Why is the Great Library so good?

I seem to read in all kinds of places how awesome the Great Library is in Civilization IV, but not why.

Two free scientists in the city it's built doesn't seem too special. Why is it good? Is it only useful in certain strategies?

It's been quite some time since I've played Civ 4, so I'm no longer familiar off the top of my head with the average acquisition date of the GL or the average economic situation (in terms of science output and expenses).

But from what I can recall, the raw science output of the two free scientists (7.5 beakers) is ~10-15% boost to the total beaker output of your whole civilization at the time, which isn't too bad. That's like having half a library in every city you have, and independent of your slider position as well! If you also have the Pyramids and are running Representation, that's 15 beakers instead of 7.5.

In addition, don't discount the GPP (Great Person Points) generated by the library and the scientists. That's 8 GPP (6 from the scientists, 2 from the library) that doesn't need to be fed, unlike regular specialists. Even if you don't care for running a specialist focused economy, that adds up to a Great Scientist in either 13 or 25 turns (depending on whether the GS is your first or second naturally generated one). That's a free academy (+50% science in a city) for you.

And if you are focusing on specialists, mash that together with two regular scientists, Pacifism and National Epic (and the Philosophical trait if you have it) and you will be rolling in Great Scientists. These tend to be used to quickly lightbulb through Philosophy, Paper, Education, and Liberalism in the space of a few turns to slingshot to a dominating position.

It's definitely one of the most powerful wonders.