Yes, this can be an unpleasant aspect of the game, though I like to think of it as a renaissance of sorts with the great minds assembling in Copenhagen to discuss quantum mechanics.
I actually had to do some testing to get my head around this. One surprising thing I came across is that if you happen to amass large quantities of faith or gold in the Ancient Era, there appears to be no penalty for recruiting from an advanced era
hhhhh's "
Cost of Great Person" thread covers the basics with added detail. In particular, Lily Lancer's math as follows held for me:
diff=era of GP-world era when the GP first appears
cost=(1+0.3*diff)^diff*base_cost, round down to 5.
For example, Information era GP appearing at T165(Industrial Era), cost 1320*(1.9^3)=9050.
Note, in the Classical Era, where larger maps with more civilizations can quickly exhaust the base number of Great People, especially the Great Scientists, the exponential cost bites real quick: 30, 75, 305, 1440, 7725, 46875, 318015 for the respective eras on online speed. The cost recalculates upon reaching a new era, as the era difference is a variable in the cost, so the first Medieval Great Scientist in the Medieval Era may cost 75 points, but the next one will reset to the base cost. Similarly, the first Renaissance Great Scientist in the Medieval Era may cost 305 points, but the next one will cost 155.
I also think if by some strange miracle You are recruiting a person from an older era, the cost is cheaper.
The base cost did not appear to decrease favorably from era difference in my tests. Not sure how this works in terms of Lily Lancer's formula.
I also could not confirm a phenomenon I noted years ago where I could micromanage several projects to trigger simultaneously so I could pass on an expensive Great Person in order to pick up the following ones at base cost all on the same turn. When I tried that in the tests, I could pass on a Great Person but was unable to pick up the following ones despite having an excess of points. Has anyone else had this experience?
There are several mods on the Steam Workshop that greatly expand the number of Great People and this can really help improve the balance for larger maps and greater numbers of civilizations. Even with added Great People, it is still very much possible to run into the exponential cost.