I'm reading "S.P.Q.R." by Mary Beard now, and was surprised by the following passage:
“Barbatus’ Rome was very different from the Rome of the earliest Republic, two hundred years before, and it had ceased to be ordinary. Vast by the standards of the time, the city was home on a reasonable guess to something between 60,000 and 90,000 people. That put it roughly in the same bracket as a handful of the biggest urban centres in the Mediterranean world; Athens at this point had a population of considerably less than half that number, and never in its history had more than 40,000 in the city itself.”
40 000 for the Athens seemed like unusual small number to me, so I tried to check this number at Wikipedia — 250 000 (but only 30 000 citizens). Is Mary Beard mistaken here, or there are different evaluations?
She seems to be talking about the urban centre only ("the city itself"). It is not at all improbable that Ancient Athens never had more than 40,000 people permanently living within its walls. The rest of its population was living in smaller settlements scattered around the region of Attika, which was Athens' domain. Some of these settlements, like Eleusis and Acharnai, were quite large - large enough to provide several thousand hoplites for the Athenian levy.
We do not have sources for the size of the total population of any Ancient community. Any population total you might find (like the 250,000 Athenians mentioned on Wikipedia) has been extrapolated from the number of adult male citizens. Usually, that is the only figure we get, because it was relevant to army size and the extent of political franchise. For the same reason, estimates of the population living within the urban centre of Athens are similarly rough and not to be taken as hard fact. The same goes for Rome, as you can see from the extremely broad estimate offered by Beard.
Just to amplify /u/Iphikrates's point, there are two things we call Athens: the city and the state, the former a walled area of perhaps 200 ha, the latter corresponding to the far wider Attica region with about 2,500 sq km: the actual city in other words covers less than a thousandth of the area of the wider "Athens". So both numbers are broadly correct: 200-250,000 for the polis, perhaps 30-50,000 for the then city proper (I've read conflicting statements about an urban population outside the walls). It used to cause me no end of trouble too, so I understand the confusion. I tend to use Attica for the polis when matters of economy or regional demography are involved.