Theoretical mathematics is a branch of mathematics that focuses on abstract concepts and the underlying principles that govern mathematical systems. It often involves the study of structures, patterns, and relationships without necessarily applying them to real-world problems. This field includes areas such as algebra, geometry, and number theory, where mathematicians explore ideas for their own sake. Researchers in theoretical mathematics aim to develop new theories and proofs, contributing to the foundation of mathematical knowledge. Their work can lead to advancements in other fields, including physics, computer science, and engineering, by providing essential tools and frameworks for understanding complex systems.