Are modern Greeks related to the ancient Greeks?

Modern greece has virtually no connection with the (Hellenes)of the ancient world.Any serious scholar will tell you this is true.Modern greece was founded in 1824,and the population largely consisted of transplanted albanin and slavs as well as christian refugees from the old Ottoman emmpire.Conidering that the Athenian city state was in its prime roughly 2300 years ago,and began its fall after Alexander the Great invaded in 325 BC.The very word "Greek" is a misnomer in that it was never used as a self description by the peoples who occupied that pennisula during their era .Modern Greeks got their name during the mid-nineteenth century,mostly from European writers and intellectuals who wished to ressurect the glories of Ancient Athens and its Golden Age.Sorry but this is the truth and no amount of wishing can change the fact that in terms of culture ,history ,language and DNA,the modern Greek state has nothing to do with the old.

If one has two parents and four grandparents, then when one goes back ten generations one has potentially 2^10th, or 1024 ancestors of the 10th generation. This becomes 1 million potential ancestors at the 20th generation and 1 billion at the 30th. If each generation is roughly 25 years, then 30 of them is 7.5 centuries, which would be in the area of 1253 AD. It is doubtful, although possible, that there were 1 billion humans on earth in 1253 - therefore everyone alive today is potentially descended from everyone alive at the time that produced descendants into the current generation.

While 25 year generations is common now, it has been traditional to marry girls at age 14, therefore most generations may average 20 years, and in that case we go back 600 years to 1413 AD. This is within a century of Columbus arriving in the Americas. By the end of this century, DNA from even the remotest settlements should be thoroughly mixed into the global population.

It would be safe to say that modern Greeks have some DNA from Greek ancestors 2300 years ago, but they will also have DNA from Hutus, Mongols, and even Incas.

I would agree that the language is an important factor in determining the relation among people but it's not the only one.

Taking into consideration the above we can check other factors also:

1. Ancient Greek had a religion which is undoubtedly totally different than the modern Greeks one (if they adhere one that is). Modern Greek are in their major parts Greek-Orthodox or are at least familiar with rituals of this dogma. Ancient Greeks were polytheistic and believed in many different Gods and gods. This has changes a lot of their habits, rituals etc.
2. Endonyms are not a good criterion for getting to a objective conclusion about relation. Both people use similar word (the accent and conjagation have changes over the centuries so the meaning of similar) but that does not guarantee much. For example the modern Greeks neighbors Bulgarian use a word that does not relate them to their Slavic ancestry: Bulgaria. People don't choose their endonym but their endonyms often are misleading in determining the people origin.
3. Another important issue is how closer to ancient Greeks are the average modern Greek to the nearby people who don't consider themselves Greek, Slavic, Turkish people. I guess, judging by the intermixing, immigration, faith conversions that have occurred in this area not a safe conclusion can be made.
4. Similarly, I don't think that an actual optical similarity can be observed also. People nowadays are taller, and with usually more relative weight so little can be found matching. I am not suggesting that there was a dramatic change in appearance as though ancient Greeks looks like sub-Saharan people but we can imagine that they were darker (due to the nature of their work and also due to the climate). In ancient Greece there were lions (and I guess not only because they didn't hunt them down) which are now found in more tropical climates.
5. Due to the large changes the modern life has implanted in our lives I found it very difficult to compare culturally people with such a distinct time period in such a large context. If the context was narrower, like how close are modern Greeks to ancient ones as regards their language, phonetic system, food habits, rituals, regime, optical resemblance even social habits etc maybe a better answer could be given.

So, the question can be rephrased to how close do you expect modern Greeks to be to the ancient Greeks in comparison with other modern people. This is the part where the answer of @alexander coincides with mine.

One way to check Visually, is to look at those Ancient statues and study the nose length/style, feet, hands , eyes, etc

you find some people in Greece have that same classical look.

Cant say how many though

if you see anyone like this

or this

then most likely thats their great, great, great ............ grandfather

I don't believe this is by any means conclusive, and my evidence is a touch indirect, but I think genetic analysis gives us some interesting hints.

There seems to be a body of work that suggests comparisons can be made of historical events around the time of the ancient greeks by making comparisons between modern population.

Y-chromosomal evidence for a limited Greek contribution to the Pathan population of Pakistan in the European Journal of Human Genetics seems to suggest preliminary evidence of a tie between greek and parthian genetics, dating from the time in history when the world experienced a sudden increase in cities called Alexandria. As far as I can see this genetic information has been recovered from modern populations.

Population genetic relationships between Mediterranean populations determined by HLA allele distribution and a historic perspective in Tissue Antigens (a journal which better bedtime reading than it sounds) , also spins the story that the modern greek population betrays events dating back to the time of the Pharaohs.

The answer is rather paradoxical........it is both Yes and No.

Modern Greece was born in 1821 with The Greek War of Independence-(1821, for Greeks, is like 1776 for Americans). The Greek nation-state was born around 1828 with its First Capital on Aegina Island-(about 30 miles South of Athens and just North of the Peloponnese). Initially, the Modern Greek nation-state was primarily comprised of the Southern Greek mainland, parts of the Central mainland, Athens and the Cyclades-(the archipelago next to Mainland Greece). It would take 90 years-(from the 1820's until the end of the First World War) for what is today, the Modern Greek nation-state, to come into existence, that is to say, the inclusion of the Northern mainland, Crete and many of the Aegean islands. There was a brief return of the Ionian city of Smyrna-(present-day Izmir, Turkey) between 1919-1922, which was loosely affiliated with the Modern Greek nation-state under The Treaty of Sevres. However, other historic Greek territorial centers, such as Constantinople-(i.e. The "Old City" or section of Istanbul, namely the European side of the city), the Northern Anatolian Black Sea coast, parts of the Turkish Aegean coast and especially, the island of Cyprus, never achieved reunification with the Modern Greek nation-state. Today, much of what has been geographically and historically noted, has led to the current Modern Greek nation-state.

There are 10 million ethnic Greeks who live in Greece proper and approximately 800,000 ethnic Greeks who live in the Southern half of the island of Cyprus (included in the 800,000 are percentages of Greek Cypriots who once lived on the Northern half of the island, though were displaced after the 1974 Turkish invasion of Cyprus). There are tens of thousands-(perhaps even more) of Greeks who live in Southern Albania-(bordering Northwest Greece) and approximately 4 million persons of Greek descent who live in various Diaspora lands, such as, the United States, Canada and Australia. This is the contemporary historical and demographic reality of the Modern Greek.

As for the genealogical or ancestral nature of the Modern Greek and whether or not Modern Greeks are anthropologically related to the Ancient Greeks, this has been an age old question and apparently, it is still up for debate.

One must remember that the country of Greece-(as well as centuries old Greek Diaspora lands), experienced waves of conquerors, Traders and settlers from Antiquity, to the present-day. Minoan Cretans, Illyrians/(Albanians), Persians, Egyptians, Romans, Phoenicians, Mongol-Huns, Jews, Armenians, Georgians, Arabs, Slavs, Romanian Vlachs, Frankish Crusaders, Germanic Goths, Venetian Italians, as well as Seljuk and Ottoman Mongol-Turks, have all left a partial imprint on Greek history and on the Greeks themselves. I personally would be very surprised if there was a single Greek on this planet who could prove that he or she has a 100% uninterrupted Hellenic genetic line dating to Mycenaean times-(or earlier). This, (due to the long and complex demographic history that was discussed), would be a near genetic impossibility. However, I would be equally surprised if genetic tests revealed that the majority of Greeks living on this earth had very little or no genetic connection with the Ancient Greeks; this, would also be a near genetic impossibility.

In the 3500 plus year history of the Greeks, there is absolutely NO evidence for the widespread disappearance of the Hellenic race. Even with the well documented settlements and conquests that the Greeks endured over the millennia, there is ZERO proof of such a widespread population disappearance. Those who make such unsupportable claims, are either very ignorant of Greek History, very anti-Hellenic, or a little of both.

There was, however, one major and provable exception. We know from history that many Greeks living in Asia Minor-(present-day Turkey), were forcibly assimilated into the Turkish state and culture-(namely through intermarriage, though by other means as well) during the Ottoman Empire. Many-(though certainly not all) Asia Minor Greeks were thoroughly Ottomanized with regard to language, religion and overall self-identification as the centuries progressed-(this was especially true for the Janissare Corps). The Seljuk and Ottoman Mongol-Turks deliberately depopulated much of historic Greek Asia Minor, though the majority of the Hellenic population living in Greece proper and Cyprus.... largely survived Universal Ottomanization. In other words, much of historic Greek Asia Minor did indeed disappear with The Ottoman Empire, though there is barely any legitimate historical or genealogical evidence which proves that Modern Greek peoples-(on a widespread basis) converted to Christianity from Islam or originally descended from other lands, such as Albania or Slavic Europe. Again, those who make such unfounded claims, are fundamentally ignorant of Greek History. It is one thing to say that the majority of Modern Greeks have varying percentages of mixed ethnic descent-(such as having Albanian, Mongol-Turkish, Slavic or Italian heritage), yet, it is quite another thing to say that the majority of Modern Greeks have absolutely no genealogical continuity and connection with their ancient past without providing any legitimate historical, anthropological or genetic proof.

Overall, it is plausible to suggest that Modern Greeks have some fraction of mixed ethnic heritage, however, it is equally plausible to suggest that the Modern Greek has a sizable-(but not necessarily total) connection with his or her distant ancient ancestry. The annals of History, combined with contemporary advancements in archaeological and genetic technologies, can provide us with a wealth of evidence when looking into and examining this age old complex question.

There is an interesting map that shows the distribution of DNA among several countries of Europe.

This map shows that some haplogrupes are related to greek population (E3b and J2), actually, both haplogrupes are not usually associated to Europe, but to Middle East and Africa, which describe emigrations from the south and southeast. After 7th century we do not have many emigrations from those regions, because most known emigration came from within Europe (slavic and romans) or Turkish (haplogrupes that later where gone, one can see that Turkey has some haplogrupes that Greece does not have). Hence, those haplogrupes (E3b and J2) came to Greece earlier than those dates. Therefore, Greece still has some blood of ancient greeks, but strongly mixed with italic (R1b), slavic (R1a and I2a) and other minorities.

A study published in the August, 2017 issue of Nature claims to have established a link between the modern Greek population and the Mycenaeans based on DNA analysis from ancient remains.

From the paper's abstract:

Modern Greeks resemble the Mycenaeans, but with some additional dilution of the Early Neolithic ancestry. Our results support the idea of continuity but not isolation in the history of populations of the Aegean, before and after the time of its earliest civilizations.

Another paper published in BMC Evolutionary Biology in 2014 found genetic correlations between the current populations of Provence and Corsica with Asia Minor.

Simple answer: From ancient times all different ethnicities have been mixed with other ones more or less. The population of Greece has too. But the old Greek populations have never been exterminated, so its safe to say that present day Greeks are at a very high percentage descendants of the ancient Greeks.

Other contributions to the Greek genome come from Celts (raided Greece and some settled there), Slavs, and Goths (German tribe). People might think Turks had contributed too, but its the other way around. Todays Turks are mostly Greek in origin or "Anatolian" (non'Greek people who lived in Asia minor since ancient times).

Until the day comes that we have DNA technology (and theory) advanced to the point where we can look at the genetic lineage of large groups of people, really the best indicator we have for cultural descent is language.

Now language isn't perfect in this regard. For instance, there are a lot of people indigenous to the Americas whose language has been lost (or nearly so), and speak English or Spanish instead. There's also the Pygmies, who probably had a very unique language of their own originally, but today speak Niger-Congo derived languages (albeit with some intriguing holdovers). However, this in itself can be viewed as a good indicator of how thouroughly their culture got absorbed into the culture of the new languages.

So I think it is quite fair to view anybody speaking a modern language derived from ancient Greek as a cultural descendent of the ancient Greeks. It is also quite fair to view anybody speaking a Romance language as cultural descendants of the Romans. As Samuel Johnston said,

There is no tracing the connection of ancient nations, but by language; and therefore I am always sorry when any language is lost, because languages are the pedigree of nations

So from this standpoint, we would consider the French to be descendants of the Romans (along with Italians of course, and all other Romance speakers), but not the Germans or English.