The specialists that ChaosArbiter is talking about are the citizens that you turn into entertainers/taxmen/scientists[/civil engineer/policeman]. A good rule of thumb for specialists is that if you don't need an entertainer to stop a riot you should make a taxman or a scientist depending on whether you need more money or more research.
This is the core concept of science farms.
And what do science farms do? A quick example.
Your next tech costs 1000 beakers. With science at 100% your commerce and science buildings make 200 beakers per turn. And thus it will take five turns to learn it. If you can hire 17 science specialists (geeks) in your cities, they will produce 51 beakers per turn (3 beakers per geek). Now, instead of 200 bpt you have 251 bpt and you learn the new tech in 4, not 5 turns.
After you hire the geeks you decide to drop your science to 0%. Now you get no beakers from commerce and libraries/universities. Zero. Nada. However, the geeks you hire are not affected by the science slider. Whether at 0% or 100%, they still produce 3 bpt each. These 17 geeks will learn your next tech in 20 turns.
Now if you could hire 85 geeks, which becomes 255 bpt, this tech could be learned in 4 turns.
So science specailists are powerful. How do you hire 85 of them?
Create science farms. These are cities that are very corrupt. They net 1 shield per turn for every 10 shields they produce and they don't net 2 spt until they bring in 11 shields. These are cities far away from your capital. It takes them 10 turns to build a worker and 30 turns to build a settler. Generally they have few improvements, except maybe an aqueduct.
Since these cities are so corrupt and non-productive, don't try to make them build anything, because they cannot build anything fast unless it is rushed and that will cost you gold or population, depending upon your government type. Set them to wealth or artillery. (Artillery units are not enhanced by barracks; there are no Veteran or Regular or Elite catapults; they are safe build in the Geek Havens.) Irrigate everything around these cities. Then, once the city cannot grow any larger, rearrange the citizens to where each city can hire some geeks and not starve. Flood plains help a whole lot with this, too. So do rails. Grassland is better than plains for grassland gives 2 food per turn and plains only 1.
On a grassland site, a science farm seem to average 3 geeks at size 6.
And, since most of the population are specialists, they are not affected greatly by happiness issues, such as luxuries and war weariness. If they get cranky, hire a geek early. It slows down their growth some, nothing more.