When I’m learning a new topic, all of the details matter. If I want to understand what is going on, I need to have a firm handle on each detail. If I cannot imagine how each part operates and connects with the others, “getting” the concept is difficult. I suspect this happens for others, too. After all, if you want to understand without needing to take a result on faith, you have to know the concept as a whole.

If you take a look at any given class, you find that there are a variety of strategies employed by the students. In a way, it’s the perfect Darwinian battlefield: those with the best homework strategies end up doing well and move on to the next course. Some strategies are better than others, and this really shows up in any class. Even if your class is small (say, about ten people), you will find that students don’t all study and do homework in the same way.

When you’re in school, it seems like everything you’re learning is super important. You might even get the impression that you will definitely use what you learn forever.

The title of this post may not be words you are used to seeing together. Sure, you might think that mathematics is powerful, but does anyone actually do mathematics just because they enjoy it? If you ask someone other than a mathematician, you might expect the answer to be “no”.