Social science
Social science is a category of academic disciplines, concerned with society and the relationships among individuals within a society. Social science as a whole has many branches. These social sciences include, but are not limited to: anthropology, archaeology, communication studies, economics, history, human geography, jurisprudence, linguistics, political science, psychology, public health, and sociology. The term is also sometimes used to refer specifically to the field of sociology, the original "science of society", established in the 19th century. For a more detailed list of sub-disciplines within the social sciences see: Outline of social science.
Science
Formal science is involved in the study of formal systems. It includes mathematics, systems theory, robotics, and theoretical computer science. The formal sciences share similarities with the other two branches by relying on objective, careful, and systematic study of an area of knowledge. They are, however, different from the empirical sciences as they rely exclusively on deductive reasoning, without the need for empirical evidence, to verify their abstract concepts. The formal sciences are therefore "a priori" disciplines and because of this, there is disagreement on whether they actually constitute a science. Nevertheless, the formal sciences play an important role in the empirical sciences. Calculus, for example, was initially invented to understand motion in physics. Natural and social sciences that rely heavily on mathematical applications include mathematical physics, mathematical chemistry, mathematical biology, mathematical finance, and mathematical economics.