A mathematical model is a description o a seestem uisin mathematical concepts an leid. The process o developin a mathematical model is termed mathematical modellin. Mathematical models are uised nae anly in the naitural sciences (such as pheesics, biology, yird science, meteorology) an ingineerin disciplines (e.g. computer science, airtificial intelligence), but an aa in the social sciences (such as economics, psychology, sociology an poleetical science); pheesicists, ingineers, statisticians, operations research analysts an economists uise mathematical models maist extensively. A model mey help tae explain a seestem an tae study the effects o different components, an tae mak predictions aboot behaviour.
Mathematical models can tak mony furms, includin but nae leemitit tae dynamical seestems, statistical models, differential equations, or game theoretic models. These an ither types o models can owerlap, wi a given model involvin a variety o abstract structurs. In general, mathematical models mey include logical models, as far as logic is taken as a pairt o mathematics. In mony cases, the quality o a scientific field depends on hou well the mathematical models developed on the theoretical side agree wi results o repeatable experiments. Lack o agreement atween theoretical mathematical models an experimental measurments eften leads tae important advances as better theories are developed.