We were required (by the state I believe) to take a comprehensive test assessing our competency at physics. I struggled with test and was disheartened that four years of strenuous effort would be all for naught. I knew I needed to do something to shore up my understanding of physics if I was going to retain the knowledge decades onwards. The other reason was a simple love for the beauty and underlying simplicity of the subject.

> I finished the class, whatever I need to learn through application, life will point me toward.

In math/physics, it often won't. Solving lots of problems serves two particular purposes: To really solidify the concepts in your mind so you won't forget, and ensuring you learn the techniques and not just the knowledge.

For the former, you may find yourself in the position where you find yourself way over your head, and won't know where to start. You usually will not have a single gap, but many. You'll find yourself realizing you'll need to look up material from several textbooks to regain the knowledge you've lost. Once you begin that process, you'll pick up one of your old textbooks and while the physics knowledge may be absorbed, you'll realize you've forgotten much of the math needed to solve such problems. In the unlikely event you'll retain enough to follow the textbook, it is very unlikely you'll know the techniques well enough to solve the real world problem.

And your colleagues will. You'll be alone, and you'll drop out of that group. With physics/math, there often are hard boundaries in these groups. Those who meet the bar are in. Those who don't drop out, because it really sucks being the only person in the group who is struggling with what everyone else considers as basic.

SW engineering has a much more gradual change in skills amongst people, and usually the problems most people work on are fairly learnable in a short amount of time.

Plus, at various times, I’ve had to revisit things I learned years ago and ended up understanding it much better because I could connect it to a swath of things I hadn’t learned the first time I saw the material.

Math and its applications are a contact sport. You don’t truly appreciate it until you try to use it yourself.

This is really interesting perspective -- thanks for sharing it. I think there's something to the idea that some fields are more 'binary' than others -- that if you can't make it past some threshold of _true understanding_ that you will be denied experiences that could push that threshold further. Such a field would warrant a different strategy for learning / mastery than a less binary field.

I'm going to ruminate on this.