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I am a student in 12th grade and am fond of mathematics. I enjoy reading mathematics but when it comes to problems I just get completely stuck. Its not that I don't understand the problem but often don't know how to go about tackling it. When I see the solution, often I understand it perfectly but arriving at that solution on my own is what I find extremely difficult.

Can anybody relate to this and if so how do I overcome this problem? Any help would be appreciated.

user34304
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    I think this is quite natural. Mathematicians have had years, decades even centuries for find clever ways to solve certain problems. The best thing to do is to add this latest solution you have found to your repertoire. To do this, I learn the solution by rewriting it until I can do it with a blank piece of paper. – Simon S Apr 14 '15 at 15:46
  • Although mastering the solution is good, my concern lies in the fact that inspite of spending considerable amount of time I am not able to arive at the solution itself. – user34304 Apr 14 '15 at 15:48
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    I agree with @SimonS. Even brilliant mathematicians didn't just pull answers out of thin air. If every problem could be solved in a straightforward way, then we would have had calculus in the time of Euler. The techniques have been slowly developed and passed down from generation to generation. – Joel Apr 14 '15 at 15:49
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    Yes, I know what you mean. The only way to get better at solving a certain class of problems is to work others of the same type. There's no shame in looking at and learning solutions of those problems when they are new to you. – Simon S Apr 14 '15 at 15:50
  • I recommend reading How to Solve It, by George Polya, $10 for the Kindle version. The wikipedia entry gives some idea of the structure of the book. The book explores some problems as example practical applications of its principles. – jxh Apr 14 '15 at 15:51
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    I can relate this as I am sure many others can. Perhaps you can gave some examples of your reading material people can relate more specifically. – abnry Apr 14 '15 at 17:48

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I find the same problem, also I'm around your age so I can relate. Sometimes I feel like mathematical papers are written to be complicated. However, I think that most of the problems concerning being able to reproduce an argument given in a book or paper has to do with not understanding the argument in English. What I mean, is that people (me especially) have a bad habit of understanding the symbols but not being able to explain the concept to a 5th grader. For instance, if you read about the proof for the fundamental theorem(s) of Calculus, you might just miss the entire point of the argument in trying to understand the symbols and notations of the argument. In reality, understanding the argument has more to do with being able to translate mathematical jargon to English. And if you want to be able to write proofs, you have to be able to translate the English into mathematical language. This is easier said than done, and I'm sure most never really learn how to do it, that's why we have so many horrible mathematical papers. But if you learn how to do that, you won't have to memorize math, you'll only have to memorize concepts.

Also, don't think that these mathematicians that use complicated jargon are smarter than you, they most likely are similar to your intelligence. They have more experience, but in the end, they'll mess up in ways very similar to us. So if you apply all the above and still don't understand the concept or argument, move on to a different source.

Zach466920
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I empathize. You will be relaxed to hear that my problem is same but I never lose hopes. I am a 11th grade student. I would be in 12th grade if I have not wasted a year. I was really far from "What maths really is". After coming in 11th grade I found how beautiful this subject is... I believe in reading books rather than being taught so, this problem often encounters me also. I know that you pass from difficult stages as I do. I would like to add a quote of Einstein here,

“Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand.”

I know that when you ever get stuck, you try to imagine the case very rigorously. When I am skimming the material and all I am understanding easily, then sudden a problems encounters me that urges me to imagine about that rigorously. So it is where, I sometimes get stuck for 3-4 days sometimes. the solution is the one attempted by scientists. Most of the scientist leave the problem for sometime if they are not getting it after even a very hard work. And it is reported that when they return to the problems again, many issues are clarified easily.

I have also experienced this many times and trust me, it works! So my suggestion is same for you. Do this whenever you are stuck for long time... :)

Sufyan Naeem
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Yes, finding a solution to a new problem is hard work. It is very satisfying on the rare occasion when it happens. However, in most engineering work it is not finding your own solution, but being able to find someone who has already solved a problem like the one you are trying to solve and "borrowing" his solution. Most progress is a synthesis of previous work, finding creative and novel applications for old ideas.

Paul Hanson
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