I've had a quick look and I'd like to repeat some of the things that I said along with some game specific advice.
1. Don't build things that you don't need.
You have some pretty useless buildings and top of the list is a courthouse in your capital. Your capital will not suffer corruption or waste so you are simply giving away money with buildings that are not worth it. The fact that you were spending more on building maintenance than on science should be of concern IMO.
2. Many people will tell you not to build temples and cathederals but to use the lux slider instead. Personally I think that they have their place in some games but only when they are needed so I'm tempted to lump some of them into the useless building catagory. (I don't rate colloseums though,; they really are not worth the shields or upkeep!) You've used both religious buildings and the lux slider and so you are spending more cash keeping people happy than you ned to. This could be spent on research. I left the buildings alone (even though I was tempted to sell them) but I did drop the lux slider to zero as no town needed it. I also put those specialists to work and this enabled me to double research as you can see from the F1 shots, before and after the alteration to the sliders.
3. If you want to research fast, use a representative government. At the moment you have one option: Republic. I ditched Monarchy and after a few turns I came out of anarchy (after razing an American town for a laugh) and adopted Republic. Now look at the F1 screen.
Without doing much at all I've increased you science budget from 93gpt to 317gpt so you will research three times as fast. Maybe if you had been in Republic from the start you would be behind in the tech race.
I could talk about building some more towns on your island plus more on the island to the north but this will take time. What I have done has had an immediate effect. If you carry on with this game, I suggest that you switch those bank builds to settlers and workers. More towns=more commerce and you've got room for quite a few.
To be fair to you, the start was not the best as you were on a small island whereas many of your rivals were on a big continent. Getting rid of the Chinese must have helped so well done on that. (However you must have broken a deal with them as your rep is ruined. I couldn't trade that spare iron with the Romans for a tech as word has spread of your broken trades.) I am not sure how far into the IA your rivals are but I reckon that you could catch up. The AI get obsessed with Nationalism, Communism and Fascism which enables the human player to get the important techs.
Next time though, use Republic asap!