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This is a meta question about mathematics. It is not inspired by an actual problem. Also, I'm not sure to what extent the distinction I'm drawing makes sense.

Question:
How can I decide if an obstruction encountered while trying to prove a statement is due to a limitation of the approach or a genuine obstruction, which all possible proofs must overcome?

user642796
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vuur
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  • I suspect you can probably prove that there's no algorithm that can deterministically answer this question in general. Sort of like Hilbert's 10th problem. – Gregory Grant Aug 25 '15 at 18:12

1 Answers1

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I don't have any theoretic observations. Instead, I encourage you to always consider examples, lots of examples, whatever can be worked out as relates to the current inquiry. On this site, we often see questions about $n$ by $n$ matrices from people who do not know the answer for the $2$ by $2$ case. We see number theory questions/conjectures where people do not know what happens for numbers up to 100. If you find a counterexample, you have an obstruction. If you never find a counterexample, the details of each worked example will lead you toward a correct proof, if such is available. In the latter case, you look good saying "I considered the following type of examples, it has always come out true so far"

Here is a famous episode, two jpegs that overlap:

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Will Jagy
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