when to fill specialist slots?

I play on immortal and am having trouble with my science game. It is taking me until the industrial or modern eras to catch up, which I know is way too slow and I will get killed on diety. I think my problem starts with the education tech and specialists.

Once I get education, when should I use specialists? My general rule has been "when all the +3 tiles are being worked in the city," but I am not sure that's the best rule.

When do you fill the slots? As soon as you get universities? After the city gets to a certain pop? After you get a cargo ship with food?

And a related issue, when you do fill the guild slots? I'm having real trouble in culture games keeping all the slots filled to keep beakers going and art pieces coming.

I only started playing Immortal recently. I usually put two scientists in my university right after I build it. Typically I will take the specialists off mining spots so that I don't slow my growth down.

This slows production down but eventually the city will grow and work those spots again.

I fill the guild slots when I want to make the great artists, etc. If I want to crank them out I get them filled. If I'm not going culture and I am going with the popular ideology then I will leave them empty for awhile sometimes.

Don't underestimate the power of having gardens.

Usually in your capital you have an 83% science modifier (NC + University), so you want to fill all scientist slots ASAP. At the same time the capital should grow as fast as possible for even more science.

Decide depending on the size of food box resp. time it takes for a new citizen to be born, the food tiles available and % food/growth modifiers.

With a food cargo ship for the capital you can have both: max scientists and good growth.

Prioritize the science specialist slots and growth. If needed (war / wonder) switch to production tiles while leaving as many science specialists working as possible.

If you send food caravans to the capital, especially over water, you can work production tiles and specialist slots.