The Foundations of Mathematics

The Foundations of Mathematics is a branch that studies the basic principles and logic underlying all mathematical concepts. It seeks to understand how mathematics is built from fundamental ideas like numbers, sets, and logical rules. By exploring these core elements, mathematicians aim to ensure that mathematical reasoning is consistent and reliable. This field connects philosophical questions about truth and existence with rigorous formal systems, helping us understand not just what mathematics is, but how it can be securely constructed and justified.