👉 Confirmed mathematics encompasses the well-established principles and theorems that have been rigorously proven and accepted within the mathematical community. These include fundamental concepts like arithmetic operations, geometric properties, and algebraic structures, as well as advanced topics such as calculus, number theory, and topology. The core of confirmed mathematics is built on axiomatic systems—sets of basic assumptions from which all theorems are logically derived. For example, Euclidean geometry relies on five postulates and common notions, while calculus is grounded in limits and the properties of continuous functions. This body of knowledge is validated through proof, ensuring its reliability and consistency across various applications in science, engineering, and everyday life.
