According to Vault, mathematics and physics research can be divided into the following areas:
Applied Mathematics
Applied mathematicians “use mathematical theories and principles to address real-world problems. They might create mathematical models to calculate the characteristics of new products, systems, or population trends.”
Theoretical Mathematics
Theoretical mathematicians work with pure and abstract mathematical concepts to expand and define the scope of mathematical knowledge.”
Experimental Physics
Experimental physics uses experiments to gather information.
Theoretical Physics
Theoretical physics constructs theories to explain experimental results.