Mathematical theory refers to the abstract principles and concepts that form the foundation of mathematics. It encompasses various branches, such as algebra, geometry, and calculus, which explore relationships, structures, and patterns. These theories help mathematicians understand and solve complex problems by providing a framework for reasoning and proof. 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, make predictions, and develop new technologies, demonstrating the importance of mathematics in everyday life and scientific advancement.