# Closing of “Is this proof of a^{1/2} being either integer or irrational circular/incorrect?”

The following thread was recently closed not longer after I posted the original version of this question Is this proof of a^{1/2} being either integer or irrational circular/incorrect?. This is certainly a topic that deserves community input before closure. No doubt other topics like this will arise in the future so discussion may prove helpful for future purposes. Could those who voted to close please explain their reasons below. Note that the OP has already clarified his question to make it precisely clear that the question is not a duplicate (why Pete L. Clark says it should be closed) and I agree with the OP. Please discuss here before voting to close (so much for wishful thinking)

• Is there any reason you feel this addresses a general policy issue rather than the specific issue of whether question 4572 should be closed? – Larry Wang Sep 15 '10 at 17:57
• @Kaestur: Implicit in this are subtle policy issues regarding how much subjectivity to allow. Questions about whether a proof is correct, or whether some justification is so "obvious" that it can be omitted are, ultimately, subjective. But learning how to make such judgement calls is an essential component of learning how to compose proofs acceptable to one's peers. So I think it is useful to permit some amount of subjectivity in order to allow discussion of such topics. One often learns this by osmosis, but forums like this can help accelerate that learning curve - which textbooks cannot. – Bill Dubuque Sep 15 '10 at 18:18
• I understand that you feel strongly about this issue, but please try to keep the question title, at least, more neutrally-worded. – Larry Wang Sep 15 '10 at 23:54
• @kaestur: I don't wish to appeal the closure. I don't want to waste any further time on what is clearly a lost cause. The software model is fundamentally flawed. 5 people should not be able to speak for the whole site. – Bill Dubuque Sep 16 '10 at 0:06

I've voted to close, because the thread is turning into a flamewar over what seems to be nit-picking, and I think all the important points have been said and re-said.

• I find it quite disturbing that it seems to be the same handful of people responsible for most of the closing votes - imposing their narrow views on the rest of the site. When the site first started a goal was to make it more inclusive than mathoverflow. Sadly it seems that quite the opposite has occurred. – Bill Dubuque Sep 15 '10 at 22:45
• FWIW, @Bill, I wouldn't have accepted the proof either were I a grader. But I don't see how the thread was useful in any mathematical way, and I don't want this website to be characterized by these kinds of arguments. Also, this site is definitely more inclusive than Mathoverflow: notice that questions at (almost) any level are accepted. – Akhil Mathew Sep 16 '10 at 2:09
• @Akhil: I do appreciate your explanation even though I disagree. It is extremely frustrating to have worked so hard to try to explain certain points to others and then have the thread closed before I could post a long thoughtful reply. This is the third time that has happened here and it seems to be the same folks always closing these questions. Please, could you try to be a bit more open-minded in the future. – Bill Dubuque Sep 16 '10 at 4:03
• Lest you forget, the most recent other question you helped close on me was bit.ly/90vr4W which, as you can see from the many votes to my partial answer, proved interesting to many folks. I think it could have been much more helpful had I been able to finish it. But, alas, the question was quickly closed in the middle of editing my long answer (10 minutes after my first draft was posted). Now there's little motivation to finish it since, being closed, it will get little exposure. Nor did the associated meta thread bit.ly/99xW5N help get it reopened. That's quite frustrating. – Bill Dubuque Sep 16 '10 at 5:10
• @Bill: I have explained why I voted to close that particular older one; it's a separate issue that reflects my philosophy (namely, that the possible existence of a good answer does not in itself justify a badly written question's being open). On this question, I think it is even more clear-cut, namely that both sides have already explained their positions quite amply, so closure will have no effect other than possibly damping a flamewar. – Akhil Mathew Sep 16 '10 at 20:40
• @Akhil: Perhaps you should introspect a bit and consider the global ramifications of your "philosophy". The threads that you helped to close perhaps could have stimulated some student to go on to study one of these topics, perhaps leading to publications or thesis work. I've seen that happen many times in other math forums. Why take some action that forcefully prevents that possibility simply because of some subjective judegement about the quality of the phrasing of the question? – Bill Dubuque Sep 16 '10 at 22:02
• @Akhil: As for this topic, don't you think the participants should be the judge of whether or not they have "already explained their postions quite amply"? There may have well been others - that like I - were planning to compose a thoughtful reply when time permitted. I saw no "flamewar". I just reviewed the whole thread and I saw nothing heated at all. Yes, there were frustrations trying to get points across, but nothing remotely resembling a flamewar (perhaps you've never seen a real flamewar, e.g. on a usenet newsgroup). In fact progress was being made at the time the thread was closed. – Bill Dubuque Sep 16 '10 at 22:11
• @Akhil (continued). Many people invested a lot of time effort attempting to explain these subtle matters. You invested one second of effort to click on close and stifle the entire discussion. Do you honestly think that is fair? – Bill Dubuque Sep 16 '10 at 22:13
• @Bill: The philosophy of discouraging questions that are bad even if they could admit a good answer is largely intended to discourage bad behavior from the OP: it's lazy to ask an overly vague question, and it's likely that the answers (however helpful) won't be useful to her. For instance, I don't like the question "What are you favorite theorems?" although I might certainly learn something interesting from it. For this particular question, the extent of a long debate alone makes it quite clear to me that it wasn't a mathematical discussion--or the issues would have been long resolved. – Akhil Mathew Sep 17 '10 at 13:08
• @Akhil: The question is about the correctness of a proof. Such questions aren't off-topic here. Moreover, as I stressed above, one of the primary values of a site like this is that students have access to expertise to help them learn how to write good proofs - to learn what details are essential and must be included, and what details are trivial and may be omitted. Not every student has the same privileges as did you. They may not be able to learn such things elsewhere. Voting to close such topics may rob students of their only available access to expert advice. Think globally, not locally. – Bill Dubuque Sep 17 '10 at 14:56
• I agree with Bill here. Even i was surprised as to why the question was closed. The OP needs a clarification and its our job to provide one. If this question was closed then why not the question which says that $5^{n}+n$ is never prime, which is based on computing, rather than some mind work. – Chandru1 Sep 18 '10 at 8:25

I don't see how the question is ambiguous or vague, and I think that the question itself is not an exact duplicate - it is asking about problems with a particular proof of a statement, while the prior question was asking how to prove the statement.

Given its history, I wouldn't argue against anyone who wanted to close the question as "subjective and argumentative," which I agree fits the question, but since most of the discussion has been taking place in comments, I don't see this as deserving of an instant mod-close. (My interpretation is that closing as S&A is intended to prevent many individuals posting their own subjective opinions as answers, which fragments the discussion while keeping the question high on the "active" list.)

• Your vote to close contradicts what you wrote above. Could you please edit the above to reflect reality. – Bill Dubuque Sep 15 '10 at 23:27
• @Bill: To clarify, when I said that closing as S&A was not super-urgent, I meant that I wouldn't use my ♦ super-vote, and if it is reopened, I will not vote to close again. I waited for more users to weigh in and cast a pseudo-normal vote (at 3 instead of 4 because Isaac agreed). I don't know what more to say about the topic that other people and the words subjective+argumentative themselves haven't already covered. – Larry Wang Sep 15 '10 at 23:38

As I said, I feel that this newer question is, mathematically speaking, a duplicate of the previous question. The material that has not been duplicated is subjective and argumentative: it has long since been agreed that the original response in question was not a complete proof. (If it matters, I was the second person to assert its incompleteness, and I filled in the missing details in a comment.) The discussion has now shifted to whether this is "acceptable" in various senses.

Most of the participation has been in the comments, many of the participants seem frustrated with each other, and many of them have commented that they are finished, or want to be finished, with the question but keep getting dragged back into it.

So I could have listed subjective/argumentative as well, and perhaps I should have. (Of course, I can only choose one.)

Of course people need not agree with me, but as a policy matter, I do not see why discussion on meta is necessary before casting a vote to close. (From what I have read, Mr. Dubuque seems to advocate that almost any vote to close should be discussed on meta. This is a tenable position, but not the standard one.)

Finally, if I were Douglas S. Stones, the continued existence of this question would annoy me to the point of seriously contemplating taking my PhD-level math expertise elsewhere. Probably even those who view his answer as being "bogus" (not such a nice word) consider the bogusness to be a forgivable sin, and I hope they will take this into account.

• Regarding your last paragraph, Moron's question could easily be edited to remove mention of any specific name, greatly alleviating those concerns. I agree that the choice of "bogus" was not the best one (he is quoting someone else's characterization of the proof - for those who may not be aware of the prior history). – Bill Dubuque Sep 15 '10 at 19:43
• To be sure, it is certainly not my opinion that "almost any vote to close should be discussed on meta". I don't know how you got that idea. As you surely know, I have a much less conservative view than do you on this and many matters, but certainly not that extreme. I do think it is quite unfair that 5 people can speak for the entire site and close discussion - after which it is very difficult if not impossible to reopen due to asymmetry in the software design. – Bill Dubuque Sep 15 '10 at 19:48
• I've removed the word 'bogus' from the title; now it only lives on in the body, where it is identified as a quote. – Larry Wang Sep 15 '10 at 20:39
• @Bill, @Pete: I think the source of the confusion on the "discuss on meta before voting" issue comes from this meta question, specifically AgCl's answer. Let's try to prevent that conversation from spilling over into this one. – Larry Wang Sep 15 '10 at 21:00

I'd just like to point out that my answer came after most of the other discussion. It seemed to me there was something valuable to take away from the whole business, and I'm glad the question remained open long enough for me to chime in.