Formal sciences began before the formulation of 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 Indian, Greek and Islamic mathematicians 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 6th century BC, China in the 5th century BC, and Greece between the 4th century BC and the 1st century BC. 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 into a relatively advanced level. Pierre de Fermat and Blaise Pascal (1654), and Christiaan Huygens (1657) started the earliest study of probability theory. In the early 1800s, Gauss and Laplace developed the mathematical theory of statistics, which also explained the use of statistics in insurance and governmental accounting. Mathematical statistics was recognized as a mathematical discipline in the early 20th century. In the mid-twentieth century, mathematics was broadened and enriched by the rise of new mathematical sciences and engineering disciplines such as operations research and systems engineering. These sciences benefited from basic research in electrical engineering and then by the development of electrical computing[disambiguation needed], which also stimulated information theory, numerical analysis (scientific computing), and theoretical computer science. Theoretical computer science also benefits from the discipline of mathematical logic, which included the theory of computation. |

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