Pythagoras

Pythagoras was an Ancient Greek philosopher and mathematician. (PROSE: Empire of Death)

Biography
The Doctor met him before their fourth incarnation. (AUDIO: The Labyrinth of Buda Castle)

The Fourth Doctor recalled Pythagoras as a lovely fellow who was good at billiards. (COMIC: Gaze of the Medusa) Though the Fourth Doctor thought him a brilliant man, he noted that "He thought beans were evil!" (AUDIO: The Labyrinth of Buda Castle)

The Thirteenth Doctor claimed to have borrowed some sunglasses from either Pythagoras or Audrey Hepburn. According to the Doctor, he wore shades when he was drunk. (TV: The Ghost Monument)

According to the Eighth Doctor, when a student of Pythagoras suggested to him that the square root of two is not a rational number, Pythagoras ordered to drown him. (PROSE: Option Lock)

Pythagoras was burned to death in his school. (PROSE: Option Lock)

Philosophical beliefs
Pythagoras believed in metempsychosis, i.e., transmigration of the soul, also known as reincarnation. (PROSE: Empire of Death)

Scientific achievements
Pythagoras was the first to discover that maths is the basis of science. (PROSE: Option Lock)

Pythagoras proved that the Earth revolved around the the sun 19 centuries before Copernicus. (COMIC: Gaze of the Medusa)

By plucking a string, he discovered that the relation of a note to its overtones is always a fraction. (PROSE: The Algebra of Ice)

Pythagoras proved a theorem that determined properties of a hypotenuse. (PROSE: Byzantium!)

Behind the scenes

 * In the Brazillian dubbing of The Ghost Monument, Audrey Hepburn and Pythagoras were changed for Carmen Miranda and Palmirinha, respectively.