I asked a question about a currently active Internet discussion (What is the reason for the "left to right" rule?)

I specifically asked about the algebraic reason of one mathematical rule which drives towards the correct solution.

This was met by an "On Hold" and "how much more such questions do we have to endure".

I will honestly say that this infuriated me (I rewrote my EDIT a few times to remove the politically incorrect elements). I would have understood if it was closed because there was zero research done, when an answer was one google search away. Been there, seen that. "What is the result of $8 / 2(2+2)$?" would have been such a question.

Is my question objectively bad? if so - why?. Is it completely outside the realms of the site, or should it have been asked differently?

I will take answers at face value to better understand how Math SE works.

I will also note (because I have to note is somewhere, otherwise I will explode) that I understand why people are repulsed from math sometimes, should they meet a teacher like the Math SE comments to my question.

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    $\begingroup$ There's been several questions asking about this recently, and some people have seen this already being asked & discussed in various places many times in the past, so my guess is that people dismiss it without looking at it particularly carefully. I admit I did this with your question so, although I didn't comment, I was one of the people who voted to close. Looking at it again now, although your question is to a certain extent opinion based, I now believe I was in error & it fits within the guidelines of MSE. As such, I cast the third reopen vote ($5$ in total are needed to reopen the post). $\endgroup$ – John Omielan Aug 4 '19 at 8:58
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    $\begingroup$ On main you said 'I initially asked it on Math Educators because my question is not "what is the result" but "why a particular rule".' You then deleted it there for no apparent reason. I wonder why and how this is then relevant to it being on-topic here. I actually don't mind the question here. That said, the best place might be History of Science and Mathematics if you explicitly ask about the historical developpment. $\endgroup$ – quid Aug 4 '19 at 10:38
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    $\begingroup$ @quid: I initially thought it as a "why do we teach that (what is the reason behind)", thus Math Educators. Then when building my question and looking closely at a Meta question there about the intent of the site I realized that it (the site) is rather for questions about math education as a job, and that my question was more "fundamental" (in the sense it looks for a mathematical answer, rather that why it is taught). The history part is less relevant, it is rather what maths are behind that rule (and it looks that the answer is "none, is is an arbitrary convention", which is an OK answer. $\endgroup$ – WoJ Aug 4 '19 at 10:46
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    $\begingroup$ @WoJ thanks for the reply. It's not an arbitrary convention. It could be different but it's not arbitrary, which is why the history angle could be relevant. But that's tangential. $\endgroup$ – quid Aug 4 '19 at 10:52
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    $\begingroup$ I don't think the question should have been closed in the first place. Be aware that many active users here have an extremely narrow concept of what is an allowable question here. In particular, I have a feeling that your question's "crime" is that the answer is likely in the negative (i.e. there is no algebraic reason for left-to-right vs right-to-left), but nobody felt they could give an authoritative answer to this end, so they decided to close (and likely delete) it rather than leave it unanswered. $\endgroup$ – Theo Bendit Aug 4 '19 at 12:17
  • $\begingroup$ math.stackexchange.com/questions/211086/… $\endgroup$ – user645636 Aug 4 '19 at 21:36
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    $\begingroup$ Sorry about contributing to the snark/condescension. For my part, the line where you said something to the effect that "half the internet is discussing this" pressed certain buttons, and triggered a violent reacon. I hazard a guess that I wasn't the only one to react that way! $\endgroup$ – Jyrki Lahtonen Aug 5 '19 at 12:02
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    $\begingroup$ @JyrkiLahtonen: it was trending heavily on Internet, to the point where the question was asked to Cédric Villani, Fields Medal recipient and member of the French government. The interest for that mathematical expression raised discussions here and there - something math usually does not trigger (at least in the general population). If I was a mathematician I would be happy to see any kind of interest in my subject because even if it is silly, one extra person which gets interested enough to pursue in that subject would be a victory (being a physicist, I know how it is) $\endgroup$ – WoJ Aug 5 '19 at 12:21
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    $\begingroup$ Perhaps we should start a new Internet trend that involves less mathematical formalism and have the world discuss whether "There exists a natural number $x$ such that $x>y$ for every natural number $y$" is true or false. Just as in the original trend, the correctest answer is that no-one should ever write this way, and in this case, formal language involving $\exists x\forall y$ or $\forall y\exists x$ would get rid of the natural language ambiguity, just like using fractions or parentheses would get rid of the (assumed? conventional?) ambiuity in the original case ... $\endgroup$ – Hagen von Eitzen Aug 9 '19 at 6:45
  • $\begingroup$ @quid: In my personal opinion, WoJ's question is actually best suited for Math SE rather than MathEd SE or HSM SE, since it is asking for whether there are mathematical reasons ("I believe there are algebraic reasons. [...] more than a convention [...] derived from their algebraic features") for the conventions. And I have posted an answer to explain mathematically motivated considerations that may influence the choice of conventions. It is not about education nor about history. $\endgroup$ – user21820 Aug 10 '19 at 17:29
  • $\begingroup$ @user21820 sorry to veer off-topic a bit but I don't see how you addressed the specific question of left-to-right at all. (I took this to main.) $\endgroup$ – quid Aug 10 '19 at 21:22

Please don't be "infuriated" by having a Question placed on hold. It is an invitation to improve the problem statement, not a personal criticism.

While I did not review your Question, I can sympathize both with those who voted to close it and with you for having a genuine curiosity about the rules for order of precedence. Perhaps you can find a better way to frame it, with a view to making it more susceptible of answering by a reasoned mathematical argument.

Two types of context are particularly germane here. The first is to share why the Question is important to you. Problem statement questions that don't resemble the crisp formulation of homework exercises may invite suspicion that the post is made out of "idle" curiosity. While curiosity is a fine thing, it should motivate the asker's efforts even more so than it is expected to motivate your Readers.

Which brings us to the second form of context, namely researches you've done to satisfy your curiosity before posting. Often the recitation of ground that has already been covered will give Readers assurance that not only is your curiosity not a merely idle one, but that the OP is well-informed about the problem and does not need a reply that proceeds from "first principles".

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    $\begingroup$ Thank you for the balanced answer. I was not infuriated by having been placed on hold. After 8 years or so on SE this is a mechanism I learned to actually like as it improves the quality of questions. What infuriated me is the condescension of the comments. Coming to a site with a genuine question, trying to explain what I actually mean (not being an expert) and being met with this just means that I won't come back. This is probably fine for the site and the efforts around the new code of conduct may not send a signal but this is the aftertaste I have. $\endgroup$ – WoJ Aug 4 '19 at 19:26
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    $\begingroup$ (cont'd) I used to teach at the university and I cannot imagine answering to a student that his question is "lame" or "painful" just because I did not take the time to actually listen. Should my question be obvious a delete would have been fine. Here I just saw people too important to provide an answer. Anyway - the paper by Prof Wu is the perfect answer and now that I know it, I can come back to the one person who made the effort to discuss the actual question and have a civilized conversation. $\endgroup$ – WoJ Aug 4 '19 at 19:27
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    $\begingroup$ I am also not looking for some kind of drama - just trying to show that people who may come to the site with some questions which are not, as you put it, "crisp" may end up not coming back and the site will become a circle of mutual adoration (which would be a pity) $\endgroup$ – WoJ Aug 4 '19 at 19:28
  • $\begingroup$ @WoJ: Frankly, I don't think Wu's paper is the "perfect answer", as all it deals with are exponentiation and basic arithmetic operations. My answer agrees with Wu's paper about polynomials (and I independently thought of that same example), but goes much further to deal with other notation and how one might give mathematically reasonable justifications for the typical precedence conventions for them. Moreover, Wu's paper completely fails to actually deal with the underlying issue in your inquiry, which is the conflation between juxtaposition and the multiplication symbol. $\endgroup$ – user21820 Aug 10 '19 at 17:37
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    $\begingroup$ On the other hand, questions that do resemble the crisp formulation of homework exercises rightly risk running into "no, we won't do your homework for you". I much prefer questions that are motivated by honest curiosity, however idle. $\endgroup$ – hmakholm left over Monica Aug 10 '19 at 20:37

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