When you want to form a new habit, how do you go about it? Do you purchase equipment in the hope that spending money will “force” you to stay consistent? Perhaps you try to stay accountable by enlisting the help of a friend. Maybe you announce a project publicly, to show that you’re serious, or sign up for a class on a subject you’re interested in. This can apply to many situations, from getting better at writing, running every day, drawing, learning mathematics or science, playing a sport, or any other activity that’s important to you. Each one requires consistency, and a habit is the best way to build that consistency.

There are plenty of ways to enjoy mathematics. You can attend a classroom lecture, you can read a textbook, you can look at a news article, you can watch a video, or you could just play with some concepts yourself. There’s not one way in particular that is better than any other. Rather, each one has its own advantages and disadvantages. It depends what you’re looking to get out of your session.

As a student in mathematics and physics, I’m part of two different worlds. On the one hand, proofs and abstraction come from the side of mathematics. On the other hand, physics is where concrete examples and applications are the norm. In physics (at least, within the scope of undergraduate education), we only care about the mathematical tools that we can apply to a given problem.

Learning mathematics in school and doing mathematics in general are not the same thing.