Mathematical axioms are fundamental statements or propositions that are accepted as true without proof. They serve as the foundational building blocks for mathematical reasoning and theories. Axioms are essential because they provide a starting point from which other statements, known as theorems, can be derived through logical reasoning. Different branches of mathematics may have their own sets of axioms. For example, in Euclidean geometry, the axioms include basic truths about points, lines, and planes. In contrast, set theory has its own axioms, such as the Zermelo-Fraenkel axioms, which define the properties of sets and their relationships.