As the Greeks studied science, how did it begin to change their relationship to their religion and to their gods?

As the Greeks studied science, they started to realize that they didn't need the gods to explain the natural occurrences like disease, famine, weather, and etc. They started to look less highly of the gods and have proven these anomalies in an another way that can be explained. If they figured famine was due to drought or weather change, why need gods to explain to people that it is their gods own will and power.