One of the most discouraging parts of learning pure math is the feeling that your understanding drops off as you move into more abstract territory. And that feeling isn’t wrong — in fact, it’s expected. The diagram above illustrates a common truth: as the abstractness of a concept increases, our level of understanding tends to decrease. This doesn’t mean you’re not smart enough. It just means you’re playing the game at a higher level.

The key is to not expect your understanding of advanced, abstract ideas to feel as solid as your grasp of earlier, more concrete ones. That’s normal. The real goal in developing mathematical skill is not to eliminate this curve, but to shift it upward and to the right — in other words, to slowly increase your ability to make sense of increasingly abstract ideas. Over time, as your experience and intuition grow, the whole curve moves away from the origin.

So if you feel lost at first — that just means you’re exactly where you’re supposed to be.