In my most recent question regarding whether to abandon an open math problem, I got (surprisingly) much more dialogue than I anticipated. I had expected very quick answers that all say something like, "yes, you are mistaken, stick with what's current."
Instead, I got some great answers that advocate for both choices.
There is a concise answer that has 46 up-votes -- the most net up-votes.
Then Pete Clark's answer has 26 net up-votes and Dan Romik has 9 net up-votes.
I think Pete Clark's and Dan Romik's answers (and additional comments) are the best.
Am I doing something "wrong" if I choose one of their answers, instead of choosing the answer that is the most popular, based on up-votes?