How to learn math, such that we enjoy it? I'm finishing high school now, and have the impression that anyone who studies math beyond high school does so because they enjoy it. Occassionally, I manage to solve a math problem, and feel a deep joy and satisfaction. And so I try to read some math (undergrad) textbooks, but most of the time I feel frustrated with the tedium of learning some new theorems and concepts. Maybe I'm trying to read about proofs (Velleman), or attempting some of Spivak's problems, and after a while I get restless and feel like doing something else.
Is this normal? Is this frustration, boredom, and need for disciplined perseverance an intrinsic and essential part of learning math? Do things eventually fall into place, and that's where you get to see the beauty? Or is it supposed to come almost instinctively and every step is supposed to be a fun challenge, and I should consider trying something else that feels more natural?
 A: If you are learning math for fun that is a pretty good indicator you enjoy it. I have to take breaks occasionally no matter what I'm studying. There aren't many people that immediately understand EVERY concept instantly. It may also be that you are trying to leap or skip to certain things without having developed a sufficient amount of what I call mathematical maturity.In fact if you were to go on to be a math major you may not even touch on proving things until your junior year. A great book for developing this-learning logic,proofs,and both discrete and continuous math is "Mathematical Thinking: Problem solving and Proofs" by West and D'Angelo. It's very easy to follow and great for self-study. It is also very broad in terms of sampling a lot of different topics. If you are wondering about whether this is a field you want to make a career of don't worry about that either. Most colleges don't require you to declare a major until the end of your sophomore year. So you can try it for size without having to make a commitment while primarily focusing on the general ed requirements that are the same for everyone.
