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Is there a faster way to solve math problems? I'm talking about proving theorems, proving certain properties of a function, etc. The way I do it is I write out the problem and all relevant definitions and theorems, and consider simple examples or sketch the function if I'm given one. But it involves a lot of trial and error. Sometimes I feel like I will never be able to solve the math problem. Do you have any ideas?

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    Much has been written about problem solving technique. A classic book is How to Solve It by Polya. A lot of good material can also be found at artofproblemsolving.com. For example The Art and Craft of Problem Solving by Zeits is a good book. – littleO Sep 10 '13 at 01:07
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    Not to sound too cliche here, but practice makes perfect. Also, once you are used to a subject, your intuition will guide you. – Alexander Sep 10 '13 at 01:07
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    I find that a good way to solve a problem faster is to ask on this site. – Git Gud Sep 10 '13 at 01:12
  • @1mathboy1: See my response here: http://math.stackexchange.com/questions/187340/expanding-problem-solving-skill/187500#187500. Practice, practice, practice and learn proof strategies and think about multiple ways to approach problem solving. Those books are very helpful to help build a very important skill. Colleges should require classes like this formally. Regards – Amzoti Sep 10 '13 at 01:16
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    Is there any way to paint a painting faster? – Zev Chonoles Sep 10 '13 at 01:16
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    Does anyone else think Polya's book is trash? – Git Gud Sep 10 '13 at 01:20
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    @Zev: Use a camera. ;-) – Asaf Karagila Sep 10 '13 at 12:59

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"When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork." - Paul Halmos

"Painful and creatively frustrating as it may be, students and their teachers should at all times be engaged in the process - having ideas, not having ideas, discovering patterns, making conjectures, constructing examples and counterexamples, devising arguments, and critiquing each other's work." - Paul Lockhart

"If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says, try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences, verify as many particular instances as are needed to convince yourself of the truth. When you have satisfied yourself that the theorem is true, you can start proving it." - George Polya

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