A Sense of Play
In mathematics, there’s a sense of play that must be achieved if one wants to really understand what is going on in mathematics. Contrary to what people might think, this sense of play and “just getting” mathematics is not some sort of genetic feature (or at the very least, not only genetic). It’s the result of immersing oneself in mathematics and freely playing with the concepts. After a long time, this play translates into what people call “intuition”.
Have you ever opened up a graphing calculator program and tried out different functions? Have you looked at their features and thought, “this is interesting”? Have you ever opened up your mathematics book and simply read it of your own accord to see if there were cool things you had missed?
That is what it means to have a sense of play.
Having a knack for mathematics is not so different from being good at a sport, or a musical instrument. Sure, having the right technical skills is important, but being really good at something requires one to experiment and refine one’s process. In this sense, trying new things and playing with numbers, functions, and other mathematical concepts is key to improving one’s “skill” in mathematics.
This sort of aptitude doesn’t necessarily translate to solving more complex problems or suddenly learning new concepts faster. What it does do is give one a better way to “see” a concept, making it more approachable and familiar instead of challenging because one does not know how to proceed.
Develop a sense of play in mathematics and test things. Take out a piece of paper and try some equations out just for the fun of it, and you may surprise yourself by the relationships and patterns you find.