it is a bit baffling that 99% of the articles talking about greece go on and on about a period that after all lasted 300-400 years and until the macedonians it was sort of politically irrelevant. this compared to the thousand years of hellenised eastern roman empire where not the same philosophical works have been written, but "byzantine domination", really?
those were greeks and the main inspiration for both the great idea (it was about restoring byzantine prestige, certainly not "athenian"), and the state structure afterwards, with kings called constantine and the church as a relevant part of the state.
"modern greeks don't seem to have much to do with the old ones". that's right. I wonder what happened in those 2000 years we keep wanting to ignore.
There are two things culture, (language and traditions), and DNA make up. The culture is a mix of Mycenaean, (earlier settlers and the Indo European invaders mix (where the Greek language comes from), plus Minoan influence they gained after conquering the place.
Greeks, just like their neighbors, the Albanians, and Sardinians have the highest mix of Early Neolithic Farmers, then some West Hunter Gatherer, and some Yamnaya culture (probably that's where they got the Indo European language, that eventually became Greek).
So, DNA wise, they are a mix of locals + some PIE invaders, that eventually became the Greek culture and language. This is a similar story to all European populations, but the mix % might change.
As for culture, there are two hypothesis: The culture was already preformed, and the PIE setlers imposed it to the locals they invaded, or it just arised in place, when people mixed together. Same story with the Illyrians just up north.
So far 2. wins, since there are still some Pre Indo European words that survive today (eg. Larissa, is not a Greek name, but it was of the people that were there before). Greek culture is something that rose overtime in that land, hence autochthonous, but the Indo European language won over the other local languages.
A modern comparison would be something that happen to Latin America. Eg. Most modern Mexicans are a mix of the Spanish settlers, and the indigenous population, that created its own unique ethnicity. Ultimately the Spanish language won, even though the settlers were a minority.
But the culture that arose is definitely not spanish, and it is a distinctive mix of both spanish and local traditions.
A similar process happened with the European populations during the Bronze age.
I realize that it might be the whole point that it shouldn't matter whether modern Greeks are descendant of ancient Greeks. But I still find it odd that an article about the topic nowadays doesn't mention DNA analysis such as this one: https://www.science.org/content/article/greeks-really-do-hav...
DNA analytics in the context of the ottoman empire would be a melting pot. As I understand it, succession to the sultanate was usually not by primogeniture as much as from the set of candidates, including other ethnicities in the Osmanli family, with much concubinage there would be all kinds of races.
Outside of the sultanate the army was a melting pot. Labour was grabbed from everywhere. Racial origins were no bar to advancement. Post service, not everyone (few even?) return home.
I am sure some ancient greek DNA remains extant, but I am also sure a lot of other DNA is at large in Turkey, Greece, Albania, FYROM...
The Article: "... When the researchers compared the DNA of modern Greeks to that of ancient Mycenaeans, they found a lot of genetic overlap. Modern Greeks share similar proportions of DNA from the same ancestral sources as Mycenaeans, although they have inherited a little less DNA from ancient Anatolian farmers and a bit more DNA from later migrations to Greece. ..."