Going wide, but staying ahead in science... How do I do it?

I'm not sure if this has been mentioned but if you are looking to found new cities it can be useful to keep a lookout for mountains. If you settle next to one eventually you can build an observatory that gives a 50% science bonus. If you settle your second or third city on a mountain it may be worth building the national college in that city and running food routes to it as well as planting Academies nearby.

Jungles with trading posts are also valuable ways of increasing science.

Also try to keep the more powerful Civs at war with each other by paying them to DoW on the diplomacy screen. If you can get them to DoW a friend that counts as a backstab. Other Civs will be reluctant to befriend them and therefore that Civ will miss out on Research Agreements.
Also make sure you have some friends you can sign research agreements with.

Also don't neglect espionage. It's best to send your spies to a Civ that is ahead of you in science but not in the lead. The leading tech Civ will use their spies defensively but if you put your spies in the 2nd leading Civ you should have a better chance at tech stealing. You can use the demographics screen to help you work out who is ahead and also by what Units and Wonders your neighbors are building.

I also recommend buying or building universities in your science cities as soon as you get education. If you have friends it is well worth taking a loan so you can get these buildings quicker.

If you have trouble I would suggest turning the difficulty down 1 and play Babylon or Korea. Borg of those Civs have huge benefits to Science.
The Oracle is a good wonder to build as it gives you a free Scientist Point which will make it easier to get a Great Scientist once you get universities.
 
However there's definitely something going on when Russia reaches the Atomic Era in 1890.

Yeah, there's something wrong. It's just not what you think is wrong.
 

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