A formal science is a branch of science studying disciplines concerned with abstract structures described by formal systems, such as logic, mathematics, statistics, theoretical computer science, artificial intelligence, information theory, game theory, systems theory, decision theory, and theoretical linguistics. Whereas the natural sciences and social sciences seek to characterize physical systems and social systems, respectively, using empirical methods, the formal sciences use language tools concerned with characterizing abstract structures described by formal systems. The formal sciences aid the natural and social sciences by providing information about the structures used to describe the physical world, and what inferences may be made about them. Etymology The modern usage of the term formal sciences in English-language literature occurs at least as early as 1860, in a posthumous publication of lectures on philosophy by Sir William Hamilton wherein logic and mathematics are listed as formal sciences. Going even further back to 1819, a German-language textbook on logic was published by Wilhelm Esser, elucidating the significance of the designation formal science (Formalwissenschaft) as applied to logic; (an English-language translation of it is provided in a William Hamilton's lecture): History Formal sciences began before the formulation of the scientific method, with the most ancient mathematical texts dating back to 1800 BC (Babylonian mathematics), 1600 BC (Egyptian mathematics) and 1000 BC (Indian mathematics). From then on, different cultures such as the Greek, Arab and Persian made major contributions to mathematics, while the Chinese and Japanese, independently of more distant cultures, developed their own mathematical tradition. Besides mathematics, logic is another example of one of oldest subjects in the field of the formal sciences. As an explicit analysis of the methods of reasoning, logic received sustained development originally in three places: India from the , China in the , and Greece between the and the . The formally sophisticated treatment of modern logic descends from the Greek tradition, being informed from the transmission of Aristotelian logic, which was then further developed by Islamic logicians. The Indian tradition also continued into the early modern period. The native Chinese tradition did not survive beyond antiquity, though Indian logic was later adopted in medieval China. As a number of other disciplines of formal science rely heavily on mathematics, they did not exist until mathematics had developed to a relatively advanced level. Pierre de Fermat and Blaise Pascal (1654), and Christiaan Huygens (1657) started the earliest study of probability theory. In the