Everybody around here says that the mayans are an excellent science civ. I don't really get what's so incredibly awesome about +2 beakers from their pyramid UB. What can you do with the mayans to make them a science powerhouse??
And also, what's the best great person to pop first with your UA? In general, how can I make the mayans really shine??
The answer to the second is the same as the (partial) answer to the first. Maya will get a Great Scientist before anyone but Babylon, which means an early academy and faster progress. But this is just part of the equation. Consider:
1. Firstly the pyramid is not just +2 from a UB. It's +2 from a very cheap UB that can be built in any city you have. Think of it as being the equivalent of Korea at the stage when they get Drama & Poetry (the first specialist building unlockable along the science tech path being the Amphitheater, fast faithing to cathedrals aside) - except that at that point Korea has to take population off duty in each city to get the same bonus the Maya get right at the start of the game.
2. On a related note, +2 science is not +2 science forever and ever. The Maya tech advantage kicks in earlier than Babylon's first GS or Korea's one-off library boost, and much earlier than Korea's or than Babylon's GP production bonus becomes relevant. This means quicker progress through early techs, putting you in a better position to get Education early, grab key Wonders before anyone else, etc. While it's true that the 2-3 very quick GPs make it difficult to get Great Scientists later in the game, because you've reached the relevant techs so much earlier than anyone else you have more time to develop them - your university specialists churn out the points more rapidly, and you're simply ahead of the curve techwise anyway so can afford to slow down a little (but not too much - I got an unpleasant surprise when Bismarck went from 6 techs behind me to tech leader between the Industrial and Modern periods, possibly through faith-buying GPs).
3. Unlike Babylon, Korea or indeed anyone else, the Maya don't need to worry about prioritising archery, on a tech path they otherwise don't need immediately, early in the game. So they're pretty much free to beeline to Theology (which just happens to be on the science tech path) straight away. With civ start bias enabled, the Maya tend to spawn around plantation luxuries, so again can use their standard tech path to improve their early cities as well.
4. Science isn't just about pure beaker production. It requires buildings and, of course, key Wonders. And which is the only civ in the game that gets a Great Engineer as part of its UA? Take a guess. Normally with the Theology beeline you'll get your second or third GP just as you reach Architecture, which means you can rush Porcelain Tower straight away - and that GE effectively turns into a GS. Plus you have a bonus from research agreements.
5. The Pyramid (and UA) have another effect - religion. The Maya will get a Pantheon earlier than most civs, and with a Great Prophet from the UA (usually as second or third GP as I play), can enhance religion early as well. This isn't so important against AIs, which seem to prioritise neither Messenger of the Gods nor Interfaith Dialogue, however your wide Maya empire will love farming science from those trade routes as soon as it can do so, and extra faith production means faster missionary production which means more science from Interfaith Dialogue. At higher difficulty levels, Babylon and Korea may not get any religion at all, let alone first pick, so these bonuses may be closed to them (and neither is likely to get as much out of Messenger of the Gods as the Maya).
Overall, the Maya are a subtly and cleverly-designed science civ - their UA isn't about raw production, it's about securing a strong game position early on. They get to choose early GPs and those most useful for their strategy, they reach key techs earlier in the game than other civs, and the tech-free atlatlist gives them the flexibility to optimise their early tech progression.
per new city with Messenger of the Gods + Pyramid. Rapid expansion behind Atlatlists and Composites will protect you from most anything, even Hiawatha and Montezuma. Disclaimer: Trying this on Deity is stupid... you will die very very hard 
