I am interested in learning pure mathematics and I want to be better at it so I want to know what skills and abilities are most important for this field so I can improve them. I have asked two related questions here before, this one about improving 3D visualisation or visualisation in general, and this one about arithmetic calculating or calculating in general like calculating many more steps in my head faster and more accurate so I can know if certain approach in proof or a problem like integrals will lead to nothing . However, the answers I received suggested that these skills are not very useful or relevant for pure mathematics (although I think they are important). So, what are the skills that I should focus on developing and practising? I have heard that pure mathematics requires a lot of creativity, abstraction, and rigour, but I am not sure how to measure or improve these aspects.
I would appreciate any advice or guidance from experienced pure mathematicians or anyone who has studied or worked in this field. What are the skills that you use most often ? How do you practice or improve these skills?
Edit: I should also mention that I am a self-learner of pure math and I don't have anyone to help me or to talk to about math I work pretty much alone and currently I am studying the undergraduate topics, but I study math to be able to do research. So I guess I am interested in both the skills and abilities of undergraduates and researchers, but for now I need to know the skills and abilities of undergraduates.
Edit: I also want to know what it means to be good at pure math in general. What does it even mean to say someone is better or smarter than someone in math? I mean, if I compare myself to someone like Terence Tao he is much better than I am or I will ever be even in 100 lifetimes. And the question is, why is he better? The short answer is, he is smarter than me, but what does that really mean in mathematics? What does “smart” mean in pure math? Being smart in math means having many abilities that he has and I don’t. But what are those abilities exactly and how can I improve them? But at least if I can break down what exactly being smarter means, I can identify each skill and try to develop it and become generally good at mathematics. That is why I asked this question, hoping to get some insight from other people who have more experience and knowledge than me. I know I will not be a brilliant mathematician or maybe not even qualified to be one in the first place. Also, I am a self-learner. I don’t have someone to talk to about math and everybody around me is not even interested in math. I study alone and I don’t have any help except online.