Please forgive me if I did not post this correctly. I'm writing following https://mathoverflow.net/help/reopen-questions. I would like to ask for my question to be reopened: https://mathoverflow.net/questions/135605/how-to-discover-counterexamples-and-required-objects. I do not understand why it would be deemed "off-topic." I am grateful for the comments there which support it. Here is some of the calculus:

Before posting my question, I read When and how is it appropriate for an undergraduate to email a professor out of the blue?. This was a question which had been open and now answered, posed by an undergraduate asking for advice from professors. Moreover, that question could apply to professors of any subject and yet remains extremely helpful. My question concerns the study of math specifically.

Similarly, my question seeks advice from professors and research mathematicians. Since it appears that research mathematicians encounter counterexamples and objects which must be created, they seem to be in the most apposite and reasonable position to answer and so I have posted on MathOverFlow.

Also, professors would experience and be privy to more learning and studying styles from many diverse students. This bolsters and corroborates this question's fitness for MathOverFlow.

I think that many other math students, and not just undergraduates, would benefit from this question.

requirethe expertise of aresearcherin mathematics. You are essentially asking how should a student develop the skill for finding counterexamples generally. This seems more suitable for Mathematics. $\endgroup$