I've been focusing on self studying mathematics for the past couple months, and I'm currently working on discrete mathematics. Here's my attempt at a metaphor to describe my issue.
Imagine you have a jar, whatever is in the jar represents the knowledge you possess. When learning something like the natural sciences (physics, chemistry, etc.) it's like pouring a liquid into the jar. The ideas form more smoothly in your mind, and fit in more naturally with the knowledge you already have.
But when I'm studying math in particular, sometimes it feels like dumping lego bricks into that jar. It can feel jarring and unpleasant. Each theorem, definition and proof is like a singular lego brick. And you see how the pieces might fit together, but the bricks aren't quite connected to eachother yet. In fact, they just form a jumbled mess right now.
If that made sense to you, I just want to know if this is natural. As interesting I find mathematics, the jarring feeling I described earlier can make it really unpleasant to read through a book. And this can be very discouraging. It's like you find something interesting, but at the same time you find it unpleasant. How do you overcome this, is it just a matter of persistence?
Best Answer
I majored in math in college over 50 years ago-- this is from my distant experience of that time.
A previous writer (littleO)had an important comment about finding the right book. Some authors seem to be trying to demonstrate their cleverness rather than trying to really convey to the reader the motivation and intuition for the math. So if one text doesn't seem to work for you, look for another.
However I also understand the jarring feeling one has about first encountering some ideas in mathematics. First-- I think you have to come to appreciate the jarring feeling--and enjoy the feeling of being challenged by it. The process of understanding doesn't necessarily happen as quickly as in the the natural sciences so you shouldn't be discouraged too soon. Quite unlike reading a novel, it usually takes a number of passes over the same material. If you're having difficulty understanding--work hard trying to understand-- then get away from it and come back to the same section a day or two later is often helpful. And also it's extremely important to actually do some exercises in a textbook. I don't think you can learn math properly without doing these.
Eventually the jarring should change--perhaps suddenly, or perhaps gradually-- into understanding, not only in a formal sense, but also an intuitive sense. That can make you want to experience more.