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there is a large literature about what Mathematics is. but what about what mathematics is not.

for instance the question displayed in the following image is, for me an example of what mathematics is not(it is quite common to see such kind of question in social media). It is not mathematics because its solution relies on a linguistic joke: 20 for three). Not mathematics lateral thinking, perhaps. Note:Brigadeiro is a candy) enter image description here

so my question is about references and examples of what mathematics is not.

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    $\begingroup$ Mathematics is not cheese. Mathematics is not family feuds. Mathematics is not the colour blue. Mathematics is not that time last year when we went to the fair. Mathematics is not ... very imprecise questions which, until they are made much, much more precise, allow an infinitude of answers. $\endgroup$
    – Torsten Schoeneberg
    Sep 4 at 4:49
  • $\begingroup$ @TorstenSchoeneberg; there is a caveat : people tends to see math everywhere (in chesse(appadvice.com/app/math-and-cheese/846339884), family feuds, etc. ). see for instance this page from the international mathematical union: everywhere.idm314.org/.Worst: we do not teach our students about what mathematics is and what it is not ... they don't make any reflection about this :( $\endgroup$
    – Humberto José Bortolossi
    Sep 4 at 20:43
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    $\begingroup$ To me, it is unclear what the question is asking and could do with clarification and more context. $\endgroup$
    – Adam Rubinson
    Sep 6 at 9:25

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While I don't know of any outside references that definitively answer your question, the following decision rule pops into my head:

Does the correct answer to the question permit counterexamples? If so, then it's not a mathematical question. (If not, then it may or may not be a mathematical question.)

For instance, the question in the image that you posted would not be a mathematical question because Juliana could very well have prepared those brigadeiros at any of the listed times. (Perhaps one time is much more likely than the others, but all times are possible.)

Note: I wouldn't bet my life on this decision rule being 100% correct, and I don't claim that it definitively answers your question, but it seemed like it might useful enough to share.

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    $\begingroup$ A restatement of your decision rule: if the question's correct answer is not definitive, then it is not a mathematical question. $\endgroup$
    – ryang
    Sep 4 at 11:37
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    $\begingroup$ Ah, well, "yes", but I vividly recall first learning the phrase "morally correct", about fancy mathematical assertions, many years ago in grad school, from Nick Katz, a very serious mathematician. It means that the spirit of the thing, the idea, is correct (and, implicitly, is of interest, and is useful), but it needs tightening up before it will be literally correct. :) $\endgroup$
    – paul garrett
    Sep 5 at 0:21
  • $\begingroup$ @ryang, how does your criteria handles this, for instance? hsm.stackexchange.com/questions/6159/… $\endgroup$
    – Humberto José Bortolossi
    Sep 5 at 11:36

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