I have been looking @ alot of AAR, ppl are playing on king, immortal levels and still achieving high levels of science (500-1000sppt) I have manage to get 300sppt if I am lucky on prince level. Ill try and work the tiles around my city for the best science ppt and build science building. But some of the player are acheiving this with only a handfull of cities (5-8) I get 12-15 cities and still only get about 200-500ppt. What am I doing wrong?

Specialists, max out all the specialist slots.
I also usually like to get all the science wonders in one city (generally cap) to boost it the most.
Being beside a mountain allows for Observatories, and +50% science is huge.

Honestly though, most importantly, get the Porcelain tower and sign RAs.
This doesn't affect your science/turn, but it gives you more from your RAs than the AI, and the AI will sign RAs with or without you.

For raw science libraries, unis (staffed) and good growth will do you well. Add in the observatories wherever possible and you'll keep up just fine through Emperor.

For instance, I just peeked at a recent game I did where my goal was raw science and a 10city x 10pop empire. On turn 230 I have 11 cities at 9pop or better and 513:c5science:. To illustrate the effect of Unis/specialists, one of the 10 pop cities is a puppet and has only a library, and produces 15:c5science:, another is a normal city and has a staffed Uni (still 10 pop) and produces 28:c5science:. At 230 I was starting a round of public schools in most of the cities, and at turn 270 I was producing 780:c5science:. Those same two cities were at 13pop by then and the puppet was at 20:c5science: (still just a library) and the other city was at 55 :c5science: after getting an (unstaffed) public school.

(unstaffed) public school.

Well, that's almost real-life right there! Underpaid, understaffed, and underwhelming.

if you're going for raw beakers only, you are ignoring 2 important sources of science - RAs and GSs. I'd generally recommend utilizing at least one of these two supplementary sources if you're playing above price.

That being said, if you really want to go raw beakers, focus on happiness and food, and the population/science will follow. It's doable up to immortal level, but pretty difficult there.

Well, that's almost real-life right there! Underpaid, understaffed, and underwhelming.

I have 3 and 5 yo kids, that hits too close to home. :(

What the others have said and never clear jungles.

If you take the left side of rationalism and the right side of freedom, you'll be able to run more specialists, manage happiness from those larger cities and gain 2 beakers per specialist. Running just 5 specialists each city, that's an extra 10 beakers per city before the multipliers. With the rationalism policies, universities (+33% without the policy 50% with it) and observatories in all those cities, that 10 becomes 20. In he city with the national college that's another +50% so the 10 becomes 25. All this just from the specialists after taking the policy in rationalism. Each scientist specialist is another 3, so an additional 9 per city that has both university and public school if their slots are filled.

In total that's 19 per city before multipliers from running 5 specialists, if 3 of them are scientists. that's a possible 38 beakers for normal cities and 47.5 from the NC city. Plus the science from population.

If you're playing as Korea, add another 2 beakers per specialist from the UA, before the multipliers.

I have 3 and 5 yo kids, that hits too close to home. :(

Yeah, a buddy of mine home-schools his kids(around the same age as yours) because of that problem. On the topic of in-game science, I'm not to good at the whole RA thing, but even so, I still manage to get mech. inf. in the late 1700's/early 1800's. Not spectacular, but waaaay ahead of the AI on Prince. Tall beats wide, and happiness is actually a factor, especially if you take Rationalism and the policy that gives you a science boost when happy. Get science buildings up when you tech them, tech towards Civil Service for the food boost, grow your cities, ESPECIALLY your capital, grab the science wonders if you can, and save GS's for expensive techs, instead of using them right away. With a handful of GS, you can bulb through entire eras, if you line things up right. It takes a while to get the hang of things, but it really helps. Liberty is a great policy to take for an early rush strategy, getting the GS to bulb Education is great.

Looking at my science city 'Fong Sai Yuk'

48 from terrain
16 from buildings
26 from specialists
28 from population
28 extra from population

City Modifier: 200%

City Total: 428.25

Civ Total: 1269