Jacob Slavenburg in The Hermetic Link tells us a very interesting story of how Pythagoras was granted the ability to remember his past lives by Hermes Trismegistus.

He recalled his earlier lives and said he first had been Euphorus, secondly Aethalides, thirdly Hermotimus, fourth Pyrrhus and now he was Pythagoras.

Porphyrius, The Life of Pythagoras

He tells us how this extraordinary story was confirmed by Diogenes Laertius, who writes that, according to rumor, Pythagoras seems to have said of himself that he had lived earlier as Aethalides, among others.

And who was this Aethalides? A son of Hermes.

Aethalides had been given permission by his father to wish for anything he desired, except immortality. He chose eternal recollection of everything that happened in this life, as well as the life beyond the grave and on into new incarnations.

This gave him precise memories of all previous lifetimes, and this included the life of Pythagoras, the reincarnated Aethalides, as well.

I found this from A. E. Waite in a footnote to ‘The History of Magic” by Eliphas Levi, chapter vi ‘Mathematical Magic of Pythagoras’.

“He himself (Pythagoras) had been (a) Aethalides, a son of Mercury; (b) Euphorbus, son of Panthus, who perished at the hands of Menelaus in the Trojan war; (c) Hermotimus, a prophet of Claromenae, a city of Ionia; (d) a humble fisherman, and finally (e) the philosopher of Samos.”

Euphorbus was a minor warrior from the Trojan War and mentioned briefly in the Illiad. The humble fisherman from Delos was Pyrrhus, and the philospopher Hermotimus recognised the shiled of Euphorbus in the temple of Apollo. One of his past lives was as a beautiful courtesan, Alco.