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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?

Sol
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    I have the feeling this question will be closed. Let me say, though, that these frustrations you experience are quite normal. I haven't met someone who can persevere perfectly, and never encounters obstacles – and I have had the privilege of knowing some extremely talented people. Especially since you are only a high-schooler, focus on learning things that bring you some joy. – Alekos Robotis Nov 27 '17 at 12:43
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    One point is that if you're not loving the book you're currently reading, feel free to try other books. Number theory can be a fun subject to learn about, for example. Also, doing math takes mental energy, so it makes sense that you'd need to take a break sometimes. Kind of like how kids who love basketball take a break after playing for an hour or two, but they never doubt that they love basketball. – littleO Nov 27 '17 at 12:50
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    Related: https://math.stackexchange.com/questions/1714966/what-books-should-i-get-to-self-study-beyond-calculus-for-someone-about-to-start/1714986#1714986 – Ethan Bolker Nov 27 '17 at 13:35
  • Thanks for the advice! – Sol Nov 27 '17 at 19:07

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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.

David Reed
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