I’m a very practical person when it comes to math and science. If I can’t do something useful with it, I’m not really concerned with learning it. If it’s easy and it looks cool, then I’ll definitely pick it up. Once it gets hard, if I can’t see a good application of the math, I don’t care for it anymore.
One implication of this is that I have found some math classes to be absolutely torturous. I spent all of abstract algebra thinking about how useless it was to factor polynomials. Who cares if this function has a zero at some exact value? I could easily put it into a computer, plot it, and have an answer that’s good enough.
The thing is, though, a lot of mathematical ideas have no directly visible application, but are actually very useful. Finding zeros in polynomials comes up all over the place. If you’ve got a matrix and want to find the eigenvectors, you have to construct the characteristic polynomial of that matrix and find zeros in it. When I realized this, I decided that it was actualy very useful to understand these polynomial creatures in all of their full gory detail.
When you’re repeatedly exposed to ideas that you first think are stupid and worthless, and then come to realize are actually quite useful and important, you learn a sense of humility. That’s good. I needed one of those.