Is there any issue with the general studies department of a Jewish day school teaching Greek mythology to the students?
It's addressed in responsum YDII:53 (see first paragraph on linked page) from the late Rabbi Moshe Feinstein to Rabbi Yehuda Parness, shlit'a. (Though the question there was a Jewish fellow who teaches social studies at a public school to mostly non-Jews, and the curriculum includes Greek mythology. We can debate whether it's ideal to include such material when designing a Jewish dayschool curriculum.)
Rabbi Feinstein observes that there are serious issues, but if it's taught in the right way, it can shed a great deal of positive light on Judaism. It shows what silliness was so prevalent back then (you call them gods, and they're all drinking and raping and murdering?), and what Judaism was up against, and how different it was at the time. So I think it's more on the "how should it be taught" than "may it be taught"?
On a lighter note, Rabbi Aaron Rakefet says it's only after studying Greek mythology that he's understood how certain powerful contemporary politicians can act so foolishly in their private lives!
While it's not as widely-known today, many greats of the Mussar movement believed in studying literature as a means towards a better understanding of human nature and how to improve it. I don't know if Greek mythology was on their curriculum (as opposed to something more "down-to-earth" like Tolstoy).
Rabbi Yissochar Frand, quoting his tradition from Rabbi Yaakov Weinberg, says the Talmudic prohibition on "Greek wisdom" was limited to a special system of communication (or dialect) reserved for the Greek political class. "The ban does not include Greek mythology -- though that may have other issues" is the quote, if I recall.
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I would guess not, being that the popular story of Rome with Romulus drinking from the dog is in Medrash .
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