How did Greek culture survive?

Answer 1

The Byzantine Empire was the Roman Empire.

Byzantine Empire is a term which has been coined by historians to indicate the eastern part of the Roman Empire after the fall of the western part. The so-called "Byzantines" did not use this term. They called their empire the Empire of the Romans or Romania or Rhomais in Latin or Basileia Rhōmaiōn or Rhomania in Greek. Romania was a short form for Roman Empire. It was not related to the country which was later called Romania. All the peoples who lived the Roman Empire saw themselves as Romans. They had been granted Roman citizenship by the emperor Caracalla in 215. The so-called "Byzantines" did not even use the term eastern Romans, which is often used by historians for them. Western and eastern Roman Empire are also terms which have been coined by historians. The Romans and the peoples in the Roman Empire only used the term Empire of the Romans.

The term Byzantine was chosen by a German historian in the 16th century as a derivation from Byzantium, a Greek city which had evolved into a Roman city under Roman rule and which was then redeveloped, turned into an imperial capital and renamed Constantinople (City of Constantine) by the Roman emperor Constantine the Great in 330. It is used to indicate the fact that not long after the fall of the western part of the Roman Empire, this part of the empire became centred on Greece and Greek in character after it lost most of its non-Greek territories. Greek replaced Latin as the official language of this empire in 620, some 150 years after the fall of the western part. Both the terms Byzantine and Byzantine Empire became common in Western Europe in the 19th century.

Answer 2

It became fashionable amongst the Roman upper class, so when the Greek city-states were absorbed into the Roman Empire, it continued to flourish. After the barbarian takeover of the western Roman Empire, the Eastern Empire survived and, being Greek, with Greek language and culture, even though they called themselves Roman, continued for another thousand years. Also, Alexander had sowed Greek culture in the Persian Empire when he took it over, and Greek culture spread through the Middle East, surviving there even after the Islamic conquest.