math

Math, short for mathematics, is the abstract study of quantity, structure, space, and change. It uses symbols and logical reasoning to formulate and investigate general patterns, relationships, and structures. At its core, mathematics pursues proofs that establish truths beyond numerical computations and empirical observation. The discipline encompasses a range of subfields, often divided into pure and applied strands. Core areas include arithmetic, algebra, geometry, calculus (and analysis), probability and statistics, and number theory. Other important domains are topology, combinatorics, mathematical logic and foundations, and applied branches such as numerical analysis and mathematical physics.

Historically, mathematics emerged from counting, measurement, and astronomy in ancient civilizations, with formal axiomatic development in ancient Greece, further expansion in the Islamic and Indian traditions, and rapid growth during the Scientific Revolution and modern era. The development of rigorous proof, formal notation, and computational tools has shaped both theory and practice. Mathematics is widely used as a language of science and engineering; it underpins physical laws, algorithms, data analysis, finance, and technology. Practice emphasizes definitions, theorems, and proofs, but also modeling and computation, with methods such as abstraction, generalization, and proof by deduction. The discipline values rigor, clarity, and logical consistency, while its tools continually adapt to new problems and technologies.