Taking a break from the game, and thinking about the great library, the two leaders that could potentially take it furthest are Trajan from Rome and Gorgo from Greece. Early culture is important, so Rome for example could totally ignore infrastructure and go on a wild settler spam early on, as every city it makes gives two extra culture right away. Free roads are a big plus as well. On the tech side Rome could beeline to iron working and grab legions. But before we even consider the math what do we get?
The main issue is that a lot of the ancient and classical eurekas are based on worker improvements which is something you want to do anyway. Even if we do settler spam entirely early on we still want to build improvements after great library is done, so those eurekas aren't worth much. Writing is required to build the GL, so we're potentially left with the sea techs up top, sailing, astrology, celestial navigation, shipbuilding; infrastructure techs such as currency, mathematics, engineering and lastly construction. I'm going to discount archery because it seems unlikely to go settler spam without making any slingers, so then the remaining eurekas are whatever type of improvements that we don't have resources to build on.
So that's potentially eight eurekas but three of them are purely for coastal cities. With the right conditions it could be worth it to execute such a narrow strategy to catch up on science. However I do think people miss the fact that the great library also gives two great work of writing slots though, and the only non wonder building that gives that is the ampitheater which costs 135 production to build after constructing a theater district. That's at least 270 production plus two districts and the great library itself costs 400 production.
In the end, the great library is probably not worth building unless you're executing a strategy to build it and to maximize eureka gain. Otherwise it belongs in the group of wonders that mainly serve to store great works and it's still unclear how much those are worth. If those are worth building then the Great Library is relatively cheap for two slots compared to the other wonders in this category.
The main issue is that a lot of the ancient and classical eurekas are based on worker improvements which is something you want to do anyway. Even if we do settler spam entirely early on we still want to build improvements after great library is done, so those eurekas aren't worth much. Writing is required to build the GL, so we're potentially left with the sea techs up top, sailing, astrology, celestial navigation, shipbuilding; infrastructure techs such as currency, mathematics, engineering and lastly construction. I'm going to discount archery because it seems unlikely to go settler spam without making any slingers, so then the remaining eurekas are whatever type of improvements that we don't have resources to build on.
So that's potentially eight eurekas but three of them are purely for coastal cities. With the right conditions it could be worth it to execute such a narrow strategy to catch up on science. However I do think people miss the fact that the great library also gives two great work of writing slots though, and the only non wonder building that gives that is the ampitheater which costs 135 production to build after constructing a theater district. That's at least 270 production plus two districts and the great library itself costs 400 production.
In the end, the great library is probably not worth building unless you're executing a strategy to build it and to maximize eureka gain. Otherwise it belongs in the group of wonders that mainly serve to store great works and it's still unclear how much those are worth. If those are worth building then the Great Library is relatively cheap for two slots compared to the other wonders in this category.