Theoretical foundations of mathematics

Theoretical foundations of mathematics are the fundamental concepts and principles that underpin all mathematical reasoning. This includes the study of logic, set theory, and the nature of numbers and structures. Essentially, it seeks to understand what mathematics is, how it works, and the assumptions that support mathematical theories. By examining these foundations, mathematicians ensure that mathematical systems are coherent and reliable, enabling them to tackle complex problems across various disciplines, from physics to computer science. It forms the bedrock for both pure and applied mathematics.