Perhaps in high school Algebra 1 or 2 you first learned about even and odd functions. The idea seemed simple and pointless at first: an even polynomial function had an even degree, and an odd polynomial function had an odd degree. Like many students, you may have thought, "Duh. Who cares?" Ah, just like almost everything in math, this is the general feeling FOR YEARS until you have that beautiful, glorious, "aha" moment. The real beauty of these facts is revealed in intro college quantum courses.