Modern historians on the Ancient Macedonians and ancient Macedonia

[Ptolemy]

Early Macedonian religion clearly consisted of two distinct elements: The worship of the conquering Makedones under the Argead kings, and the pre-existing culs, mostly Thracian, of the territory seized by them. The religion of the conquerors was Hellenic: there is sufficient evidence for their worship of the chief Hellenic deities at an early period.

therefore, we should expect that even in the fourth century the Macedonians regarded the Bacchic rites as distinct from the purely Hellenic elements of their religion.

"The ancestral rites of Alexander the Great" by Ernest A. Fredricksmeyer

[Ptolemy]

The Macedonians claimed their descent from Hercules, and therefore had a kindred feeling with all the Dorian brotherhood; but as they were far inferior to the other states in civilization, they made little figure in history until the year B. c. 360, when the crown devolved upon Philip, only surviving son of Amyntas.

Ancient history, illustrated by colored maps, and a chronological chart, for the use of families and schools. By C. A. Bloss ... Revised and improved by John J. Anderson. by Bloss, C. A. (Celestia Angenette), 1812-1855.

All the stories relative to the early history of the Macedonian Monarchy and they were various —agree in tracing the origin of the family to the Temenids of Argos.

It was a common Greek opinion, moreover during the reign of Alexander, son of Amyntas is that the family of that prince was of Hellenic extraction; so much so that he found a place at the Olympic games, to which none but a genuine Greek could lay claim.

History of the world from the earliest period to the present time : collected and arranged from the best authorities
Author: Duyckinck, Evert A. (Evert Augustus), 1816-1878, p 443

[Tsontos]

"Elsewhere, Herodotos notes that the Spartans, the Korinthians, the Sikyonians, the Epidaurians and the Troizenians are of the 'Dorian and Makedonian ethnos'."

Jonathan Hall, Ethnic identity in Greek antiquity, Cambridge University Press, 1997, p.64. (Hall cites Herodotos 8.43.)

[akritas]

Of course Macedonian Kings after Alexander were agents for the spread of the Greek culture and Institutions throughout the Eastern Mediterreanean,...

[Borza, In the Shadows of Olympus, page 282]

[Ptolemy]

[quote]By Demosthenes the interval was spent rallying Greek opinion against the "barbarian", as he UNJUSTLY and INACCURATELY called the Macedonian. (the near-Greekness of whose culture is now revealed in a clearer light by such archaeological finds as the painted frescoes at Vergina, uncovered in 1977). That Demosthenes' PROPAGANDIST and political efforts almost succeeded is shown by the closeness of Philip's final victory on the field at Chaeronea (338)

"The Oxford history of the Classical World", page 132

[akritas]

[Mogens Herman Hansen,Polis:An Introduction to the Ancient Greek City-State,Oxford University Press, page 82]

So, the really problematic regions are Epeiros and Macedonia. For these my estimates are definitely much too low, and to reach the total number of Greeks—including Epeirotes and Macedonians, another half a million or rather more have to be added to the result I have obtained.

To conclude, if we include Epeiros and Macedonia, the total population of the Greek world comes to 7.5 million, and that is a minimum figure.
If we change one or more of the variables, we can reach 8 or 9 or perhaps even 10 million.