In the ancient era I may have +32 science and it takes 18 turns to research the Wheel, for instance. In the modern era I may have +520 science and it still takes me 18 turns to research Atomic Theory, for instance. Why does the increase in science points not hasten the research itself? Or does it? Thank you.
It does decrease the time for researches significantly, just the techs take more points. Researching The Wheel takes 55 science points in a regular speed game, so that would take two turns at 32 points per turn. Atomic Theory takes 2470 science points on regular, so that would take five turns at 520 per turn. However, if you didn't upgrade science researching Atomic Theory would take seventy-eight turns. So, upgrading science does speed up research, just researches take longer too.
Different technologies cost differing amounts of science points. For example, the Wheel costs a paltry 55 science points, while Atomic Theory costs 2470 science points.
The numbers in your post don't make too much sense to me; I think it's more likely you're confusing the amount of science generated per turn with the amount of scientific progress toward a specific technology. These points are consumed when you acquire the technology.
As you progress through the game, your science generation will naturally increase through the construction of science-oriented buildings like the University. This is so that as the required amount of science points increases, so does your scientific income. This means that the approximate amount of turns to research an Ancient Era technology won't differ too much from the approximate amount of turns to research, say, an Industrial Era technology.
Some techs have a higher amount of science points needed for researching them. So +22 science into a tech that needs 110 science will take 5 turns