mathematical

Mathematical is an adjective used to describe things related to mathematics, the abstract science that studies quantity, structure, space, change, and related concepts. It encompasses the language, methods, and objects of mathematics, including numbers, formulas, proofs, models, and theorems. The term traces to Latin mathematica and Greek mathema, with the suffix -ical forming an adjective.

In practice, mathematical reasoning emphasizes abstraction, generalization, and logical deduction. A mathematical statement is typically supported by a proof, and mathematical models translate real phenomena into precise structures that can be analyzed and tested. The domain spans conventional branches such as arithmetic, algebra, geometry, calculus, and analysis, as well as more advanced areas like topology, number theory, and mathematical logic. The word is also used to describe tools and practices, such as mathematical notation, mathematical software, and mathematical education. In everyday usage, mathematical can imply rigor and exactness, though it may also reference numerical or quantitative aspects. The distinction between "mathematical" and "numerical" is subtle: mathematical denotes the broader discipline and its abstractions, while numerical emphasizes calculation with numbers.