Consider mathematics. If you already know enough math to derive the quadratic equation, you might make a small change, like adding X^3 or X^4. See where your own techniques take you before looking up the answer. With just a few pen strokes, you will be playing with an equation for which there is no general solution, or no known solution. In mathematics it will take you very little time to start playing at the boundaries of human knowledge, and it's relatively easy to memorize a few starting points that many hours of passenger travel fly by.