# Answers composed entirely mechanically, e.g. by computer algebra systems

Some users post many entirely machine-composed answers, e.g. integrals computed by Maple (e.g one user has over 150 such answers).

Should such "answers" be CW?  Should they be comments?

Update 2/8 $\$ Some answers and comments below seem to misinterpret the scope of the question (which I thought would be clear from the examples). To clarify, the question concerns only answers that consist of a CAS command followed by its output (the "answer", e.g. here). In particular this question does not concern answers that additionally include explanations of the way the answer was derived (be they human or machine generated explanations). There is absolutely no intent to discriminate against machine-assisted answers (having been a Macsyma developer I have much respect for such symbiotic collaboration).

Note that if someone wanted to gain rep quickly for nefarious purposes, then this loophole provides an easy quick method for doing so. Even a user with little knowledge of mathematics can feed these problems into a computer algebra system - even a bot could do so.

• I would prefer comments over CW. I find it hard to imagine any good question that would be aptly answered by a CAS computation. On the other hand a comment indicating the value a CAS gives is certainly useful. – Lord_Farin Feb 6 '15 at 17:27
• In many cases the problem is with the answer and the question, e.g. math.stackexchange.com/questions/1136486/… – Carl Mummert Feb 6 '15 at 17:38
• I guess this user is more of a bot than anything else. As far as I know, bots are usually removed. – Mister Benjamin Dover Feb 6 '15 at 17:54
• I would say this is analogous to the users who post answers to complicated integrals with no shown work. For example, this. – dustin Feb 6 '15 at 18:48
• @dustin Not analogous. Cleo's answer could not be produced by CAS (at least those in common use), as the author of that question remarked. It may be lacking in many ways, but it's not a Copy-Paste-Run-Copy-Paste [CPRCP] job. As for the original question: I'd rather CPRCP answers be deleted or converted to comments. When they come up in LQ review queue, I vote to delete. – user147263 Feb 6 '15 at 19:07
• @FamousBlueRaincoat analogous by it could have been looked up in a table of integrals which to me is about as much effort as using a computer. Also, what is CPRCP? – dustin Feb 6 '15 at 19:10
• @dustin Not convincing unless you know of a table of integrals containing that specific integral. – user147263 Feb 6 '15 at 19:11
• @dustin If I had to guess, that account is owned by a person who works on commercial CAS integration software, and is using the integrals here to help improve their algorithms. They probably are not allowed to reveal the methods because they are considered trade secrets (I know folks who refused to work on Mma because of this) – Bill Dubuque Feb 6 '15 at 19:39
• @dustin: I agree. The answers by Cleo were equally problematic, and really only moderator attention would have been able to resolve the issue IMO. – Carl Mummert Feb 6 '15 at 21:21
• @dustin Reworking my query, I see that the user received a total of 82 upvotes, 68 downvotes, and 8 accepts on posts containing 'aple' (which seems to miss ~4 posts on the list in the OP, perhaps due to these posts being more recent). At any rate, this comes to 804 rep. Divided by 146 questions the query saw, this is about 5.5 reputation per answer. – user88319 Feb 7 '15 at 2:36
• An answer should show how to solve the problem. If it is (essentially) solved by using Wolfram ,etc., then the answer should state so and preferably include relevant code, so it can be repeated. (This does not preclude using such systems as result checking or labour saving devices. I am chronically bad with basic algebra and am very happy to check them with Macsyma before submitting.) – copper.hat Feb 7 '15 at 18:49
• @FamousBlueRaincoat: Shame that you didn't use the opportunity to define these as CCCP = Copy Code, Compile, Post. Or CRAP = Copy, Run And Post. Or something else amusing. – Asaf Karagila Feb 8 '15 at 16:52
• @BillDubuque No, I don't. By the same token, I don't think it would be good if the site were to devolve into thousands of answers that were merely a few lines of arithmetic simplification used to solve integrals, like here. I'm not arguing that Maple answers are generally good, but that they are no more bad than an equivalently unmotivated pencil-and-paper-produced equation dump, and as such should not be put to different standards (as far as making CW, converting to comment, etc.) – user88319 Feb 9 '15 at 4:26
• @BillDubuque: the user in question frequently posts garbage. I think this is by design because that user has frequently questioned the practice of performing analytic derivations of integrals and sums as anachronistic. Perhaps he's in sales for Maple. (It wouldn't surprise me considering his disrespect for the subject.) That all said, his garbage answers are typically down voted with appropriate comments. I doubt anything else needs to be done. – Ron Gordon Feb 13 '15 at 9:14
• Bill, for future reference, try to remember that for people not in the USA, 2/8 means August 2nd. It's better to write "Feb. 8th" or something like that. – Asaf Karagila Feb 15 '15 at 22:43

I appreciate people taking the time to show how a problem can be solved using a computer (I have done it myself several times) and, honestly, I do not see why they should be deprived of the little symbolic recognition that a few rep points mean; it is often not a trivial task to coerce a computer to do what one wants. Not everyone knows how to do this, quite a few are not even aware that it is possible to do it (specially in more elaborate areas, like commutative algebra and such), and one can learn quite a bit by being exposed to this information.

On the other hand, answers which simply give a number, as in this example, and not even an indication of how they were obtained, should not be CW but, IMO, simply downvoted.

• It would be helpful to clarify what you mean by "showing how ..." Does that include an answer that consists wholly of a CAS command and its ouptut, e.g. here and here and here – Bill Dubuque Feb 7 '15 at 0:14
• I am perfectly happy with those three answers. They can be more helpful than some of the beautiful deus-ex-machina arguments that you yourself sometimes come up with, for example. – Mariano Suárez-Álvarez Feb 7 '15 at 0:17
• It appears that many users are not happy with those types of answers given the many downvotes. – Bill Dubuque Feb 7 '15 at 0:54
• Further, it needn't be "few rep points". As the link in my question shows, it is easy to amass many thousands of points this way. We may soon have "trusted users" whose knowledge of math is limited to knowing which CAS buttons to push. Are those the types of users we wish to trust with mod-like powers? – Bill Dubuque Feb 7 '15 at 1:24
• @BillDubuque As I commented on the OP, the user whose questions you linked in the OP gained a total of 804 rep: more than a few, I'll agree, but also well less than 'many thousands'. – user88319 Feb 7 '15 at 20:21
• @Strants The point is that it is very easy to gain rep this way. If someone automated this then they could easily empower an army of sockpuppets. A crank could use them to cast many upvotes on his bogus proofs (e.g. of RH). A politican could use them to alter community consensus on meta polls, etc. – Bill Dubuque Feb 7 '15 at 21:14
• Sockpuppets can be used to gain rep with this sort of answers and with any other sort of answer... In fact, the immense majority of reputation gotten through sockpuppets in this site (and there has been a lot!) has been with votes on answers not of the sort discussed in this question. If that is the point, Bill, I am afraid it is a very uninteresing one :-| – Mariano Suárez-Álvarez Feb 7 '15 at 21:18
• Having been a mod, you know that there are several mechanisms in place to watch for sockpuppetry, and that we have very acute users who are also on the watch for such ghastly activities. A significant part of the work done by mods, in fact, is in dealing with this. – Mariano Suárez-Álvarez Feb 7 '15 at 21:21
• @Mariano Of course that's not the point - that's merely one example of how said loophole could be abused. And yes, having been a mod I know how ridiculously impotent are the SE heuristics. There is surely orders of magnitude more abuse going on than what has been detected by the weak SE heuristics (which can easily be defeated by any half-competent script kiddie). But let's get back on topic. – Bill Dubuque Feb 7 '15 at 23:34
• Well, you yourself wrote that «The point is that it is very easy to gain rep this way» because «If someone automated this then they could easily empower an army of sockpuppets» and so on, so that seems to be your point. I should say that our current policies also do not protect us against alien invasions! – Mariano Suárez-Álvarez Feb 8 '15 at 0:08
• Re: "Are those the types of users we wish to trust with mod-like powers?" On SO there are 10K+ users that have gotten most (90%-99%) of their rep by asking questions. You'd think you don't want to let them edit answers and so forth, but the system does. Fairly trivial questions asked in (say) 2008 can have hundreds of upvotes on SO. Even here, the more trivial a question is, the move upvotes it seems to get, unless it is somehow closed first. – Fizz Feb 8 '15 at 11:39
• To continue my previous comment, recent examples I'm aware of where the answer is easily found on Wikipedia: math.stackexchange.com/questions/1137628/… and math.stackexchange.com/questions/1135959/… – Fizz Feb 8 '15 at 11:48
• An probably my favorite recent example from another SE site: electronics.stackexchange.com/questions/152090/… The bounty says "The question is widely applicable to a large audience." ... of felines! – Fizz Feb 8 '15 at 12:46
• @Mar Yes, as usual, you can easily divert discussions with strawmen arguments by pulling quotes out of context, etc. Sadly this seems to be par for the course on meta these days. – Bill Dubuque Feb 8 '15 at 16:18

This depends on the question and the precise type of answer. If somebody wishes to simply know the value of some definite integral or some anti-derivative they might be perfectly happy with an answer of the form: Using SomeCASCommamnd you get Result. (Such an answer can also be non-trivial.)

If the intent of the question is beyond any reasonable doubt to do something 'by hand' (typical examples, last digits or generally values modulo $n$ of exponential expressions) and somebody posts a CAS-solution simply brute-forcing it) then this is an unhelpful answer or perhaps even a non-answer and should be treated as such.

If the intent is unclear this is an issue with the question and should not necessarily be held against respondents.

Whether the answer is CW or not is mainly irrelevant in my mind, yet I do not see any reason for it to be CW. In the latter case a comment might still be appropriated, though sometimes even this might not be desirable.

• Questions that simply ask for the value of an integral are usually off-topic anyway -- in particular, if they can be done trivially with Wolfram Alpha, and only ask for the value of the integral, then they don't show enough research effort. – Carl Mummert Feb 6 '15 at 21:32
• Of course. I even meant to include this explicitly, but it seemed orthogonal to the question at hand. It is however not the case that each question that would ask for what I said is necessarily trivial since your "in particular" does not always apply (though more often than not for questions we see in practice). For example, for questions at the edge of what todays CAS can do it might be necessary to use the right CAS or a CAS in the right way and so on. Even context might be present in the question. Anyway, the quality of the question is not the subject here. – quid Feb 6 '15 at 23:31
• @Carl: For you. For me it depends very much on the integral, and in all cases Wolfram Alpha is completely irrelevant. – Brian M. Scott Feb 7 '15 at 0:33
• @BrianM.Scott it is a bit tangential however I do not see why Wolfram Alpha is completely irrelevant. To get the point across: say, if 150 years ago somebody had asked what is $14352688 \times 231483$ one might have replied, but now it seems somewhat of an odd question to ask. – quid Feb 7 '15 at 0:51
• @Carl Mummert: a lot of people ask question here where the answer is found on the Wikipedia page on the topic. They even get upvotes, sometimes a substantial number e.g. math.stackexchange.com/questions/1137628/… I don't see how these show anymore prior research effort than not having tried Wolfram Alpha... – Fizz Feb 8 '15 at 11:26

## Sometimes it's not fine

If:

• Only raw calculation result are involved. These type of questions are better up as a comment, since they donot help the asker in any ways (actually) but only show what's unnecessary concerning an answer. Example of such an answer:

Q: What are the last three digits of $3^{297}$?
A: According to XYZ CAS it's $963$

I think this is the only point this question's about, but I think more detail needs to be involved?

## Sometimes it's fine

If:

• If the question or a minor step involved with it can be done both by hand and a CAS and the answer-er explains how to "actually do it" and if it is tedious for the answer-er (not for the OP, the question was meant to teach something to OP), then it may be fine to do it.Example of such an answer(kinda exxagerated):

A: ... the previous thing can be expanded easily, but it's tedious so I use a CAS and get: $$(x+y)(y+z)^2(z+x)^3=\scriptsize x^4 y^2+2 x^4 y z+x^4 z^2+x^3 y^3+5 x^3 y^2 z+7 x^3 y z^2+3 x^3 z^3+3 x^2 y^3 z+9 x^2 y^2 z^2+9 x^2 y z^3+3 x^2 z^4+3 x y^3 z^2+7 x y^2 z^3+5 x y z^4+x z^5+y^3 z^3+2 y^2 z^4+y z^5$$ So we can...

## Sometimes misinterpreted

Sometimes some answer-ers put up answers without explanation. It should not be taken for granted that a CAS has been used (it may be or not be). It's better to judge using your own intelligence when it fits.

## Provide Feedback

I think I tried to add relevant points but some may agree/disagree. I feel this post should be free for everyone to edit (after discussing in comments, preferably) so that additional point can be added and irrelevant removed.

I think @ADG has provided a nice summary of when it is and isn't acceptable to post answers involving CAS. CAS is a lovely tool that I certainly use to check my hand-derived results and sometimes to get around tedious algebra that isn't the entire point of a problem.

However, CAS can be downright misleading, if not thoroughly disconcerting, if used mindlessly, even if technically correct. I'll discuss a real example here on M.SE.

The problem concerns a double integration. Really, the trick to analytical evaluation lies in a change in the order of integration. That is where the thinking is. Maybe a CAS can recognize the thought pattern and produce the correct answer. I don't know of one, however. All I know is what happened when someone (a Maple salesperson?) answered the question with Maple I/O.

So, I reproduce the pure CAS answer:

$$-1/12\,{\frac {2\,{\mbox{_3F_2}(1/6,1/2,1/2;\,7/6,3/2;\,1)}\Gamma \left( 5/6 \right) \Gamma \left( 2/3 \right) -{\pi }^{3/2}}{\Gamma \left( 5/6 \right) \Gamma \left( 2/3 \right) }}$$

To the inexperienced reader trying to learn something, this is enough to discourage. Seriously, if you were struggling in Calc III and were presented with this answer, wouldn't you be tempted to give up?

The sad part is that the answer is quite correct, numerically. But we have generalized hypergeometric and ugly-looking gammas. That integral must be so very hard!

This is why CAS-only solutions are unacceptable in many cases, even if the OP only asked for the result of evaluating the integral. There is a level of thought - at this time, human thought - that the problem deserves, and that someone posting an answer at M.SE needs to describe. The OP needs to be taught to recognize that a change in order of integration can reduce some of these double integrals to simple single integrals.

In this case, as the accepted solution explains, the double integral evaluates to $\pi/24$. That's it. I don't care if the CAS solution agrees with this somehow, either numerically or through a complicated series of identities; the CAS has failed to present the answer in a useful form. It, and any answer like it that favors mindlessness and I/O over understanding and exposition, should be downvoted thoroughly.

• Mutatis mutandis the very same objections could be raised against many a human-written answer on this site that while theoretically correct are so misleading that they are simply wrong. – quid Feb 13 '15 at 11:53
• @quid: quite true, and I have seen many many instances of that as well. (And, to the purveyors of such "correct" nonsense, I have to explain that up and downvotes do not indicate correctness but usefulness.) That said, there is a special perniciousness to some purely CAS-derived results that are clearly the result of a fixed algorithm. I tried to illustrate this in my answer here, and I imagine there are many more examples. On the other hand, human-written "answers" I think you mean include those that provide hints based on ideas not fully worked out. – Ron Gordon Feb 13 '15 at 12:01
• Yes, I mean certain "hints" among others. I agree that the CAS situation has some specifics to it. Yet, then I do not see how the situation would be helped concerning the (legitimate) points you raise if such information were provided in CW or as a comment instead.// Given your comment on OP it seems though that I misunderstood your position a bit. Sorry. – quid Feb 13 '15 at 12:08

Whether an answer is useful or not depends on much more than whether it was produced by a human or a machine. The one case where a machine-produced answer is not likely to be helpful is that of a student trying to solve a homework problem. But even there, the machine's result might show that the student's approach is wrong. For example, it often happens that the student is looking for an exact solution when what is really needed is an existence proof. If the exact solution turns out not to have a "closed form" expression, or to be expressed in terms of special functions, that would be an important clue.

In "real life", as opposed to homework, when someone asks a mathematical question they are usually interested mainly in what the answer is; the algorithm by which the answer was obtained is of secondary interest. I see no reason to disqualify machine-produced answers there.

• I see you have many (265) Maple answers, including many answers consisting of only a Maple command-and-ouput, e.g. here, here, and here. It would be enlightening if you elaborated on why you think such "answers" are helpful, and why they should not, instead, be comments. – Bill Dubuque Feb 15 '15 at 23:12
• @BillDubuque it might help if you could explain what does it change if it is CW or a comment. The sole thing that transpired so far was the influence on points, but then this was somehow not the point either. If you do not like this type of answer that's fine; you can ignore them, down-vote them, write a better answer, etc. – quid Feb 15 '15 at 23:45
• How would a CAS be able to tell that there is no closed form? – Tobias Kildetoft Feb 16 '15 at 5:22
• @Tobias e.g. for indefinite integration of certain classes of elementary functions, most CAS use a decision procedure (extension of the Risch algorithm due to Bronstein, Davenport, Trager ...) – Bill Dubuque Feb 16 '15 at 15:10

I cannot think of a reason why it would ever be helpful to something which could, with trivial effort or thought, be retrieved from computer algebra software as an answer - this is to say, answers which, like those linked to in the question above, provide only the input and output to a computer algebra system, especially when the input is not particularly cleverly composed (i.e. using common functions in obvious ways). Why should our site be a duplicate of this one (or various common softwares), when that one is really much better at taking suitable questions and immediately giving correct results? Correct results (even numerical) are often helpful as comments, especially on problems that seem otherwise intractable, but otherwise, it's sort of like addressing the question somewhere else. Such answers should be downvoted.

One of this site's strength is that it can offer strong explanations of how to resolve questions and can actually, perhaps, help people learn mathematics. In my opinion, the best answers on this site use a lot of words beyond what is strictly necessary for the mathematics - they use extra words to clarify tricky things, offer insight into bizarre twists in proofs, or draw attention to important tricks. Sometimes "You can use CAS to solve this/aid the solution by doing ________" is helpful, but there is a marked danger here: CAS is a black box. It doesn't tell us how it works. Even an answer which primarily relies on CAS should do more than provide the proper input and the output - what else it ought to do varies, but perhaps it should explain exactly what the functions used are doing, gesture to important bits of it, or explain how the problem can be broken into commands amenable to CAS.

We don't need any new criteria to judge that answers which just feed the question directly into CAS with no further explanation are poor quality. Such answers are, as a matter of their empty composition, of lesser quality than what other answers this site has produced and of lesser quality than we should expect of future answers.

• Computer algebra systems are used all the time to get information about mathematical problems,in all sort of areas —from the obvious, combinatorics and calculus, to homological algebra, geometric topology and whatnot. They are a very genuine source of information, if not proofs, and there is even a very well respected journal on experimental mathematics. – Mariano Suárez-Álvarez Feb 7 '15 at 0:02
• @Mariano I'm certainly not saying that CAS are not helpful to mathematics - but I see no reason why M.SE should be a intermediary between the question asker and the computer. I'm sure there exist instances where an answer demonstrating a clever use of CAS are helpful - even if it ultimately does solve the question using features of CAS, I'm willing to consider it if it gives some context around what the results or the inputs mean. (I can imagine that telling someone about methods like cylindrical algebraic decomposition could give them insight into math, even if they have no idea how it works) – Milo Brandt Feb 7 '15 at 0:08
• If the OP is not aware that his problem is amenable to a CAS solution, then it is quite useful for MSE to be such an intermediary. – Mariano Suárez-Álvarez Feb 7 '15 at 0:10
• Your answer seems to be based on the false premise that everything that can be retrieved from a CAS can be so retrieved "with trivial effort or thought." – quid Feb 7 '15 at 0:11
• @Mariano To be clear, I am not arguing against answers that include use of mechanical help, only answers that consist wholly of a CAS command with its output - see the huge list of examples I linked in my question. – Bill Dubuque Feb 7 '15 at 0:16
• @Mariano Yet, I think such a realization is notable enough that it merits more comment than just posting the input and output to CAS. Certainly, describing what the functions used do is helpful - and really, if all you wanted to say was, "If you have Mathematica/Maple/MatLab, you can use Integrate[f[x],{x,0,1}]", that's surely a comment. I edited my post to (hopefully) clarify the scope that my thoughts apply to. – Milo Brandt Feb 7 '15 at 0:20
• Some may contend our site is already a duplicate of Wolfram Alpha: type in any question, and it is (nearly always) indiscriminately answered. In fact, answers here tend to show work, which is something W|A doesn't do. – apnorton Feb 7 '15 at 2:05
• @anorton For five bucks a month, it does – user147263 Feb 7 '15 at 2:25
• @FamousBlueRaincoat If I am not mistaken, registered users can see 3 step-by-step solutions a day, even without having to pay. Or did they change it in the meantime? – Martin Sleziak Feb 7 '15 at 6:49

I have noted the same user that Bill Dubuque mentions: he now has almost 300 answers, most of them providing Maple code (more than 10 have been removed in the last 24 hours). Unfortunately, Bill Dubuque's question has been misunderstood as "what to do with posters that provide CAS answers", when in reality it is about posters that massively provide them according to what it seems to be an agenda (otherwise, CAS answers may be fine with me, depending on the context).

What I suspect is that the user in discussion is far from innocent and is probably working for Maple, subtly advertising their products. While I admit that this kind of advertising is intelligently done and on the light side of annoyance, there is a risk of slowly turning MSE into a commercial battleground (a thing that Wikipedia moderators know very well).

What I suggest is that moderators check whether this user's IPs are in any way connected to Maple domains (or to some reseller's domain). I also suggest them contacting this user and explicitly ask him whether he works for any software-selling company. I guess that this can't be banned from MSE, but at least it should be made transparent (disclosed as such in the profile page).

• +1 - this does indeed look like an issue, as some portion of the posts do resemble Maple advertisements more than mathematical answers. But it is not only something for moderators. Users of the site can always be on the lookout for inappropriate "answers", and use the downvoting and deletion tools to handle them without moderator intervention. – Carl Mummert Aug 30 '15 at 13:09

It may be a secondary point, but not a minor one I think, but in many cases the attribution of the result to a computer program is given in the Answer. So it's not "composed entirely mechanically", and the attribution to the source of result is a Good Thing(tm) by Community standards.

On the central point, I see no justification for a rule that such Answers should be CW. Could many such Answers be improved by further explanation of how the result was derived? Sure, but that is the case with the majority of Answers (even mine!), at least to an extent that improves content for future Readers.

The proposed rule seems fraught with difficulties of implementation and unintended consequences, to wit:

Who would draw the line as to how much of the content results from a program, and how much from a Human Being(tm)? What if the Answer were prepared by a Human, but checked with assistance of software, and one or more defects corrected? Would anyone know, absent the disclosure of this by the post itself? If it were disclosed, should the preparer be penalized for having done so?

• The question concerns only answers composed entirely by machine, i.e. the answer consists entirely of CAS command followed by the answer it outputs (see the many examples linked, e.g. here.) – Bill Dubuque Feb 8 '15 at 15:33
• @BillDubuque this answers contains not only a CAS command but also the human-written (it is to be assumed) explanation "The Maple code" and "outputs." Given the very start of this post, I think your example might not qualify as "composed entirely by machine" in OP's view. – quid Feb 8 '15 at 15:45
• What are you talking about Bill? You link in your Question to a user with "over 150 such answers", and I looked at the top page of those search results before describing them as I did, that the user him or herself has added the attribution to Maple. If you wished to give other examples (I looked at your Question's linked examples today and yesterday, without detecting any change), then update the Question. – hardmath Feb 8 '15 at 15:54
• @hardmath Please see the edit to the question. The question has nothing at all to do with "attribution" and I am quite puzzled why you thought it might. – Bill Dubuque Feb 8 '15 at 15:58
• Thanks, Bill. A comparison was made here to another user who posted far fewer (about 30 answers in all, inactive since last October), who posted succinct answers to difficult integrals with no indication at all of source or the method used. Naturally some might suspect that a CAS or book was involved, but in the user you singled out, there seems no room for suspicion: the attribution is explicit. – hardmath Feb 8 '15 at 16:03
• @hardmath Ok, I see. It was not clear from you penultimate comment that you meant to compare to that user (which is discussed briefly in comments on the question). – Bill Dubuque Feb 8 '15 at 16:09
• @BillDubuque: The issue of attribution is connected in my Answer through the possible penalizing of a poster for disclosing the use of a CAS, when the site policy calls for attribution. I was pointing this out as "an unintended consequence". If Answers are not helpful, either by machine or mankind, downvoting, deletion, and/or demotion to Comments is appropriate. – hardmath Feb 8 '15 at 16:19
• When I composed the question I was not aware of that definite integral bot. I confess that I am surprised that those answers - pulled out of a hat like magic - are not heavily downvoted. – Bill Dubuque Feb 8 '15 at 16:37
• @BillDubuque the answers seem mathematically correct, and plenty of users subscribe to and even try to spread, and would even enforce if they just could, the idea that only answers that are false can be down-voted. – quid Feb 8 '15 at 18:30
• @BillDubuque Let me try to rephrase. As far as I know the answers are correct. As a consequence of this, adopting for the moment some widespread believe, I see no justification to down-vote them. (You might also want to note that the answer linked to in fact has close to 50 down-votes; in that sense it is heavily down-voted and only even more heavily up-voted.) – quid Feb 8 '15 at 18:47
• In the specific case of a symbolic form of a definite integral, the numerical value can be verified to many digits of precision. The user in that case has explained that the terseness of these answers is necessitated by a medical condition. – hardmath Feb 8 '15 at 18:47
• @hardmath: does a medical condition force a user to post on this site? If not, then there is an easy fix for posting 'number-only' answers... – Carl Mummert Feb 8 '15 at 20:01
• @hardmath: I am talking about a user whose name rhymes with Leo and whose profile claims that they are unable to engage in conversation or post "long" (i.e. reasonable) answers because of some unspecified medical condition. I find that explanation uncompelling - such a condition, if it exists, is incompatible with being a user on a site whose purpose is to interact with other users. – Carl Mummert Feb 8 '15 at 20:08
• @hardmath: those answers are the sort I would describe as "numbers only". They are not mathematics as I understand it, and therefore I view them as off topic for this site. For example, math.stackexchange.com/questions/576304/… – Carl Mummert Feb 8 '15 at 20:23
• @CarlMummert: Seen in isolation it can be baffling that a net of 16 upvotes were awarded. However note that for the same Question another user provided a justification for the same result and earned 17 net upvotes (and was awarded a bonus). I respect your high standards, but that Answer (from 2013) was improved upon by further explication, so I'd say it belongs where it is. – hardmath Feb 8 '15 at 20:31