👉 Proof mathematics involves demonstrating the validity of a mathematical statement or theorem through logical reasoning and rigorous argumentation, without relying on empirical evidence or experimentation. The core of a proof is to show that the conclusion necessarily follows from the given premises or axioms, often by constructing a sequence of logical steps that lead from the starting assumptions to the desired result. This process typically involves definitions, previously proven theorems, and logical rules such as modus ponens (if P implies Q, and P is true, then Q is true) or mathematical induction. A well-structured proof not only verifies the truth of a statement but also provides insight into the underlying structure and relationships within mathematics, serving as a foundational tool for advancing mathematical knowledge.
