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Have a nice day. Please write serious answer. :) I have a problem and reduce my motivation. problems as follows; I am learning math is really very fast. I can read few books only one day. I understand the issues very quickly. example, I read the Yitang Zhang's full article in only one night. next day I read all GPY (Goldston-Pintz-Yıldırım) papers. I read all the articles on this subject in a few days. Five or six days later, I knew everything about it. (I learn about GPY sieve method; Sieve theory; Bombieri-Vinogradov theorem; I read all Bombieri-Iwaniec papers; learn about Maynard-Tao method and finally I read Polymath papers) whereas a few weeks ago I know only basic analytic number theory. I learned everything just over a week. I understand very easily even the most difficult issues. I'am fast in research (read papers,read books+create new idea), learning new and difficult technique. , but when it comes to solving difficult exam problems, I'm bored. I can not imagine the problem. I'm like math encyclopedia (I read a lot of advanced books and research papers, I have knowledge in all areas of mathematics. but I'm too weak problem-solving skills.) sometimes very surprised everyone because I dont solve basic arithmetic problems; calculus problems. Shocking people who knew my math ability.full concentration for days without sleep I learn a lot of theory; papers; reading books but I hate exams and problems. I love big and open problems. but I do not want to deal with exam questions.

My question; Is this normal? if not normal; How can I improve my problem solving ability? Please give me advice.

Thanks ! :)

Rieendstac
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    As I have learned, knowledge is like a handy tool. But if the user does not use the tool, it is useless.$$\color{white}{\text{;) Secret message here!}}$$To overcome this, I spend time on this site, not only to hone my skills, but to help others. The problems here are quite varied. – Simply Beautiful Art Sep 27 '16 at 00:15
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    You must work on your problem solving skills the same way you build up your knowledge of theorems. Build up from simple problems. It takes lots of practice and hard work. Many textbooks have lots of problems to work through. – mathematician Sep 27 '16 at 00:23
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    @Llan might be very basic for you but just in case. It is helping me a lot... try to read this book: https://en.wikipedia.org/wiki/How_to_Solve_It – iadvd Sep 27 '16 at 00:29
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    Why bother with exam problems? Surely there's a better way to make use of your talents once you demonstrate them to someone at a math program, for example – manofbear Sep 27 '16 at 00:36
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    I understand very easily even the most difficult issues There is a distinction between understanding something, and learning to recognize when, where and how to use it. I can understand the rules of chess in a day. I can read up on openings and endgames in a week. I can spend a month replaying games of the masters and understand every explanation at each step. However, that alone won't teach me how to play chess well and apply all the acquired knowledge. That takes actual practice, until not only do the moves make sense, but until the pieces fall in place and everything feels natural. – dxiv Sep 27 '16 at 00:36

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Well, my suggestion (to improve the problem solving ability) would be to practice the problems along with the theory; it'll be a pain to do the exam problems if all you've studied is the theory, but if you practice a couple of problems as you work through the concepts it will be less painful. For example, I am teaching myself linear algebra; I'm in middle school, taking geometry, and I was able to read through a couple of textbooks and watch some YouTube videos and learn a decent enough portion of the topic (in my mind) and also solve problems because as I learned, I did problems, working through the examples in the textbooks, or just googling a few problems.

Now, this is just me, but I find it important to know the problems as well as the theory, for three main reasons. One, because although math is beautiful in its own right, it is used for many applications, and here the problem portion is arguably more important than the theory. So it is good to know for that. Two, because math is beautiful from a theory viewpoint, but can be even more beautiful if you know the problems; things just click better. For example, as I was teaching myself linear algebra, I didn't understand column space very well, but later as I learned about it, stuff about solving systems began to click better in my mind. ("Click better" is a poor expression, but that is really what it was like for me - it was like pieces of a jigsaw were falling into place.) Finally, if your goal is to solve complex, broad problems involving a whole lot of theory, surely it will be easier if you know at least the basics of the problem aspect.

To conclude, I believe that problem solving ability is indeed important no matter where you want to go with your current ability (which is indeed impressive). Working through problems as you study the theory should help, and though it may slow down your overall times in understanding a concept due to the extra time taken to work problems, the benefits will be great.

Hope this helps!

auden
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    Amazing that you're studying math on your own so early on! I didn't study math on my own (or really appreciate it much at all) until my senior year of undergrad, and now I think it's one of the most exciting and worthwhile things to study. – manofbear Sep 27 '16 at 00:40
  • Hope it goes well for you – manofbear Sep 27 '16 at 00:40
  • @manofbear, thank you! Math is the best to study - so interesting. Good luck in your own work. – auden Sep 27 '16 at 00:41