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Sometimes, the asker does not have sufficient background to verify an answer. How should one handle such cases?

Some of the signals on whether to accept such an answer are whether it 'looks' good, the reputation of the answerer (in the relevant subject area), upvotes, and that relevant comments are addressed. However, it is common for upvoters not to really verify the answer either.

I suggest that (despite the policy against 'me too' comments) it is ok for users to comment that they verified the argument, and that it is also ok for the asker to politely ask for such a comment. We may want to have some form of 'reviewed by' tag to separate these from regular comments. Also, none of this is meant to detract from that MathOverflow answerers are usually well-meaning persons who prize accuracy. For both the answerer and the community, having a confirmation that one did not make a mistake can be valuable.

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    $\begingroup$ The up/down votes already let you say what you think of an answer. Personally, I don't see why it's a big deal if an answer gets accepted. $\endgroup$ Mar 26 at 20:47
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    $\begingroup$ @SamHopkins I don't think it is simply about accepting or not an answer, but about having confidence in the answer's accuracy. $\endgroup$ Mar 27 at 1:05
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    $\begingroup$ @AndrésE.Caicedo I see. Well, I think that "I checked this argument and it make sense"-type comments under answers are fine, in the right circumstances (e.g. when the argument is long, involved, or surprising), but I don't think we need a whole separate system for them. $\endgroup$ Mar 27 at 1:09
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    $\begingroup$ I've even seen comments to the effect of "wow, this is a genuinely new idea!" posted under an answer: check out for instance the accepted answer of mathoverflow.net/questions/253059 $\endgroup$ Mar 27 at 1:10
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    $\begingroup$ I don’t think you should trust a published paper without personally understanding it, much less a short post on a website. Adding a thin veneer of “peer review” to MO would be bad in the sense that it would encourage people to be overly trusting of it. If you need something here for a paper or something, do your due diligence! $\endgroup$ Mar 27 at 11:11
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    $\begingroup$ @AndyPutman Perhaps you verify all the main proofs in the area you are working on, but in other areas one sometimes reads a survey of results (with some illustrative proofs) that were verified by others. $\endgroup$ Mar 27 at 16:15

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As most commenters on the question seem to agree, adding special protocols or machinery for this seems misplaced: MathOverflow isn’t a peer-reviewed venue, it can’t be, and we shouldn’t encourage people to treat it as such.

I agree though that it’s often useful to know if other users (especially with a reputation as knowledgeable/reliable on a topic) endorse an answer’s correctness, and that as a less-expert reader, it’s reasonable to ask for help judging that. So equally as commenters, browsers, and moderators, we should recognise such information in comments as valuable.

That said, there’s almost a better way to word such comments than just as bare endorsements/requests:

  • Can someone please confirm if they think this answer is correct? — Uncertain OP.

  • I have read this answer and endorse it as correct. — Big Expert.

These can be improved both in content and tone by being more specific:

  • Thanks, this seems to answer my question, though I don’t immediately follow the functional estimates in step 3. — Uncertain OP.

  • The functional estimates follow by techniques of vibrational factorisation, see e.g. Münster’s book. — High-Rep User.

  • +1 good counterexample, functional estimates v ingenious — Big Expert.

  • This works but seems rather more complicated than necessary; I think you can also replace the quadratified term in the variator by a pseudoconstant and then appeal to Kaškaval’s Theorem for the estimates. — Anonymous User.

All these replies show that the commenter has read the answer carefully enough to believe it’s correct (so, just as much as a bare “endorsement” comment implies), but say something more as well. Similarly, this query shows that help judging the answer from others is welcome, but also pinpoints the uncertain spot.

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    $\begingroup$ I like this answer, but I disagree about the peer review remarks. In my view, MO posts typically undergo something like a high-quality peer review—I believe they are often better refereed than published work. We get feedback of experts and revisions, approvals, etc. What more does one want from peer review than this? $\endgroup$ Apr 10 at 15:51

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