Studying mathematics in high school or even college rarely gives you a sense of what mathematical research is all about. The strongest impression that often emerges is of a field in which practically all is known—and has been known for a long time.
In a soon-to-be-published autobiography, mathematician Saunders Mac Lane, who spent much of his career at the University of Chicago and helped develop a branch of algebra called category theory, expressed just this sort of sentiment about his time as a student at Yale University in the 1920s.