# How to answer proof-verification questions?

Sometimes, questions ask for verification of a valid and overall solid proof (some examples: What is the $\dim L(X,Y)$?, Prove $(\overline{A \cap B}) \subseteq \overline{A} \cap \overline{B}$., If $f_n(t):=f(t^n)$ converges uniformly to continuous function then $f$ constant).

Standard behaviour seems to leave a comment similar to “yes, looks good to me.”. (See the above examples.)

In my opinion, this is not a good practice. First, comments are, in theory, ephemeral, and second, these questions still appear to be unanswered.

I think the best way to handle this would be to answer “yes, your proof is correct.” as a community wiki answer (thus allowing other users to add minor improvement suggestions).

• I think the best way to handle them is to tell the asker what's wrong with their proof / tell them their proof is correct and close the question as a duplicate when a duplicate exists (like in almost every case). When a duplicate doesn't exist, it's more tricky, but IMO the best thing to do would be to correct the proof / tell the asker their proof is correct and also encourage other people to post other proofs (so that this particular post can become the canonical dupe target for this question). The math.SE culture doesn't work like that, unfortunately. Mar 28 '15 at 16:20
• (Disclaimer: I posted a comment telling the OP of the first linked question that their proof was correct and started looking for a duplicate, then got busy and forgot. Sue me :) .) Mar 28 '15 at 16:21
• As an aside, the proof-verification tag is one of the few meta tags that I really like. When I'm interested in finding some old unanswered question to mull over, it's very nice to be able to ignore this tag or exclude it from searches, which is very handy. This hits a happy medium between being a searchable Q&A archive and being the best place to get help on math on the web.
– davidlowryduda Mod
Mar 28 '15 at 16:35
• I don't see why it has to be a community-wiki answer if the proof takes some effort to decipher.
– Fizz
Apr 11 '15 at 21:03

Most of the time it is in my opinion and observation possible to give a more detailed answer.

Points that can often be addressed include:

• Suggesting minor improvements of the presentation or variations.
• Giving a high-level summary of the argument.
• Mentioning points where details might be added (even if not strictly needed).
• Putting the argument in a larger context.
• Suggesting alternative arguments.

I do not mean to say that all the time all this should be done. I only mean to say that almost always at least one of this can be done.

Doing so will not only make for a more interesting answer, but can also raise confidence in the veracity of the answer and thus the proof in OP.

Anybody can post "This is correct." If this is of any value at all depends mainly only on who said it and possibly the score. This is not optimal for an answer. An answer should be able to stand at least a bit on its own. It should not just give the binary information in/correct but also addres the "why."

This is a bit like when conducting a session of a course where students present their solutions of homework to the others. I think, normally, an instructor should make some remarks during or after a student's presentation beyond "This is correct."

Thus, I do not consider it good practice to post a "This is correct." answer, at least not early on. (As a comment it is fine.) The point is precisely the question will appear to be answered while actually it does not have a detailed answer.

There is also a practical concern. Very short answers generate an automatic "low quality"-flag. First, treating these flags is work. Second, somebody answering in such a way should at least pay attention to make very clear that the answer is not a "misplaced" comment, which is not always the case. Leading to confusions, and still more work.

• Bullet 5 also includes alternative (possibly shorter, more elegant, more general, etc.) proofs, right? Mar 28 '15 at 20:58
• Yes, with the caveat that I do not think that an answer that only gives a different argument yet does not address what OP did themselves is a valid answer to such a question.
– quid Mod
Mar 28 '15 at 21:18
• I think an answer like "Your proof of [thing] is fine, but the following approach yields a shorter proof:" is fine, since it's both, interesting and an answer to the question "Is my proof correct?". Mar 28 '15 at 21:20
• Yes, as long as there is an evaluation or at least mention of the proof this is alright. It can even be quite helpful. What I do find problematic are answers that just give a different proof of the statement, completely ignoring the question. asked.
– quid Mod
Mar 28 '15 at 22:25
• Perhaps another possible bullet: if you can coerce the poster into divulging which part of the proof they are uncertain of, then the relevant material can be explained so that the poster can decide for themselves whether it is correct or not. Apr 5 '15 at 20:26

At least when the question has been there for some time and nobody has found anything to say about it except "yes, that is correct", then I think it is appropriate to post an answer to that effect, possibly as CW.

This will prevent the question from being listed as unanswered.

(For example, this question had a CW answer with "yes, that is correct" posted after 3+ years. Several people from the review queue actively deleted that answer which I think is strictly a disservice to the site and the community).

• I think there are better ways to handle this. One could encourage OP to turn the proof-verification question into a self-answered question. If OP is not around anymore somebody else could do it; if the proof is so flawless that there is nothing to say, it's just a copy-paste. (That this happened could be briefly documented.)
– quid Mod
Oct 8 '18 at 19:42
• @quid: so the proof itself is the answer to the question whether the proof is correct? Stripping the proof out of the question seems to completely change the meaning of the question. But this is why I think that these questions should be discouraged in the first place, or that we should prompt the asker to be more specific. "Is this proof correct?" What part are you unsure about? What makes you think it might not be correct? If the OP adds that info, we can write more informative answers. Oct 8 '18 at 21:23
• @Carl what I'd propose is stripping it out of the question, yes. There could be a not somewhere "this was initially asked as a proof verification." If the post in the modified form is not worth it, another solution would be to removed the thing entirely.
– quid Mod
Oct 8 '18 at 21:40
• IMHO losing most proof verification questions would not be a bad thing - they are asked in good faith but are not really questions about mathematics, in the usual way they are posed. Oct 8 '18 at 21:41
• @CarlMummert: I don't disagree about that -- but as long as we do have them I don't see any value in keeping them artificially neither-closed-nor-answered. Oct 9 '18 at 2:30
• @Henning I agree, I had already upvoted this suggestion. Oct 9 '18 at 10:52
• It's not very clear then why you proposal goes into the direction of having them answered then. I mean you could also propose closure.
– quid Mod
Oct 9 '18 at 17:07
• @quid: I don't think we currently have a closure reason that fits these questions. Also, posting a CW answer can be done by a single user, closing the question is a more involved process. Oct 9 '18 at 19:26
• Any close reason can be recorded as "other." We also don't have a policy that allows such answers. Also if no one upvotes or accepts the answer it does not achieve the goal of getting it of the unanswered list.
– quid Mod
Oct 9 '18 at 19:29
• Beyond these technicalities a main issue I have is with the "when the question has been there for some time"; your example is 3+ years old so I'll grant that's clearly a long time; yet just today I saw examples posted within a day however. If such answers are given sometimes they'll become more popular over time; the delay-condition will not be understood.
– quid Mod
Oct 9 '18 at 19:33
• Here is one within a minute or two.
– quid Mod
Nov 19 '18 at 7:28