The function of axiomatic systems in mathematical logic is to provide a structured framework for establishing the validity of mathematical statements. They consist of a set of axioms and inference rules that serve as foundational building blocks. By systematically deriving theorems from these axioms, axiomatic systems ensure logical consistency and clarity. These systems are crucial in formal proofs, allowing mathematicians to explore complex concepts while maintaining rigor and precision. Through their axiomatic nature, these systems facilitate discussion and development within various branches of mathematics, ensuring that conclusions drawn are universally understood and accepted.