Understanding Mathematics by Peter Alfeld, Department of Mathematics, University of Utah

Do you feel that being lost in mathematics is the natural state of things?

Being lost in mathematics just means that you are not ready for that piece of mathematics. You have to build a bridge from the mathematics you do understand to the new mathematics. The main trouble with being lost is that all subsequent mathematics you encounter (e.g., in subsequent lectures or chapters of a book) is likely also to be lost on you. Before going on you must understand what's happening now. Practically speaking this means that when taking a course you must make sure not to fall behind, even it that takes some effort right now. If you do fall behind your time and money is likely to be wasted.

If you do find yourself irretrievably lost in a class you need to take major action. Talk to your teacher and ask for advice. It might be best to withdraw from the class and take it over again, or even take a more basic class first. This will be more effective and more efficient in the long run.

It's sometimes hard to understand new mathematics (and even harder to invent new mathematics). This applies to everybody regardless of experience. But as you gain experience the difficulties diminish and you can take bigger steps. So you get more efficient, and a task that looks so formidable at first shrinks to being manageable. So being lost in mathematics is not the natural state of things and prolonged exposure to that state can be avoided!

Here's a famous quote by Albert Einstein

Do not worry about your difficulties in mathematics. I can assure you that mine are still greater.

Fine print, your comments, more links, Peter Alfeld, PA1UM