Hellenism arose in Judaism during the time of the Greek empire, particularly under Alexander the Great. Initially the Greek and Jews seemed to get along well, but eventually religious tensions among Jews arose over the matter. Rabbi Ken Spiro gives an overview of the history:
[After Alexander the Great was impressed and spared Jerusalem]
The initial interaction seemed to be very positive. To the Jews, the Greeks were a new and exotic culture from the West. They had a profound intellectual tradition that produced philosophers such as Socrates, Plato, and Aristotle (who was Alexander's tutor for two years). [...] While much of the upper crust of Jewish society, along with the rest of the population of the Mediterranean world, readily embraced Hellenistic culture (some to the point of denouncing their Jewish identity), the vast majority of the Jews remained loyal to Judaism. [...] It would be wrong to view the conflict as purely Greece versus the Jews. Internal tension within the Jewish community contributed significantly to the conflict. Many of the Hellenized Jews took it upon themselves to "help" their more traditional brethren by "dragging" them away from what they perceived was their primitive beliefs into the "modern" world of Greek culture.
From the point of the established Jewish community, Jews following this path were assimilating into the surrounding culture and giving up on Judaism. From the point of view of the Hellenistic Jews, they were pursuing modernity and not necessarily abandoning their culture, history, and religion -- though they were willing to violate Jewish law to fit in, like reversing circumcisions so they would fit in at the (Greek) gymnasia.
According to somebody summarizing Rabbi Dov Nimchinsky, Director of Curriculum and Instruction at the Robert M. Beren Academy, this tension led to the division between the Pharisees and Saduccees.
See also: Wikipedia
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