If I saw a lot of effort in an answer (e.g., assume that there are a lot of derivations, code, and plots), but I'm not sure that the math is correct, should I upvote to encourage the person answering it?

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    $\begingroup$ @amoeba yes, I know if the answer is wrong, no matter how much effort in there I should not upvote. But I am asking, if I do not know if the answer is correct, but see a lot of efforts, what should I do. $\endgroup$ – Haitao Du Apr 20 '17 at 20:25
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    $\begingroup$ @hxd1011 I sometimes do upvote in such cases. Usually when I know that I can trust the answerer. $\endgroup$ – amoeba Apr 20 '17 at 20:29
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    $\begingroup$ Upvoting a high-effort-but-wrong answer would mislead later readers into thinking the answer was correct. I'd say that if you can take some action to confirm that it's actually correct (doing a simulation or checking a reference, for example) then you'd usually be doing the site a service (and at least commenting to that effect would be very useful along with the upvote). I regularly do internet searches and perform simulations both when answering questions and sometimes when trying to evaluate answers I'm not quite sure of (particularly when the answer is surprising). $\endgroup$ – Glen_b Apr 20 '17 at 23:32
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    $\begingroup$ As your confidence with material increases (so you can better judge an answer you were previously less sure about), upvote good older answers as you happen across them. $\endgroup$ – Glen_b Apr 20 '17 at 23:40

Some users on this site feel compelled to provide input on things they don't understand and this sounds like a more nuanced version of that...Obviously you can vote however you want but, since you asked...

If you are sincerely unsure about whether or not the answer is correct, I don't know why you'd upvote it: that adds noise to the system and could mislead future readers if the answer turns out to be wrong. I don't see the purpose in giving an "A for effort". Let the people who do understand the answer be the ones who vote. Just because an answer looks complicated or sophisticated doesn't mean it's right. I'd venture to say that a view like the one I'm putting forward is the reason that complicated questions (and the resulting answers) don't get as much credit on this site as the repetitive questions and answers that a greater proportion of users can more easily relate to and understand.

Caveat: I'm talking about the scenario where the correctness of the math is a crucial part of the answer. If it is secondary, and the general approach to the problem has value regardless of whether the math is right, I could see a purpose in upvoting even if you're unable to evaluate the math.

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    $\begingroup$ +1 Good advice. Congratulations on reaching 1k rep! $\endgroup$ – amoeba Apr 20 '17 at 22:36
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    $\begingroup$ As much as I hate to discourage people from upvoting (since we already suffer from a lack of upvotes in a number of ways), I have to agree (indeed I'd say it extends beyond actual mathematics, because sometimes it's a failure in the application of insight/more general reasoning) -- there are a few answers on site that are highly upvoted but wrong or partly wrong. In a couple of cases I suspect they hit the *Hot Network Questions" page. There are comments about what the problems are (and in some cases, more correct answers have been posted later -- ... ctd $\endgroup$ – Glen_b Apr 20 '17 at 23:22
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    $\begingroup$ ctd... -- if there's neither I'll say something myself), but they just get no traction -- there's other answers and a number of comments (at least some of some value) that make it hard for new, low information readers to be clearly aware there's a real problem (they usually see neither the barely-voted on comments nor the much lower rep answers, and even if they do see them, there's little reason to take them seriously over all those upvotes). Over time a few experts come along. Fewer still read the whole thing and realize the high-vote answer is wrong and vote accordingly ... ctd $\endgroup$ – Glen_b Apr 20 '17 at 23:23
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    $\begingroup$ ctd... but there are always more less-expert people coming along and many upvote the popular-and-plausible answer, so it stays "at the top" ... apparently forever. $\endgroup$ – Glen_b Apr 20 '17 at 23:23
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    $\begingroup$ (+1) An up-vote means "This answer is useful" - we're reminded of that in the mouse-over text. Making such a recommendation to a colleague, client, or student, if you didn't understand the answer, would be dishonest, & risky. $\endgroup$ – Scortchi - Reinstate Monica Mod Apr 21 '17 at 8:05

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