Definition from wiki: http://en.wikipedia.org/wiki/Science

Science, in the broadest sense, refers to any system of objective knowledge. In a more restricted sense, science refers to a system of acquiring knowledge based on the scientific method, as well as to the organized body of knowledge gained through such research.

Fields of science are commonly classified along two major lines:

• Natural sciences, which study natural phenomena, including biological life;
• Social sciences, which study human behavior and societies

These fields are empirical sciences, which means the knowledge must be based on observable phenomena and capable of being tested for its validity by other researchers working under the same conditions.

Mathematics is sometimes classified in a third grouping, called formal science, having both similarities and differences with the natural and social sciences. It is similar to other disciplines in that it involves a careful, systematic study of an area of knowledge; it is different because of its method of verifying its knowledge, using a-priori rather than empirical methods. Mathematics as a whole is vital to the sciences; indeed, major advances in mathematics have often led to critical advances in the physical and biological sciences. Certain mathematical approaches are indispensable for the formation of hypotheses, theories, and laws, both in discovering and describing how things work (natural sciences) and how people think and act (social sciences).

Science as defined above is sometimes termed pure science in order to differentiate it from applied science, the latter being the application of scientific research to specific human needs.