The branches of science, also referred to as sciences, scientific fields or scientific disciplines, are commonly divided into three major groups:
Formal sciences: the study of formal systems, such as those under the branches of logic and mathematics, which use an a priori, as opposed to empirical, methodology.
Natural sciences: the study of natural phenomena (including cosmological, geological, physical, chemical, and biological factors of the universe). Natural science can be divided into two main branches: physical science and life science (or biology).
Social sciences: the study of human behavior in its social and cultural aspects.
Scientific knowledge must be based on observable phenomena and must be capable of being verified by other researchers working under the same conditions. This verifiability may well vary even within a scientific discipline.
Natural, social, and formal science make up the fundamental sciences, which form the basis of interdisciplinarity - and applied sciences such as engineering and medicine. Specialized scientific disciplines that exist in multiple categories may include parts of other scientific disciplines but often possess their own terminologies and expertises.
Formal sciences
The formal sciences are the branches of science that are concerned with formal systems, such as logic, mathematics, theoretical computer science, information theory, systems theory, decision theory, statistics.
Unlike other branches, the formal sciences are not concerned with the validity of theories based on observations in the real world (empirical knowledge), but rather with the properties of formal systems based on definitions and rules. Hence there is disagreement on whether the formal sciences actually constitute as a science. Methods of the formal sciences are, however, essential to the construction and testing of scientific models dealing with observable reality, and major advances in formal sciences have often enabled major advances in the empirical sciences.