Foundations of Mathematics is a field that explores the fundamental concepts and principles underlying mathematics. It addresses questions about the nature of mathematical objects, the validity of mathematical reasoning, and the relationships between different mathematical systems. Key areas of study include set theory, logic, and proof theory. This discipline seeks to establish a solid framework for mathematics, ensuring that mathematical statements are well-defined and logically consistent. Prominent figures in this field include David Hilbert and Kurt Gödel, whose work has significantly influenced our understanding of mathematical foundations and the limits of formal systems.