The fundamentals involved with rapidly gaining scientific discoveries lie in science spending, scientific institutions, scientist citizens and diplomacy. The more you have of the former three and the better you have of the latter, the faster you can get those discoveries. (So far, in my 2nd game of Civ3 as regent, I've been able to discover Stealth by the beginning of the 19th Century. I don't know how this compares to other Civ3 players, but in comparison with rival Civs, I'm sometimes in the Modern era before some are even in the Renaissance. Those closest to me in the tech race are usually 5 or 6 discoveries behind, minimum.)
Anyhow, back to the 4 fundamentals; all of them can be linked to one thing, money. The more money you're earning, the more you can put into scientific research, the more you can afford to buy and maintain scientific institutions, the more you can afford to have scientist citizens, and the more you can afford to buy the what I call the "secondary" advances (By secondary I mean those advances that do not lead to other advances and do not allow for any crucial wonder/unit/improvement advance...some examples would be Free Artistry and Amphibious Warfare). I find it better to just buy or trade for those from other civs when they acquire them, unless whatever improvements those discoveries bring are vital to my game strategy.
So the more important question that should be raised is "How do I get more money"? For that, here's a list of what I've found to be useful in bringing in the moolah
1) Government type: Democracy is probably the best government choice for those who choose to take a more peaceful, scientific and cultural approach to the game. The added 150% in productivity also transfers to your ability to build scientific improvements/wonders faster. Democracy also lowers corruption significantly, thus allowing for more money to be spent and not wasted. This brings me to...
2) Corruption: The less corruption you have, the more shields and taxes are allocated to your income, rather than the garbage. If you want tips on how to keep corruption down, just take a look at the helpful post "Stickied" at the top of this forum.
3) Tile improvements: Roads will improve commerce which will thus increase the amount of money you bring in. When choosing to mine a mountain, pick the ones with gold or iron, they get you more commerce or resources, respectively. Get a lot of workers out there, improving tiles as needed. For example, if you have a city of 5, don't spend the time of 4 workers improving all those tiles in one go. Just improve 6 or 7, max, then move on to the next city that requires improvements. There's no point in improving tiles that won't be used for many turns to come. Just ensure you have enough workers to keep up with the demand.\
4) Peace: Try to stay out of wars, especially if you're in a republic or democracy. War weariness will force you to either increase the luxury rate, meaning you'll probably have to drop the science spending, or create entertainers by removing people from the field, thus removing the commerce they brought in. Also, if you plan on being the aggressor, you'll need to build up an army and support it, meaning you'll have to reallocate resources and funding to building and maintaining (resp.) your army, leaving you unable to build scientific institutions and less cash to pump into your scientific spending. But don't expect to stay at peace throughout the whole game; you'll be attacked at least once so make sure you have a sufficiently sized army to keep your cities and borders defended, and a few offense-intended units to repulse any pillagers from your improved territory. Just on a side note, I remember when I spearheaded an attack to conquer the continent I was on so I could grab some resources, luxuries, land and cities. Unfortunately, I had to trim down my science spending to almost 0% due to war weariness/unit costs/lost trade, etc. so for 20 turns I did not make a single discovery. That gave time for the other civs not involved in the war to come close to catching up. A rule of thumb I learned: Always plan on having a war last longer than planned. But you can see what effects conflicts have on science.
5) Empire size: To simplify, the more cities you have (within a limit that makes corruption and insignificant issue...once again, see the post at the top of this forum), the more revenue you're earning (also the more you're spending on institutions, but if you balance it out right, you'll do great), the more scientists you possess and the more resources/luxuries you should have at your disposal to trade. All of these have side-benefits/disadvantages/problems that I could go into, but won't because it'll take too long, but you get my drift
. Expand early, develop early/mid, win mid/late. Those get mixed around a lot, but there's no such thing as an entirely accurate or precise simplification.
6) Improvements & Wonders:
i) Science - When building wonders that improve science, try to concentrate them in the one city gaining you the most commerce (therefore science) and with a quick enough productivity to keep you up ahead in the Wonder Race (this is very important early on when you're about neck & neck with or even behind other civs in the science race). Also go for libraries in all your cities, Universities in cities with 6-8 or above pop and research centers in cities with 12+ (or if you're doing financially well late enough in the game, you can just throw them in whenever you feel like it). The reason for limiting some institutions to certain sizes is that sometimes the benefits are outweighed by the costs. Try to keep them at least balanced.
ii) Commerce - Create wonders and improvements that help you save or make money. Some do it directly (e.g. Smiths Trading Co., the Banks, Wall street, etc.) while others have an indirect effect on the amount of dough you rake in (e.g. Pyramids). The latter are the one that save you the cost of having to build, maintain or upgrade improvements and units.
7) Early Exploration: Early on in the game, check out those huts. You'll often find they contain some good Ancient era advances that'll give you a good head start over the other civs. Sometimes you may also find settlers who'll help in expanding your empire; another bonus. Although sometimes you'll find some barbarians, but that's all part of the risk.
When you try to leap ahead in science, you take the risk of having your civ take on serious injuries or even death. Always be sure to keep your defenses on high, especially in your frontier towns. The larger and more important a city, the larger/better the defensive force in the garrison should be. Also try connecting all your cities by roads (and railroads) later on so you can devote units from the center (in both the physical and usually productive sense) to the defense/counter-attack more quickly.
Here are two small tricks I use:
1) In the Domestic Advisor screen you'll notice that if you toggle the science rate, you'll get a discovery in the same number of turns with a lower percentage. For example, when researching Rocketry, you'll still get the advance in 4 turns with 30% spending as you would with 80%. Make sure that when you're starting the path to a discovery to keep spending as low as possible while also keeping the number of turns to that discovery as low as possible without going too far into the negatives (If you're only losing 1-3% of your account balance then that shouldn't be a problem. You can usually make it up with this next trick)
2) Also in the Domestic Advisor screen, the turn before you make a discovery, toggle the science spending as low as possible while keeping the number of turns to that discovery at 1. This saves you the money you would've wasted on overlap.
-Maj
P.S. If I spent this much time on my assignments I'd probably be getting better marks. But then again...if I liked my courses as much as I did Civ 3, I'd probably be spending more time writing those assignments
