I play on Monarch, and it is definitely possible to outperform the AI in tech, but it is usually necessary to kill off at least one (preferably two) neighboring civs in order to be really dominant. I go for the Great Library early on, which brings me even with the AI, and then I go all-out for Sun Tzu, the Sistine, Copernicus, Newton and Adam Smith's. Bach is nice if I can grab it, and I usually ignore Leo's.
Taking out a neighbor during the Middle Ages is usually a good idea (if you can trigger your golden age doing this, it will make the wonder building easier). Build up a bunch of Knights and pick fight. Hopefully, you will get a leader out of the war, with whom you should rush the forbidden palace. If the war goes really well, just wheel your army about and pick a fight with another neighbor. The reason you want to do this is threefold:
More cities for you, less for the AI.
More strategic resources for you, less for the AI
More luxury resources for you, less for the AI.
I don't feel comfortable until I have local access to at least 5 (preferably more) luxuries and all known strategic resources. Then its time to build up your new possesion, and do a round trades with the other AI's for gold/turn. That will improve relations and make you a ton of money (not to mention crippling their science rates).
I should mention that you must be careful, if you start the wars, not to do any more harm to your diplomatic reputation than absolutely necessary. If you cannot goad the AI into declaring war on you (best way is to demand things until they get to "furious" and then tell them to remove their troops from your territory), then you should formally declare war and then attack.
Often, my neighbors are not the "main rival" of my civ. They merely have the misfortune of being next to me... and hey, most of the time THEY attack ME, so all's fair. The key is locking up lots of luxuries and selling them to the other AI's for gold/turn. Once you have the tech lead, you can sell them a tech occasionally for OUTRAGEOUS sums of money (I like to sell them printing press... that's pretty harmless). With all that money pouring in, you can increase your science rate and rushbuild things as needed, while the AI is scratching and clawing to break even while running 70% taxes.
Pay close attention to wars on the other continent. Often, the AI's will break each other's cities, or at least capture them, which drops the cultural borders back to influence 1. Gaps will open up, and many times I've been able to sneak settlers over and grab luxuries that way. In my last game I got 2 furs, 1 spice and 1 incense that way, increasing my total access to 7 of the 8 types of luxury. End result: Hammurabi the Maginificent (3504 I think, SS win in 1824, with all 5 best cities in the world). I never fired a shot on the other continent. True, I killed the three civs that shared mine, but Persia and India attacked me (whereas I admit to coldblooded murder in the case of the Zulu). The AI was just getting to replaceable parts when I launched.