I do not think that science solves any problems. Problem-solving is usually the domain of engineering, although the two do frequently overlap.
Science also does not deal with abstractions. It deals only with what exists concretely, and with cause-and-effect. Anything which claims the existence of a thing or a causative correlation between things falls under the domain of science.
Abstractions are left to non-scientific fields like logic, mathematics, statistics, and philosophical schools like theology, aesthetics, metaphysics, linguistics, etc.