# Why are visual/graphical/intuitive solutions discouraged on MSE?

I have been active on MSE for around 3-4 days. I have noticed the fact that people either ignore or downvote intuitive/graphical/visual analogies of a problem. However I feel that intuition is one of the most important things that one should walk hand-in-hand with while learning a subject like mathematics. I have always been posting graphical ways of thinking/visualising a given problem. I had to delete a correct answer due to too many downvotes, just because my answer was graphical and not mathematically-rigorous. And the accepted answer was the one which couldn't be solved by hand and used WolframAlpha to find the correct answer. Shall I stop giving intuitive answers?

• Maybe you can be more specific and show us the answer? This answer of yours for instance I think is good and greatly helped by the graphics. But I would also understand if a heavily graphical answer recieves downvotes in a question asking for a proof, especially if a proof is not also supplied. I would guess that the downvotes are not because your answer was graphical, but purely because it was "not mathematically-rigorous" Sep 14 '20 at 5:38
• @CalvinKhor I have deleted the answer... Shall I undelete it? Sep 14 '20 at 6:09
• That is one possibility, another is to provide the link to the question or answer. Users with over 10000 reputation can see deleted answers (despite being called "deleted") Sep 14 '20 at 6:12
• math.stackexchange.com/questions/3825253/… Sep 14 '20 at 6:16
• In my opinion, this question is asking for a proof. Your answer gives 4 solutions but doesn't prove that there are no more, and the graphs are not very indicative of how the non-graphical proof can be made. I note though that the slick observation of Ross's comment on the question can turn your answer into an essentially rigourous answer, since a graph is essentially a pretty excel sheet (and its not so hard to trust a graph at integer points) Sep 14 '20 at 6:28
• @CalvinKhor So what did we conclude? You may check my other answers. I have mostly relied on visualisations to answer questions. Sep 14 '20 at 6:36
• I have checked a couple others, like here, I don't think the graphics add anything, and are only 'beautiful' when they are depicting an ideal case; e.g. if $-f(x)<g(x) < f(x)$ and $f(x)\to 0$ then $g(x)\to 0$, but this could have also been proven by using $2f$ instead of $f$, and then the picture is less nice. Also, the inequality only needs to hold in a neighbourhood of the point, but in your examples they are true for all $x$. So, I think if a graph can provide insight that is hard to say in words, like the first example, it is a good idea; Sep 14 '20 at 6:48
• If the graph is added as a remark, it might take up the screen space of a reader who doesn't really care, and now just goes to a different page because they can't be bothered to decipher the image. Also, in contrast to memes, a good graphic requires the reader to really fight with it to understand it. This is a lot of effort that not many people would be willing to put in, which may partially explain the "ignoring" of these answers. And importantly, questions in Math.SE are often principally looking for proofs, and e.g. graphs might be sometimes seen as "missing the point" of the question Sep 14 '20 at 6:48
• @CalvinKhor Thank you for your views. You may write it as an answer. I would accept that Sep 14 '20 at 6:50
• I'll see if I remember to consolidate the above into an answer later :) Or someone else can also provide their views in an answer. PS I have also extensively tried to use graphics in my answers. I do agree that the effort does not feel rewarded at times Sep 14 '20 at 6:55
• Looking at the timeline, it seems like the answer you deleted was the first answer given. I think people are more likely to react negatively to a "visualisation" or "intuition" answer, such as yours, if it is posted as the first answer unless it does actually answer the question. I know I would react negatively if I came across such an answer (one concrete reason for this reaction is that questions with answers are less visible). Sep 14 '20 at 9:46
• @user1729 didn't that actually answer the question? Sep 14 '20 at 9:47
• @SoumyadwipChanda Not really. As pointed out in the comments there, there is no justification, or even suggestion that justification is needed, that the solutions are $1, 17, 18, 19$, rather than "close to" these numbers. In my opinion, the graphic tells me that there are at most four solutions (maybe five, as graphics can be missleading and I'm not sure if it touches the line around $1$ twice). Of course, it is easy to verify that these four numbers are the solutions, but if you wrote this answer in my exam then you would miss marks for not verifying these solutions. Sep 14 '20 at 10:04
• @user1729 I finally wrote there that the values of x can be obtained by putting [x]=1,19,17 and 18. I left the rest of the workup to the OP bcz I was discouraged to post the complete solution of problems on MSE Sep 14 '20 at 10:13
• I really don't think one can find intersections of curves with other curves or lines via a graph. The graph may be useful to figure out some inequalities related to the functions once the points of intersections of their graphs is found algebraically. Sep 16 '20 at 5:11