My question: https://math.stackexchange.com/questions/4323572/why-are-we-always-concerned-with-showing-and-proofs-in-math.

I am not upset or angry that my question had been downvoted but just surprised. After I received $2$ downvotes I added a comment for down-voters to at least explain why, however no explanation has been given. It has also gathered $4$ close votes and $5$ downvotes at this point, why is this? I have read "How to ask a good question" and it doesn't seem to me like there is anything wrong with my question. This of course is just my opinion. Could someone please explain to me why it has gathered such negative responses so I can improve my future questions. Thanks in advance.

EDIT: I have uploaded my first question to hsm. Let me know what you think I should improve on. Here is the answer to my third question on hsm, my second question. Fourth.

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    $\begingroup$ I don't think the question is a good fit for MSE, as it stands. It seems to be a "discussion-based" question : although, with some refinement, it could be a good "soft" question (I make this statement optimistically, with the idea that there are good subjective askers on this site. I'm not one of them.) For example, you could ask why a notion of "exactness" (which is what is usually the result of "solving equations" i.e. an exact value) is replaced by mere "estimation" (which is the job of inequalities and bounds) in higher mathematics : that would make a better question than it is right now. $\endgroup$ Dec 4 '21 at 11:34
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    $\begingroup$ The trouble is with the lack of precision in the word "showing" , because for me , if you gave me the simultaneous equations $x+y=2,x+2y = 3$, then I am "showing" that $x=y=1$ by solving these equations, right? So the word "show" is a bit ambiguous, as is the word "proof". What lies before that, for me, could be material for a good soft question. While I cannot argue for the down/close votes (and I'm not one of them right now), I would say that you should mention that you're in high school (in India, at that!) and give a brief idea of what questions on bounds/inequalities you've seen here ... $\endgroup$ Dec 4 '21 at 11:37
  • $\begingroup$ ... that have made you ask this question. Basically, make it clearer than it is now, what kind of question you see in school, versus what kind of question you see here. I'll also take a quick look if I can direct you to existing posts somewhere, so you can have additional context than is present. $\endgroup$ Dec 4 '21 at 11:40
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    $\begingroup$ @TeresaLisbon: I don't go too school in India...But I will heed your advice for future questions. At this point i'm just going to let the question be closed. Then I will try to have it reopened by writing it in a better way using your helpful comments. At least then it should be a good question for the site. $\endgroup$
    – Ajay
    Dec 4 '21 at 11:41
  • $\begingroup$ Yes, I'm sorry for making the sweeping deduction , but I hope the rest of it was useful. Having said that : I'll still find good posts which you can read, because the bar on discussion based questions has been significantly raised over time. $\endgroup$ Dec 4 '21 at 11:42
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    $\begingroup$ After about 10 minutes of searching , I'm not sure I can find any posts that talk about why exactness is replaced by estimation/inequalities in higher mathematicsto my satisfaction. Perhaps it is related to the fact that barely any equations can be solved exactly at that level, but the question could be different. I cannot help improve the question, I hope someone else will be able to help. $\endgroup$ Dec 4 '21 at 11:56
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    $\begingroup$ I did not vote on your question one way or another and agree with Teresa: It would have helped if you explained your level. When you are rewriting your question, I suggest you contemplate another one: When you were in elementary school, you did not solve any equations, right? You were learning how to perform arithmetic operations. Then, sometime in middle school, you started solving equations. Why? How would you explain this transition from computations to equations to a 7-year old? $\endgroup$ Dec 4 '21 at 14:03
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    $\begingroup$ One more thing: There is a wonderful book, called "What is Mathematics?" by Courant and Robbins. Consider reading it. $\endgroup$ Dec 4 '21 at 14:10
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    $\begingroup$ @MoisheKohan: Thanks for the advice. I will consider reading it that book if there is a free version online. $\endgroup$
    – Ajay
    Dec 4 '21 at 14:13
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    $\begingroup$ In a way, your closed question is about history of math: How and why did mathematics become primarily a science concerned with proofs rather than with calculations? For an answer, take a look at this freely available online article. You can also ask such a question on hsm.stackexchange.com dealing with history of math and science. But maybe it was already asked there... $\endgroup$ Dec 4 '21 at 14:21
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    $\begingroup$ Update: the question on main currently has seven downvotes (and no upvotes), and has been closed and deleted. $\endgroup$ Dec 4 '21 at 22:47
  • $\begingroup$ Just as a quick note, I am currently doing my mock exams and will be unable to edit the question until late Friday afternoon when they are finished. $\endgroup$
    – Ajay
    Dec 6 '21 at 9:29
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    $\begingroup$ @Ajay Thank you for the update. $\endgroup$ Dec 6 '21 at 12:37
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    $\begingroup$ Regarding your edit here: I cannot see how your question could be improved to be more objective (i.e. less discursive answers). For it to be reopened, you would need to be asking a significantly different question, and in this case you could ask this as a new question (because, I emphasise, it would be significantly different). I think, however, you may be better taking MoisheKohan's advice and asking on hsm.stackexchange. $\endgroup$
    – user1729
    Dec 10 '21 at 10:49
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    $\begingroup$ Posted there now. $\endgroup$
    – Ajay
    Dec 10 '21 at 12:49

A central aspect of the Math.SE mission is helping students at all levels to learn mathematics. The Question you posted (on main Math.SE) asks why "at a higher level of mathematics are we concerned with showing rather than solving equations." "Why," you wrote, "are we always looking for proofs?" As context you cited your experience "as a mathematician and member of this community."

This is a remarkably "hand waving" basis for the Question, as you've been a member of the Community for two months and describe yourself as "Just a kid who wants to use math to help others :)." From your Activity page I can see evidence of $4$ Questions and $2$ Answers, which seems commensurate with a two month participation but not a substantial sampling of Community activities as a whole.

I was not one of the downvoters of your Question, but it is for me a rule of thumb to judge the appropriateness of posts by whether there is a problem statement which can be resolved by mathematical reasoning. Definitive answers indeed do not invariably present a "proof of proposition" style response, but they do invariably rely on a knowledge of rigorous mathematics.

The history of mathematics teaches a student's need to appreciate the value of proof, which differs from other kinds of rigorous argument only in its characteristic form, whereby mathematical truth is packaged as settled propositions. What are some other kinds of rigorous argument? These exist in symbiosis with proposition/proof mathematics. For example, computational methods are used to forecast weather. A weather forecast does not come with a guarantee of correctness, but there are rigorous analyses of its methods of computation, so that defends our choice of those over (say) the use of divining rods to forecast the weather.

As you mature in "doing mathematics" and helping others, I expect you will come to appreciate the rigor of its logic and be more and more willing to bear the burden of proofs as a necessary "evil".


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