Roadmap to be a good mathematician

Question

Recently, I concerned about my future.
When I was a child, I didn't spend much on studying mathematics, so I got Cs or below.
At that time, I didn't realize why I have to study. Thus, I lose my interests in studying. One day, I read a book and that books evoke me to think mathematics more seriously and give a reason to study hard. Then I chose math major.
Now I have a dream that I want to be a mathematician, I mean a really good mathematician
Therefore, I bought a vast amount of books, which are about undergraduate courses mostly and a few of them about graduate courses.
How can I study effectively with using my books? I know that mathematics is not just about solving equations. but proof why I think.
I will wait for your insightful answer! Thank you

Answer 1

I like this comment from Hacker News. It's about learning physics, but it applies to maths as well. I'll copy it below:

There is one sure way, and it’s a test of your fortitude. You find a a college textbook with the answers to the even-numbered problems in the back. You sit down in a warm or hot room, and solve them. If the textbook is in its 4th printing or so, the answers are correct. On a few, you’ll have to work for hours. Now here is a very, very, important point. All the learning occurs on the problems you struggle with. In the blind alleys. A lot of learning in physics comprises paring down your misconceptions until the correct methodology, often surprisingly simple, appears. Then, you understand how to apply the basic laws to the problem at hand, which is what physics is. I’ll emphasize the point by stating it’s converse. A problem you can solve easily and quickly yields zero knowledge.

I would recommend two outstanding textbooks. Halliday and Resnick, early editions , printed in the late 60s and 70s. If you can do all the odd problems in this two volume set, you are an educated person, regardless of your greater aspirations. Edward Purcell’s Berkeley Physics Series Second Volume on Electricity and Magnetism. Might be the best undergraduate physics textbook ever written. Did you know that magnetism arises from electrostatics and relativistic length contraction? It’s right there. You should also get yourself a copy of Feynman’s Lectures on Physics. Warning. Read it for intuition, motivation, the story of Mr. Bader, and entertainment. It’s at much too advanced a point of view to help you solve nuts and bolts physics exercises, which is what you must do. One final warning. Every one of us sits at a desk with a powerful internet-connected computer. Don’t do this. Even get a calculator to avoid this. Of course, when you are stumped you’ll want to see how a topic has been treated by others. Do it in another room.

The entire thread should be very relevant to you.