In order to maximize science, you have to maximize trade, build the right wonders (in the right places) and make good trades (the tech devaluation in 1.17 works both ways - once a tech has been around for a while, you can pick it up for next to nothing).
I go for the Great Library, and my strategy revolves around getting it. There are other ways to go about it, but this is the one I like (Monarch level):
I beeline for literature, while using the Pyramids as a shield holder in my best city (probably my capitol). If I'm not industrious, I buy masonry. Anyway, I expand as rapidly as possible, building temples in my new cities, with only a minimal military. As soon as I get literature, I build libraries in my core cities (and start them in the far away ones, in order to save shields for the courthouses to come). After discovering literature, I beeline for currency. The Great Library will be finished before I discover it, and the GL will get me everything BUT construction, currency, republic and monarchy. I will switch my outlying cities to courthouses (unless, of course, they are so far out that they're not worth it).
If I am blessed with a coastal city with low corruption, I'll take a shot at the Colossus. It is a wonder that the AI often neglects, and it doesn't take too many shields to build. Having a decent coastal city early on is a matter of luck, however.
Anyway, upon getting currency, I build marketplaces everywhere. The more overall money you have, the more you can afford to spend on science. I will also gain construction and monarchy from the GL, while I research republic. Large cities build colloseums, and my capitol starts on the Hanging Gardens while my best production city (other than the cap) starts on a "palace." After getting republic, I switch gov'ts and start researching feudalism. The capitol switches from Hanging G. to Sun Tzu... then I beeline for Theology and the #2 city gets switched to either Sun Tzu or the Sistine, depending on which city will complete its wonder first (I want the Sistine done first - it's more important to me). Meanwhile, other cities are building cathedrals and aqueducts and such things. I now normally go for Engineering, and if the AI isn't breathing down my neck, Invention too, before going for Education. If I can get Leo's, fine, otherwise, no biggie. Shields will be saved, however, for Copernicus. I often discover Education myself, rather than getting it from the Library. I want the get those universities built, and I want to get to Astronomy quickly, for Copernicus. After Astronomy, it's Banking and Economics - Adam Smith's is ESSENTIAL. Banks are built just about everywhere (there are exceptions to every rule, but I pretty much build 'em in any city that can do it in under 25 turns), and Wall Street is built asap. If I feel that I have the time (and a spare city to build Bach's), I will research Music Theory. Then over to Theory of Gravity (often the AI will go up the other tech line, getting gunpowder ahead of me, and I will buy that from them). If I can get Copernicus/Newton in one city, I obviously try to.
If all of the above goes according to plan, I will be well situated to grab a good tech lead in the Industrial Age (basically, I get my railroads and factories online, go for ToE, which gets me to Electronics, build Hoover, and then backfill).
It tends to work well, but it requires that several things go right. An early AI attack will wreak havoc on this strategy. Also, you need contact with several civs (2 at the very least) for the GL to work properly. Hopefully, your peaceful expansion will get you some luxuries. At the very least 2 - and if that's the case, you'd better have a lot of those 2 so you can trade - preferably 3. More than 3 local luxuries is excellent. I normally do my fighting in the medieval and industrial periods. A Middle Ages golden age is great for building all those wonders and expensive improvements, not to mention finally building something resembling an army.
I find that the civs that fit best with this strategy are the Babylonians and Egyptians. I wouldn't use this with the Chinese or Zulu, for example, because it doesn't play to their strengths.
Anyway, this is one way to go about it.
-Arrian