is all math beyond arithmetic just advanced arithmetic?

A person suffering from the usual laypersons' extreme confusions about the nature of mathematics posted the question linked above. Might I be right in guessing that it was closed as "not about mathematics" because of those confusions?

If it had been open, I might have posted as an answer what I posted as a comment:

Your erroneous assertion that computers can do advanced math is the clearest indication of where you're coming from. Let's take an example: "Twin primes" are prime numbers like $101$ and $103$ that differ by $2.$ Nobody knows whether there are infinitely many of them, although Euclid showed in about 300 BC that there are infinitely many primes. Suppose you ask a computer: Are there infinitely many twin primes? A computer can't answer that any more than a computer can tell you whether Purgatory exists. But you may use a computer in your efforts to answer those questions.

Would that be worthless as a way of beginning to enlighten someone about mathematics? Might it not have had that effect on many who saw it? Does that not further this site's purpose? This is supposed to be about mathematics at all levels. Does that include the level of those who harbor these typical laypersons' confusions?

(To me this seems like gratuitous disrespect to someone who posted in good faith. But my questions are above.)

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    $\begingroup$ As I have always understood it, the site is for mathematical questions at all levels. The question linked here is not a mathematical question (although it is in some sense a question about mathematics), and so the closure seems to be in line with the standards this site has had for years. When we say that this site is for mathematics at all levels, we mean that people can ask mathematical questions about calculus or other basic topics, but the question themselves should still be of a "mathematical" nature. $\endgroup$ – Carl Mummert Jul 25 '16 at 1:34
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    $\begingroup$ With that being said, I think that this general line of posting questions on meta about routine closures on the main site, which are in line with standard practice on the main site, may be becoming somewhat tendentious. $\endgroup$ – Carl Mummert Jul 25 '16 at 1:35
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    $\begingroup$ It is not completely clear whether your inquiry is about this particular questions or whether the question serves only as an illustration of a more general issue you with to discuss. If it is the former, you should add (specific-question) tag - see the tag-info. (In general, using correct tags when posting questions is useful for several reasons, both on main and on meta. In this case I have added a tag corresponding to questions about scope of the site. If I misunderstood your post, pleas do retag it.) $\endgroup$ – Martin Sleziak Jul 25 '16 at 4:00
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    $\begingroup$ I had in mind that this is an example. Some other examples are subtler. In some cases the person asking the question is overwhelmingly confused and yet it is clear what sort of answer would contribute to clearing up the confusion. $\qquad$ $\endgroup$ – Michael Hardy Jul 25 '16 at 17:44
  • $\begingroup$ I suspect in less than 100 years (make it 300 years if want, but I believe even 100 years is pretty generous) computers will be able to attack (if not solve) the first problem, the one about twin primes. And no programming would be needed either, you just verbally ask Multivac (or maybe just think it, if you're "plugged in"). $\endgroup$ – Dave L. Renfro Aug 4 '16 at 16:28
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    $\begingroup$ @CarlMummert : If this is not a mathematical question, can you suggest who is better qualified that mathematicians to answer it? $\endgroup$ – Michael Hardy Oct 14 '19 at 19:11
  • $\begingroup$ @CarlMummert : You wrote: "this general line of posting questions on meta about routine closures on the main site, which are in line with standard practice on the main site, may be becoming somewhat tendentious." What is clear about standard practice on the main site is that a small number of users who close questions are regulars in that activity, and that in their policies that determine what practices they treat as standard they are serving purposes that are not publicly avowed. And they have a policy of censorship: They effectively forbid discussions or questions on.... $\endgroup$ – Michael Hardy Nov 24 '19 at 4:56
  • $\begingroup$ ....."meta" about their practices, closing "meta" questions about those practices on bogus pretexts. $\endgroup$ – Michael Hardy Nov 24 '19 at 4:56

It seems to me that inevitably it is not possible to qualitatively distinguish confusions/questions "typical to laypeople" from many of the questions/confusions arising among 20-year-olds taking undergrad math. The latter are identifiable not by some innate qualities so much as by the narrowness of range and by specificity. If anything, "low-level" questions arising outside the heavily cliched standard U.S. undergrad curriculum might be more interesting, more honest, more intellectually genuine. So, seriously, I myself am strongly inclined to honor very-naive but/and honest, genuine questions at least as much as somewhat half-hearted, homework-confusion questions.

One can reasonably argue that "typical laypersons'" questions might be very difficult to answer usefully, because the chasm is too wide. But I think the more accurate portrayal of the feasibility of explaining things in undergrad-math standard-curriculum context is only that the scope is sooooo narrow, and the context soooo constrained. Not that the questions are better or more worthwhile.

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    $\begingroup$ I agree basically with everything in this post. It is not only that the chasm is too wide; some questions are just too broad, too vague, too discursive. For the specific example, I think many among us could imagine to write a paragraph as a reply to the inquiry linked in OP. I assume most mathematicians are somewhat routinely confronted with this type of inquiries; in any case, I am. The point is though, it is in my opinion, too discursive a subject for this site; for ex., ever since it was posted I need to constrain myself not to state my opinion on the answer propose in OP. $\endgroup$ – quid Mod Jul 26 '16 at 14:49
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    $\begingroup$ In particular it seems to me that leading lights through history, such as Leibniz and Hilbert, have struggled with the topic of whether everything in math could be resolved by "advanced arithmetic" of some kind. $\endgroup$ – hardmath Jul 26 '16 at 23:36

The quote in fuller form is that the site is "for people studying mathematics at any level and professionals in related fields."

In isolation I'd understand 'studying mathematics' following higher-education on the subject (or something close to this), and the 'any level' is to be understood in that context.

If "studying mathematics at any level" would just mean "everybody having come across some question that may be mathematics" what's the point of naming explicitly "professionals in related fields"?

In that sense, the practice of the site is rather more permissive than what I would consider as implied by a literal reading of its on-topic (and this seems reasonable to me).

Namely, the site is open to everybody having a mathematical question, provided the questions is actually a mathematical question, and it lives up to certain standards defined by the community over the years. (While these standards may not be accepted by everybody I feel it is fair to say that there is at least a plurality of users that support them; if this were not the case, they just would not have been adopted or in any case would not be enforced.)

Thus, it is not the intent to have a site for laypersons to get clarification on any-and-all confusion related to mathematics. Instead, the intent is to have a site for everybody to ask and answer mathematical questions with certain characteristics.

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    $\begingroup$ +1 for the final paragraph. IMO the site is open to laypersons and all other people who have a sufficient knowledge of mathematics to talk about it reasonably. The different from MO is that we don't artificially limit the questions to graduate-level or research-level, but we can still expect people to write about questions of lower levels with a certain amount of mathematical sophistication. $\endgroup$ – Carl Mummert Jul 25 '16 at 1:40
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    $\begingroup$ Since the site's inception (in beta), it has always been the goal to welcome mathematical questions at all levels. This does not imply undergraduate level or above (or any other lower limit). $\endgroup$ – Bill Dubuque Jul 25 '16 at 2:35
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    $\begingroup$ Yes- there is no lower limit on the level of the mathematics. But that does not imply that the site is especially useful for someone who isn't (yet) able to discuss mathematical questions or pose mathematical questions clearly. It is possible to discuss low-level topics clearly (and to discuss high level ones unclearly). The level of the question is not a factor, but that doesn't mean low level questions shouldn't meet the same standards as higher level ones, or vice versa. $\endgroup$ – Carl Mummert Jul 25 '16 at 3:09
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    $\begingroup$ @BillDubuque the answer concerns specifically the description of the target audience. I even contrast it with the practice of the site. Other than that Carl said it well. $\endgroup$ – quid Mod Jul 25 '16 at 14:24
  • $\begingroup$ There are 3 different target audiences: those who read, those who ask, and those who answer. This answer confuses the third with the second (and in some ways the first). The ideal minimum level of knowledge for posting answers is the one you named, but this meta topic is about what can be posted as questions. For that, "at any level" really means "at any level" and has always been interpreted as that. The age 13 registration minimum and the overlap with specialist sites (Stackoverflow, MO, CS, phys, stat, ...) make it higher on average in practice, but not in principle. @quid $\endgroup$ – zyx Aug 5 '16 at 15:07
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    $\begingroup$ @zyx there is the target audience of this site, which is the value of some variable in a database and displayed at various places. As explained just above "the answer concerns specifically the description of the target audience," this string. The question attempted to present as evident those questions are on-topic because of the description. I explain why this is not at all clear, but rather the other way round. The practice of the site is a separate matter. Tangentially, why do you think all those sites you name are specialist sites? As far as I know, several in fact are not. $\endgroup$ – quid Mod Aug 5 '16 at 15:34
  • $\begingroup$ Both as obvious functionality of the site and as things Stackexchange has said in many ways, the ideal pool of users who provide most answers is (much) narrower than the ideal pool of users who generate the questions which is narrower that the ideal set of users who view the pages. You need only search the SE blogs for words like "experts", or use common sense. All this is equally true on a per-question and per-tag or -topic basis, not only the site as a totality. By variable in database I hope you are not seriously referring to the site "blurb" as some SE metasites call it. $\endgroup$ – zyx Aug 5 '16 at 15:53
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    $\begingroup$ @zyx it appears quite transparent to me that I refer to the text I quote at the start of my answer, which is the target audience of this site (in the technical sense of this term as used in the SE network). It is still not clear to me why you are under the misconception all these other sites are specialist sites (as several are not). $\endgroup$ – quid Mod Aug 5 '16 at 16:23
  • $\begingroup$ Users of math.SE who are also users of sites for technical subjects like computer programming, engineering, physics, CS, chemistry, statistics, TeX, or cryptography are much likelier to have gone through some process of academic or professional specialization that includes mathematics beyond high-school level. As compared to users of random or SE sites on subjects of general interest, such as the ones for cinema, science fiction, languages, religion, skepticism, and travel. It seems reasonable to call the first type of sites "specialist" or "technical" or similar. $\endgroup$ – zyx Aug 5 '16 at 17:20
  • $\begingroup$ The "SE technical sense" description of what you call target audience says all levels, and has always been interpreted to mean literally all levels (for both users and questions). The previously unheard-of (before your answer) expectation of undergraduate level or higher does not exist in relation to questions or their askers, but it does describe what is sensible and probably intended, on average, for authors of answers. In effect you are talking only about the targeted set of answerers and noting, correctly, that it differs from the targeted readers and question posters. $\endgroup$ – zyx Aug 5 '16 at 17:32
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    $\begingroup$ @zyx There are numerous inaccuracies in what you write. If you want to discuss with me please be precise. It does not say 'all levels' in the target audience. (Yes, this is a minimal detail but I feel it is typical.) $\endgroup$ – quid Mod Aug 5 '16 at 23:56
  • $\begingroup$ Placing quotation marks around (correct, accurate) paraphrases and then (falsely) calling them inaccurate is lame, as are the other (also incorrect) semantic quibbles you have been pursuing as an alternative to answering the huge and basic point. That is, that your answer totally misrepresents the SE site description as naming the "target audience" of the site. The blurb is written for the private or public beta, where the explicit goal is to attract experts. Roughly, the beta target users are the target answerers for the post-beta site and the blurb is written to attract them. $\endgroup$ – zyx Aug 7 '16 at 6:10
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    $\begingroup$ @zyx Again, I explain how "[i]n isolation I'd understand" a certain string that is prominently displayed in information about this site. (Note the 'in isolation' and the conditional.) Superficially this may not appear to be that relevant, but I feel it was relevant in the specific context of this question (in combination with earlier contributions of its OP) as I understood the point of the question-post as the claim that as a consequence of how the site is officially described, this string, we ought to welcome laypersons' questions. $\endgroup$ – quid Mod Aug 7 '16 at 10:23
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    $\begingroup$ If you find this irrelevant please just move on. If you want to continue to disagree please explain why my reading of the sentence-fragment "for people studying mathematics at any level and professionals in related fields" is implausible even independently of the practice and history of the site. @zyx $\endgroup$ – quid Mod Aug 7 '16 at 10:26
  • $\begingroup$ You do not say whether you do or do not agree with Carl Mummert's absurd statement that the question is not mathematical. But anyone who thinks that only mathematical questions get large numbers of up-votes on this site with no down-votes hasn't been paying attention. And I wonder if you would disagree with the proposition that a far higher level of honesty prevails in intellectual activity outside of academia than within? $\endgroup$ – Michael Hardy Nov 24 '19 at 5:10

I don't usually chime in on Meta, but...

About four years ago, I asked a question on this site which, to me, feels quite similar in spirit. To paraphrase: What is analysis like at the research level? It has 125 upvotes (at the time of this writing), and no one has ever discussed closing it.

And maybe my question should be closed. But I genuinely don't see how "What is analysis like at a level beyond my current education?" is much different from "What is math like at a level beyond my current education?"

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    $\begingroup$ No, it's not the same exactly. Try explaining Macbeth to someone who understands English, and try explaining it to someone who shares absolutely no common language with you. Only one of these cases has any hope of being successful. $\endgroup$ – Asaf Karagila Mod Jul 26 '16 at 5:23
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    $\begingroup$ @AsafKaragila I think the paragraph MichaelHardy included would still have answered the layman's question. So you cannot say that there is absolutely no common language. $\endgroup$ – flawr Jul 26 '16 at 16:55
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    $\begingroup$ @flawr: I have proactively made the decision not to get involved in this discussion as a whole. I do however, disagree with the interpretation of "what is math beyond my current education" is a good question for every level of education. $\endgroup$ – Asaf Karagila Mod Jul 26 '16 at 16:57

There may be many other reasons why a question seems confused, Maybe English is not OP's native language. Maybe the OP is asking a question in a field of mathematics they are not familiar with. The question should not be closed without any explanation. Doing so will not encourage people to learn about maths.

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    $\begingroup$ Not whining, but I really want to know what I am doing wrong to get negative votes - then I can do better. $\endgroup$ – xatabay Aug 3 '16 at 20:26
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    $\begingroup$ I did not downvote the post, but it does not seem very specific to the question asked here. Also the saying "There are no stupid questions, only stupid answers." is in my experience not overly popular with some around here. Moreover, the point is not if the question is "stupid" but if it should be addressed on this site. There are good questions that just are not suitable for the site. $\endgroup$ – quid Mod Aug 3 '16 at 21:14
  • $\begingroup$ Thank you @quid. I have edited my answer to remove personal experience - is it more specific now ? $\endgroup$ – xatabay Aug 4 '16 at 7:55
  • $\begingroup$ I think it's a bit better now. I'd leave it as is now. $\endgroup$ – quid Mod Aug 4 '16 at 8:50

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