Did Pythagoras visit Judaea, Arabia, and/or India?

Question

From Wikipedia's page on Pythagoras:

Diogenes Laertius reported that Pythagoras had undertaken extensive travels, and had visited not only Egypt, but Arabia, Phoenicia, Judaea, Babylon, and even India, for the purpose of collecting all available knowledge, and especially to learn information concerning the secret or mystic cults of the gods.

An earlier revision of the article reads:

It was the standard belief in antiquity that Pythagoras had undertaken extensive travels, and had visited not only Egypt, but Arabia, Phoenicia, Judaea, Babylon, and even India, for the purpose of collecting all available knowledge, and especially to learn information concerning the secret or mystic cults of the gods.

As we are told repeatedly when trying to find out about Pythagoras' life, very little is reliably known about it. A lot of later sources use his travels to explain his various influences and tend to crowbar countries into his itinerary for this reason. For example, Egypt and Babylon are often stated to have influenced his geometry, mysticism and secrecy, while Babylon and India opened his eyes to vegetarianism, and India, some say, introduced him to vedic mathematics and Buddhism. One can't help but be sceptical of such explanations.

That said, my question is simple: does Laertius' Lives and Opinions of Eminent Philosophers actually mention Arabia, Judaea, and/or "even India"?

Answer 1

Diogenes Laërtius mentions several of Pythagoras' travels and he mentions that the philosopher visited the Chaldeans and the Magi:

ἐγένετ' οὖν ἐν Αἰγύπτῳ, ὁπηνίκα καὶ Πολυκράτης αὐτὸν Ἀμάσιδι συνέστησε δι' ἐπιστολῆς· καὶ ἐξέμαθε τὴν φωνὴν αὐτῶν, καθά φησιν Ἀντιφῶν ἐν τῷ Περὶ τῶν ἐν ἀρετῇ πρωτευσάντων, καὶ παρὰ Χαλδαίοις ἐγένετο καὶ Μάγοις. εἶτ' ἐν Κρήτῃ σὺν Ἐπιμενίδῃ κατῆλθεν εἰς τὸ Ἰδαῖον ἄντρον ἀλλὰ καὶ ἐν Αἰγύπτῳ εἰς τὰ ἄδυτα· καὶ τὰ περὶ θεῶν ἐν ἀποῤῥήτοις ἔμαθεν. εἶτ' ἐπανῆλθεν εἰς Σάμον, καὶ εὑρὼν τὴν πατρίδα τυραννουμένην ὑπὸ Πολυκράτους, ἀπῆρεν εἰς Κρότωνα τῆς Ἰταλίας· κἀκεῖ νόμους θεὶς τοῖς Ἰταλιώταις ἐδοξάσθη σὺν τοῖς μαθηταῖς, οἳ πρὸς τοὺς τριακοσίους ὄντες ᾠκονόμουν ἄριστα τὰ πολιτικά, ὥστε σχεδὸν ἀριστοκρατίαν εἶναι τὴν πολιτείαν.

^{Source: Βίοι καὶ γνῶμαι τῶν ἐν φιλοσοφίᾳ εὐδοκιμησάντων, WikiSource}

And that's about it, no mention of specific cities Pythagoras might have visited in the area, or any other details. Which is a bit suspect, as Diogenes Laërtius goes into some detail (quoting various sources) for Pythagoras' travels within Greece, to Egypt, to Italy and to... Hades.

All this, of course, are on the book on Pythagoras. In general there are several references to Arabia, Judaea and India, some as vague references to places that inspired Greek philosophy and some as references to places other Greek philosophers visited (including the Pythagoreans, but not Pythagoras himself). As an example, the preface of the work is:

Τὸ τῆς φιλοσοφίας ἔργον ἔνιοί φασιν ἀπὸ βαρβάρων ἄρξαι. γεγενῆσθαι γὰρ παρὰ μὲν Πέρσαις Μάγους, παρὰ δὲ Βαβυλωνίοις ἢ Ἀσσυρίοις Χαλδαίους, καὶ γυμνοσοφιστὰς παρ' Ἰνδοῖς, παρά τε Κελτοῖς καὶ Γαλάταις τοὺς καλουμένους Δρυΐδας καὶ Σεμνοθέους, καθά φησιν Ἀριστοτέλης ἐν τῷ Μαγικῷ καὶ Σωτίων ἐν τῷ εἰκοστῷ τρίτῳ τῆς Διαδοχῆς.

Which roughly translates to:

Some say philosophy started amongst the barbarians. Born with the Persian Magi, and among the Babylonians and the Assyrian Chaldeans, and the Indian Gymnosophists, and among the Celts and the Gauls that were called Druids, as Aristotle tells us in his book on Magic and Sotion in the 23rd book of the Succession.