Amber Habib describes the hierarchical structure of mathematical knowledge and comments upon its reliability and validity. He invites the reader to a consideration of mathematics’ fundamental components: axioms, proofs, and theorems. Habib asserts that all mathematicians work with a common choice of axioms and rules of logic; and the degree of agreement amongst them is not found in any other discipline. He scrutinises the common view of mathematical activity and knowledge-making as offering certainty and increased rigour. The chapter is then centred around three fundamental issues: problems of ahistoricity, the subject matter proper of mathematics, and its relevance or importance. © 2023 selection and editorial matter, Gita Chadha and Renny Thomas.