create new research but rather to give a reader the necessary background to understand the writings of Plato, but the Dictionary of Scientific Biography criticizes it for failing to be useful to a student of Plato and being rather a general handbook for a student of mathematics. Other criticism of this work targets its lack of originality: it is not so much a groundbreaking work as a reference work of ideas already known at the time; however, 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.

The second section, on music, is split into three parts: music of numbers (hē en arithmois mousikē), instrumental music (hē en organois mousikē), and "music of the spheres" (hē en kosmō harmonia kai hē en toutō harmonia). The "music of numbers" is a treatment of temperament and harmony using ratios, proportions, and means; the sections on instrumental music concerns itself not with melody but rather with intervals and consonances in the manner of Pythagoras' work. Theon considers intervals by their degree of consonance: that is, by how simple their ratios are. (For example, the octave is first, with the simple 2:1 ratio of the octave to the fundamental.) He also considers them by their distance from one another.

The third section, on the music of the cosmos, he considered most important, and ordered it so as to come after the necessary background given in the earlier parts. Theon quotes a poem by Alexander of Ephesus assigning specific pitches in the chromatic scale to each planet, an idea that would retain its popularity for a millennium thereafter.

The second book is on astronomy. Here Theon affirms the spherical shape and large size of the Earth; he also describes the occultations, transits, conjunctions, and eclipses. However, the quality of the work led Otto Neugebauer to criticize him for not fully understanding the material he attempted to present.

It is thought that Ptolemy was a student of Theon; Ptolemy is known to have used several of Theon's astronomical observations in his own work. The lunar impact crater Theon Senior was named for him.


  • Theon, of Smyrna: Mathematics useful for understanding Plato; translated from the 1892 Greek/French edition of J. Dupuis by Robert and Deborah Lawlor and edited and annotated by Christos Toulis and others; with an appendix of notes by Dupuis, a copious glossary, index of works, etc. Series: Secret doctrine reference series Published: San Diego : Wizards Bookshelf, 1979. ISBN: 0913510246. 174pp.
  • E.Hiller, Theonis Smyrnaei: expositio rerum mathematicarum ad legendum Platonem utilium, Leipzig:Tuebner, 1878, repr. 1966.
  • J. Dupuis, Exposition des connaissances mathematiques utiles pour la lecture de platon, 1892. French translation.
  • Lukas Richter:"Theon of Smyrna". Grove Music Online, ed. L. Macy. Accessed 29 Jun 05. (subscription access)
  • J. J. O'Connor and E. F. Robertson, "Theon of Smyrna". MacTutor History of Mathematics Archive: [1].
  • 'Mathematics Useful for Understanding Plato' translated by R. and D. Lawlor, Wizards Bookshelf, San Diego 1979.

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