In Greece we are taught that while the romans military conquered "Greece", "Greece" culturally conquered Rome. Which is partially bs copium but has some truth in it.

The romans were crazy greekaboos. All the rich romans wanted to learn greek, watch greek theater, read greek philosophers, etc.

Eventually the Eastern Roman Empire(aka Byzantine Empire), became kinda greek, especially in its last centuries.

Do note, that Greece didnt exist, though the greek identity was obviously a thing when Rome conquered "Greece". Kinda how people say "i am European" today.

Funnily enough, with the rise of Christianity(and Roman citizen identity), the greek identity declined, mostly because it was associated with paganism. Which is why greeks identified as "romioi"(romans), ie greek speaking christians.

The greek identifier rose back into prominence after many centuries(800ad), but even today, the word "romios" means greek, though it isnt used much(it is mostly found in older texts, poetry, etc). You could say that the romans did kinda culturally conquered Greece after all :)