👉 Established mathematics encompasses a broad range of disciplines and theories that have been rigorously developed and validated over centuries. At its core, it includes fundamental concepts like arithmetic, algebra, geometry, calculus, and number theory, each with its own set of axioms, theorems, and proofs. For instance, arithmetic deals with numbers and basic operations, while algebra introduces symbols and equations to represent relationships. Geometry explores shapes, sizes, and spatial relationships, extending from basic Euclidean principles to more complex non-Euclidean geometries. Calculus, developed independently by Isaac Newton and Gottfried Wilhelm Leibniz, focuses on change and motion, providing tools to analyze rates of change and accumulation. Number theory examines properties of integers and other whole numbers, uncovering patterns and relationships that have profound implications in mathematics and beyond. These areas are interconnected, with each contributing to a deeper understanding of the mathematical universe, and they form the foundation for advanced fields such as topology, differential equations, and applied mathematics.
