Sometimes getting started on a problem seems to be the hardest part. Once you find something to sink your teeth into, everything goes smoothly. What are some good things to try when you're staring at the problem with no ideas, and all the MSE commenters are asking what you've tried?
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2Many of my proofs start off as extended hunts for counterexamples. – Dec 09 '13 at 05:20
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1@T.Bongers: Though sometimes the counterexamples start out as extended hunts for proofs. – Brian M. Scott Dec 09 '13 at 05:25
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I'm so glad I asked! Here are a few of my own tips for dealing with this situation. I'm hoping others will chime in with their own.
Make sure you understand the problem as well as possible. If you can get an intuitive understanding, that's best, but make sure you at least have a formal understanding of it. Write down the definitions of all the words and notation that you're not already intimately familiar with.
Start at the beginning. Put out of your mind what you're trying to accomplish and just start writing down facts about the things you're considering and try to find ways to combine them.
Start at the end. Put out of your mind what information you have available and try to come up with some things that would lead to the conclusion you seek.
dfeuer
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2If it is relevant, compute a little, that will be evidence that the problem has been tackled. (And computing may make the question unnecessary!) – André Nicolas Dec 09 '13 at 05:19
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If the problem is at all similar to one you know how to solve, try to state exactly how it differs. Try a method that would work on the other problem, and try to state exactly where it goes wrong.
If solving the problem would easily yield some other consequences, try first proving those consequences directly.
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Figure out what the problem is really askin for you to solve/prove and then figure out what you already know about the topic. If you can break the problem down , into an easier/smaller portion that would be a great start too!
waj cheema
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