What's the best way to increase my rate of research in Civilization 5? Is it purely a function of population and buildings, or is there something else I can do to speed it up (especially in the early game)?
There are a number of different ways to boost your research:
- Great people can be used to immediately complete a tech or build academies
- Research agreements gain you an extra tech for a fee (starting at 200 gold - see comments). You can have research agreements with multiple players (and it's advantageous to do so, if you have the cash)
- Many Wonders will increase research (in their city or in other capacities)
- Buildings like Libraries and Universities increase research, and gain further research bonuses when assigned specialists
- Policies - most of the Rationalism track improves research, and Scholasticism (under Patronage) grants you research from allied city-states
- City production can eventually be set so it all goes straight to research
I've answered a question asking how to increase production which in my opinion is pretty similar - though science is global, of course, and not local to a city. You basically have the following options:
- Increase the science output of your cities.
- A lot of building types increase the science output, as you've already mentioned in your question, and they do it in a scalable way - increased science per population or increased science percentage (as opposed to a fixed bonus), very useful throughout the game.
- Very few hex types yield science, with the notable exception of the academy, see below. However, many buildings have specialist spots that can improve science. So for example, if you build a university not only is the science output of the city increased, you can also allocate citizens to specialist spots given by the university, and those spots will generate science.
- Work towards getting great scientists. You can either just use them to get technologies for free - very useful in the early game when you want to get some of the stronger technologies - or you can create academies, which gives a specific hex a lot more science output - that's basically more of a long-term investment.
- Research agreements are a very good way to get new technologies. They take time and money, true, but the monetary investment is not that high and the time it takes is not that bad considering you research your own technology in parallel. You can sign on to multiple research agreements at once, so in effect you can have a large amount of research in parallel. The downside is that you cannot control what technology will be achieved.
The above points are not orthogonal - if you want a lot of technologies you should do all of them; i.e. allocate citizens to specialist slots, use buildings and abilities that increase the speed at which great scientists are born, and sign a lot of research agreements.
Research Agreements. As many as possible, as often as possible.
If you want to keep a tech lead, you need to spread out who you make the agreement with -- if you only have a single research agreement with the most advanced AI civ, you're not going to make any progress. But if you make a research agreement with the last-place player (perhaps gifting them enough gold so that they can pay their "half) AND the most advanced civ, you're effectively researching three different technologies at once to their two.
Set up those trading posts and get to work!
The answers already given (summed):
- Science buildings (library, university, observatory, public school and research lab)
- World Wonders (Great Library and Porcelain Tower) and National Wonders (National College and Oxford University)
- scientist specialists
- Great Scientists build Academies (a tile improvement) or Discover Technology (instant science boost)
- Research Agreements (available after you research Education)
- Social Policies (most of Rationalism, Scholasticism - Patronage, Mercantilism - Commerce)
- city Production (after researching Education, you can choose to make a city build science: the science generated is 25% of the production for that city)
Here are 3 additional considerations when maximizing science output, from most important to least.
- Tech path
- Trade routes
By far the most important is Population. A citiy's base science output for a city is equal to the number of citizens. The science buildings are more effective in larger cities. A city can work more specialist slots with more citizens. If you want to increase your science, anything that increases your population will help.
- buildings: Granary, Water Mill, Aqueduct, Lighthouse, Hospital, Medical Lab
- Wonders: Temple of Artemis, Hanging Gardens, Petra
Due to the importance of buildings and wonders in science output, your path through the tech tree can also play an integral role in determining how fast you tech up. They don't always have to be the first techs you research (within each era), but waiting too long before picking up these science techs could hurt your overall game.
- Writing (Ancient)
- Philosophy (Classical)
- Education (Medieval)
- Astronomy (Renaissance - if you founded a city next to a mountain)
- Scientific Theory (Industrial)
- Plastics (Modern)
The final consideration is trade routes. Science is transferred via international trade routes (between civs, CS trade routes do not apply) when 1 of 2 conditions are met:
- One of the civs have discovered techs that the other has not. If both civs have discovered techs that the other has not, they each receive a science bonus.
- One of the civs has achieved partial or full cultural influence over the other.