Mathematical theory refers to a systematic framework that explains and predicts mathematical concepts and relationships. It encompasses various branches, such as algebra, geometry, and calculus, each with its own set of principles and rules. These theories help mathematicians understand patterns, solve problems, and develop new mathematical ideas. In addition to pure mathematics, mathematical theory also applies to practical fields like physics, engineering, and computer science. By using mathematical models and theories, professionals in these areas can analyze data, optimize processes, and make informed decisions based on quantitative reasoning.