👉 Establishing math, also known as axiomatic or foundational mathematics, is the process of defining and justifying the basic principles, axioms, and assumptions that underpin a mathematical system. This involves identifying the fundamental truths or statements that are accepted without proof and then logically deriving other mathematical truths from these axioms using deductive reasoning. The goal is to create a coherent, consistent, and self-contained framework where all theorems and results can be rigorously derived from these initial principles. This approach ensures that the mathematical system is robust and free from internal contradictions, providing a solid foundation for further mathematical exploration and application. Notable examples include Euclidean geometry's axioms or Zermelo-Fraenkel set theory with the Axiom of Choice (ZFC) for set theory.
