👉 Theoretical mathematics is the branch that explores abstract concepts, structures, and relationships without necessarily relying on empirical data or practical applications. It delves into fundamental principles and theories, often using logical reasoning and rigorous proofs to establish truths about numbers, sets, functions, and geometric shapes. Key areas include algebra, which studies symbolic systems and their operations; calculus, which examines change and motion through limits and derivatives; number theory, focusing on properties of integers and other whole numbers; topology, which explores the properties of space that are preserved under continuous deformations; and set theory, a foundation for much of modern mathematics. These fields build upon axioms and logical deductions to create frameworks that unify and extend mathematical understanding, providing a deep, coherent structure for exploring the universe of mathematical ideas.
