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    Question 126168 has four closing votes. The reason proposed by Lee Mosher is that MO is not to help users figure out poorly written proofs on Wikipedia. I personally find that reason very strange; I don't see why the origin of the proof matters. What do you think about this?

    When there is an error in a proof on Wikipedia, this is often of interest to mathematicians. The mathematical section of Wikipedia is very useful because mathematicians have invested a lot of effort there.

    I don't believe this particular question is about an error, or even about a problem intrinsic to the proof, though. There may be unclear or incorrect parts of that page, but I think the question was just about an argument the asker didn't follow.

    I think it's a good use of MO if our discussions lead to WP proofs being corrected; at the end the world is richer by a readable proof. It seems that the WP discussion pages are usually not very successful at achieving this.

    The one thing I don't like about this particular question is that it doesn't give a link to a particular snapshot of the page, and eventually it will be hard to figure out what exactly the OP was having troubles with since the proof will be corrected.

    The question was also asked on math.stackexchange, and that site seems more appropriate for it.

    I don't want to comment on whether that specific question is of relevance to MO, but I find Lee's reasoning very interesting:

    You would be better served reading about the Banach-Tarski paradox in a carefully written and edited publication.


    In my case, because I think it is off-topic for MO to be used to decipher badly written Wikipedia proofs.

    If I get confused by an answer on MO, should I better off reading a well-written book or paper rather than hanging around on MO?

    I don't understand why the source or nonmathematical background that led to a question matters at all. If a question is not of research level, clearly off-topic, poorly phrased, etc., that can be a good reason. But why does it matter if the OP got a question when reading a particular kind of material that you think is better for learning mathematics?

    Again, I'm not saying the question is good (or bad). I just don't understand why such a thing can be a reason to close. If you close a question because you think it's not appropriate for MO, then you better be objective. You should judge the content and only the content.

    It doesn't make sense the same question would be ok if the OP were reading a book you approve. If you vote to close and say a negative thing just because the OP didn't use the kind of material you prefer, it's discrimination. The content of a question, that's the only thing that should matter unless there is some serious problem (e.g., multiposting and other behavior that is discouraged in the faq).

    You don't close a thread because "that's what you get when you learn math from wikipedia." You should point out where the (mathematical) content of the question is inappropriate for MO (e.g., how it is too elementary). "That's from Wikipedia!" can't be an objective reason on its own.


    I voted to reopen this question, and said why in a comment under the question. Since Wikipedia is used as a basic scholarly resource by many, it isn't bad or MO-unworthy asking about specific details in a WP article, especially if one wishes to improve the article.


    I didn't make the Wikipedia comment, so I can't authoritatively explain it, but here's an interpretation I'm sympathetic to:

    Before posting a request for explanation of something on MO, it's important to look into it yourself, for example by trying to find out from standard sources. The appropriate questions are the ones where it's difficult to do this, either because there is no clear reference or because a non-expert can't reasonably be expected to find one. For this purpose, reading about it in Wikipedia doesn't count as sufficient investigation. Instead, that's what the references in Wikipedia are for.

    For example, we should discourage questions like "I couldn't understand the explanation of Banach-Tarski on Wikipedia. Could someone please explain to me how it works?" The question being discussed was certainly better than that, since it formulated a specific question about a particular point in the proof sketch. One argument for why the question could be appropriate is that it's not obvious which reference to look up for this specific point; however, I think a little skimming through proofs would help with that.

    I'd propose this as a general criterion: if you run into something confusing on Wikipedia that you can't figure out after further investigation, then asking on MO makes sense, but the first step should be looking up the references from Wikipedia to see whether they explain it.

    In the particular case of Banach-Tarski, the article refers to Wagon's book, which gives a beautiful and readable exposition at length. The article also includes a proof sketch, which is rather brief and doesn't clearly explain everything (as shown by this question). That doesn't worry me, since the point of a proof sketch isn't to explain all the details, but rather just to outline the proof and indicate the main ideas.


    I think it'd have been a lot easier for me to understand the reason if it had been phrased in a way that sounds more like "OP didn't do his homework before asking" rather than "You got confused? That's wikipedia for you." It's not always clear what counts as doing your homework. But it's a legitimate reason. Perhaps, it would make it easier to see why a person finds a specific question inappropriate if he said it's because the OP should have done more research on his own before asking than if he went on how a particular resource is not good for learning mathematics and how the question he found inappropriate is a quintessential example illustrating his case against the material. I personally prefer showing it objectively (e.g., by explaining how the necessary information can easily be obtained like Henry did) to dismissing a particular resource with harsh words.

    Thanks for your interpretation, Henry, it is a generous expansion of what I intended with my terse comment. If I could have added epsilon to what I wrote it would have been along the lines of Misha's comment, giving a good reference as a better guidance to the OP, similar to what I tell my students sometimes: "Don't read it there, read it here."

    Regarding Wikipedia, my comments were intended not as a judgement nor as a snarky putdown but as a phenomenological observation, one which I hoped the OP might benefit from. Wikipedia is great. But, Wikipedia simply seems not to work so as a repository of detailed mathematical proofs. One reason is that Wikipedia has a specific design which is captured by the slogan that Wikipedia articles should not contain "original research". Another is that Wikipedia pages are unstable---they are written, edited, re-edited, re-re-edited, by..... us, the users of Wikipedia.

    Anyway, yes, we ought to help improve mathematical content on Wikipedia. I did do that for a little while a few years ago, although the wikiwar I got involved in over the "surface" article helped to form my observations about Wikipedia; some guy wanted the article to be about cadcam software modelling the hoods of automobiles. I doubt that the "Banach-Tarski paradox" article will ever have that particular problem