The Romans colonized and settled Hispania and Gaul and Dacia, in large part because their wars of conquest there were also wars of annihilation and depopulation.

Such numbers are necessarily a rough estimate, but Gaul probably had a population of ~5 million before Roman conquest. Historians generally agree Caesar killed about a million, and enslaved another million or so. So it was a HUGE reduction in population.

The conquests in the east were nothing of the sort. Pompey basically just marched through and collected surrenders. The local populations were huge and urbanized, and the Latinate Roman population was never large. So while local elites might have learned Latin, the average person in the street never did.

In the roman empire, the west used latin and latin dialects as lingua franca, the eastern half used greek. It was the language of philosophy and the intellectuals, so there was no local lower-prestige language that could be replaced by latin. Latin was adopted in West Rome precisely because local languages were regarded as "lower class" and "lower prestige". So if you wanted to climb that social ladder, you better assimilate. In the East, greek already was the "higher class" language before Rome even set foot in greek city states. And the reverence Rome had to greek culture, history and language ensured that the Eastern empire stayed greek dominated.

The New Testament is not one book, it's a collection of works, by a number of authors. Most of them from the east mediterranean. Much of the population there already spoke koine greek as their native language, and others used it as it was the language of learning. Latin would only have been relevant for those in power.

Google the phrase 'canon of the catholic bible'.

Most if not all of the books of the New Testament were originally written in greek but none of the books were written at the same time. And while called books, we can almost think of them as chapters in the book we now refer to as the bible. Additionally, there were quite a number of these books being passed around the Mediterranean world not all of which made it into the current bible. As the Roman Catholic church became more pronounced they eventually held a council to determine which books would belong in the official church canon. These works became the official Catholic Church canon. Important to note, that not all of the works in the catholic bible were considered the direct word of God...but the church council viewed them as inspirational enough that they did indeed belong. This is why today, a catholic bible contains more new testament books than its protestant counter-part. Very long story short...once the church finalized on its canon of scripture, the church would then release the official catholic church's version of the now Latin bible called the Vulgate. Keeping in mind, the above is approximately 1200 or so years of history compacted into a Reddit post.

Basically the answer is very simple: Rome was not a monolingual empire, even at state level. Learned people in rome, politicians, nobles, scholars, even high ranking army officers would be educated to speak both Latin and Greek. The entire eastern mediterranean had started using greek as a lingua franca after Alexander's conquests, and Greek also happened to be a "prestige language" among the Roman elite, so they never made any effort to dislodge or replace it. They simply adopted it as the secondary state language, and thus Greek continued it's dominance in the east.

As for why the Romans were so accepting of Greek to begin with, the answer to that is also fairly simple: The greeks colonized southern Italy long before Rome emerged as a major power, and thus they'd been in constant contact with the Greek language and culture since they were a tiny city state.

The entire Mediterranean spoke versions of Greek long before the rise of Rome. Latin wasn't a widespread language among the hoi polloi because Greek was the common mutual language.

I don't believe your assumptions about newly conquered people quickly or ever even becoming Latin speakers is correct. Ruling elites maybe. In Roman Judea Greek was a lingua franca of commerce and diplomacy between various peoples. Literate people of the ancient Mediterranean world usually had some Greek. Greeks and the Levant had been interacting for a thousand years before Rome appeared. Greek was considered an intellectual and philosophical language by the Roman world.. Rome did not form many settler colonies in the Eastern Med.

Because some aspects of Roman culture were influenced by Greek culture. So unlike the Celts, the Romans let the Greeks speak their own language.

The places that became romanized were backwards regions; Roman culture was seen as superior by them and they wanted to be Roman. The East however, was more civilized than Rome, and they frowned upon everything Roman. Greek was seen as a superior language and culture to Roman (the very Romans adopted plenty of Greek things and every cultivated Roman had to know Greek to have some credibility).

My understanding was if you wanted a document to be taken seriously and stand the test of time, you wrote/translated it to Greek, not the native tongue of the author.

The idea being that Greek was a language known to around the world and was likely to stay around, unlike Aramaic

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Romans didn’t force everyone in their territories to speak Latin. Plus it takes centuries for a whole region to change languages and the Romans had only been holding the Levant for a short period at the time.

Latin was the common language for the western half of the Roman Empire. But Greek was the common language for the eastern half of the Roman Empire, including Judea. Most educated Romans were fluent in Greek as well as Latin.

May I add a question? I understand why the New Testament was writing in Greek, but why wasn’t the book of Romans written in Latin?

The parts of the Empire that were thoroughly Romanized were mainly troublesome provinces that required a lot of ass-kicking—Britannia, Gaul, Hispania, etc. After watching a vast proportion of their countrymen from all strata of society slain or enslaved, the local elites that survived hopped on the SPQR bandwagon quicker than people who play Paradox games. The Roman assimilation squad also used what we'd consider "heavy-handed PR strategies" to further integrate the conquered: merging local deities with their Roman equivalents and showing off the superiority of Roman culture with fancy innovations like roads, bath houses, Latin, crucifixion and so forth.

The other side of the Mare Nostrum was a different story altogether. These were heavily urbanized areas that had belonged to successfully-administrated states for centuries (the Persian Empire, the Greek city-states, Alexander's empire, the successor kingdoms of the Diadochi, etc). They already had a culture, and it was considered equal (or even superior) to that of the Romans. The Romans didn't have to come in and hand out their brand of civilization to the conquered while building up the area; it was already built, densely populated, well-organized and efficiently taxed. The Roman governor arrived and a laurel appeared above the head on the local coinage. These provinces required no remodeling. They were move-in ready!

The common language of the people who wrote down the New Testament (and of the regions in which they lived) was Koine Greek. The Gospels, Acts, Epistles and Revelation are believed to have been written in the first century (generally between 50 and 110 CE, depending on which part), by both Jewish Christians and Hellenized Gentile Christians, mostly in Syria and Palestine. Roman dominion in these areas was relatively new, by the standards of the time, and one could argue that the prevailing Hellenistic culture of the East was the influencer, as it evolved into Byzantine culture and would remain Greek-oriented up until the Muslim conquests.

I wonder why it wasn't written in Aramaic.

Greek was the language most educated people spoke and was often used as the language of choice amongst educated people within the roman empire. Certainly by the time of the early church, the Eastern roman empire was the more powerful and culturally significant, and Greek was the more popular language there

The New Testament is Written in Greek because the Old Testament was Helenized with Plato's Teachings by Philo Judeas. "Christianity is Platonism for the people." (Nietzsche, Prologue to Beyond Good and Evil) If you want, I'll PM you some little known history, direct from the source snips from a book vetted by Princeton.