Iamblichus' Life of Pythagoras

Indeed, no one can doubt that the soul of Pythagoras was sent to mankind from the empire of Apollo, whether as an attendant on the God or associated with him in some other intimate way; this may be inferred from both his birth and the immense, diverse wisdom of his soul. And so much for the nativity of Pythagoras.

After his father, Mnesarchus, returned from Syria to Samos with great wealth collected from a prosperous voyage, he built a temple to Apollo, with the inscription "Pythius." He took care to have his son nourished with various and the best disciplines, at one time by Creophilus, and at another...

The following is a continuation of the commentary on the nature of "terrestrial heroes":

These souls were called by the ancients "terrestrial heroes" because of their high degree of proximity and alliance to those who are essentially heroes. Hercules, Theseus, Pythagoras, Plato, and others were souls of this kind who descended into mortality both to benefit other souls and in compliance with the necessity by which all natures inferior to the perpetual attendants of the Gods are at times obliged to descend.

But, according to the secrets of ancient theology, every God, starting from on high, produces his own series down to the last of things; this series includes many essences, such as dæmoniacal, heroical, nymphical, and the like. The lowest powers of these orders have a great communion and physical sympathy with the human race and contribute to the perfection of their natural operations, particularly procreation. "Hence," says Proclus (in his Scholia on the Cratylus), "it often appears that heroes are generated from the mixture of these powers with mankind; for those that possess a certain prerogative above human nature are properly denominated 'heroes'." He adds: "Not only does a dæmoniacal genus of this kind sympathize physically with men, but other kinds sympathize with other natures, such as Nymphs with trees, others with fountains, and others with stags or serpents."

Olympiodorus, in his life of Plato, observes that an Apolloniacal spirit is said to have had a connection with Perictione, his mother; it appeared in the night to his father, Aristo, and commanded him not to sleep with Perictione during her pregnancy, a mandate which Aristo obeyed. A similar account of the divine origin of Plato is given by Apuleius, Plutarch, and Hesychius.