Foundations of Mathematics

Foundations of Mathematics explores the underlying principles and structures that give rise to mathematical concepts and truths. It involves various branches, such as Proof Theory, which examines how mathematical statements can be logically derived, and Model Theory, which studies the relationships between formal languages and their interpretations in different mathematical structures. Essentially, it seeks to understand what mathematics ultimately means, how we can prove its statements, and how different systems of mathematics relate to one another, ensuring that the entire framework of math is consistent, coherent, and meaningful.