Invariant theory

Invariant theory is a branch of mathematics that studies which numbers stay the same (are invariant) when certain operations are done. For example, if you divide two numbers, the answer may be different depending on what order you divide them in. Invariant theory studies which numbers always give the same answer regardless of the order they are divided in. It's like a special kind of guessing game: look at different ways of doing something and figure out which numbers always give the same answer.