Mathematics is often described as the science of patterns. Mathematicians seek to discover, analyze, and classify abstract objects and natural phenomena. The traditional domains of study are quantity (arithmetic), structure (algebra), space (geometry), and change (analysis). Mathematics offers distinctive and potent modes of thought such as abstraction, generalization, deduction, inference, symbols, and the axiomatic method. Mathematical truth is established through logical analysis and proof. As a universal discipline, it is rich in both theory and applications.