# What is Math.SE?

Disclaimer: This question is not about PSQs, or "Problem Statement Questions". Rather it is about what users want Math.SE to be. I bring up PSQs to frame the issue.

Background: Recently there has been a great deal of discussion (and disagreement) about how to hand PSQs. The relevant threads are here and here. The main arguments in favor of removing/closing such questions were, as I interpret them:

• Too many "bad" questions hurt the signal to noise ratio of the site and discourage the users who make valuable contributions from using it (as they get less out of it).

• Other sites such as Physics.SE and Skeptics.SE have successfully implemented standards similar to those proposed.

These points are mostly reflected in Douglas Stones's answer to Qiaochu's PSQ question. The arguments against, mostly gleaned from comments to Qiaochu's question, seem to me as follows:

• Homework questions are certainly "practical, answerable questions based on actual problems that you face" to quote the FAQ. They are occasionally quite interesting (one would hope!) and removing all PSQs is akin to throwing the baby out with the bathwater.

• It is not necessarily cheating to ask PSQs, and even if it were, policing such things is not our job.

• Many students, especially non-majors, are truly lost in the face of some exercises, and don't know how to describe where they're struggling.

Main Point: It seems to me that these different perspectives are a result of differing views on what Math.SE is. As I see it, there are three possibilities:

1. Math.SE is a place to do math (at all levels), asking questions as they arise and helping others with theirs when we can.

2. Math.SE is a place to learn and teach math, in addition to doing it.

3. Math.SE is a place for anything math and math-related.

This is not exhaustive, but I feel it roughly describes most users' feelings. The problem is that policies befitting each group are often harmful to the others. The broader the aim of Math.SE, the less effective it is at each of its goals, because the signal to noise ratio for each individual goal gets worse, and users have to spend more time dealing with elements of the site that don't interest them. Accordingly:

Question: What is Math.SE?

I don't expect consensus; anymore than I expect consensus in a parliamentary election. In any site of this size there are bound to be disagreements, and actions must be taken that will upset some users, as avoiding such actions would paralyze the site the same way requiring a consensus in parliament would paralyze a country. But I think this question needs answering before we can develop policies appropriate for the majority vision of the users of this site.

Some aspects of this have been discussed before. See here, here, and here.

• It's important to keep in mind the difference between the goal of a policy and the actual effects a policy will have. In fact, the actual intent of a policy is mostly irrelevant (but ideally is correlated) to its actual merits and demerits, and it is the latter qualities upon which it must be judged.... – user14972 May 13 '13 at 0:07
• ... while it is a good idea to discuss the topic of what people think MSE should be, we should keep in mind that simply having goals isn't everything, and my perception is that the conflict over policy is more idealism/realism-oriented rather than incompatible visions of what MSE should be. – user14972 May 13 '13 at 0:17
• @Hurkyl I'm a little confused. I'm not advocating any policy here. – Alex Becker May 13 '13 at 0:23
• @Hurkyl It occurs to me I might have communicated poorly. I should have said "before anything else we must determine the goals of our policy", not "the best we can do is..." – Alex Becker May 13 '13 at 0:32
• Ah, that's much more reasonable-sounding! Anyways, the main point of this tangent was to express the idea that the disagreement wasn't necessarily about the goals themselves, and things I want people to keep in mind if they talk about ways to achieve these goals either here, or for when we get to the next phase of discussing how to achieve them. – user14972 May 13 '13 at 0:39
• @Hurkyl Ah yes, that makes sense. I understand that some disagreement is over the effects of policy. But I think there is also a lot of disagreement over what our goals should be, and that that disagreement must be resolved first. – Alex Becker May 13 '13 at 1:00
• Many students, especially non-majors, are truly lost in the face of some exercises, and don't know how to describe where they're struggling. - But I guess they should at least admit it and show what they have tried (I guess that there's a lot of people who didn't even try to solve) - sometimes people just copy/paste the entire question here. – Red Banana May 13 '13 at 1:39
• "things I want people to keep in mind ... for when we get to the next phase". --- Ruh roh! – zyx May 13 '13 at 8:04
• Is this question about "What is Math.SE?" [bold-face mine, quoting title of OP], or are you asking "what should Math.SE be?". Those are two entirely different questions, and asking the second seems to imply that Math.SE is not what it should be, thought this may not be the case. Perhaps you are asking both questions? But then I think the title should reflect this. And if you are asking whether Math.SE is what it should be, that's another question altogether. – amWhy May 21 '13 at 17:29
• @amWhy I'm asking what presently the members of Math.SE consider the site to be for. The title is the catchiest variation on that I could come up with. – Alex Becker May 21 '13 at 17:32
• @Alex Becker: one challenge with PSQs is that even users who agree on what the site is for may disagree with it. For example, some users who think the site is for teaching think that answering PSQs is teaching; others think the site is for teaching but answering PSQs is not teaching. – Carl Mummert Dec 10 '14 at 1:24

Math.SE cannot afford to be a place for everything math(s)-related: that way lie endless ‘proofs’ of the Goldbach conjecture, ‘demonstrations’ that Cantor was wrong-wrong-wrongity-wrong and $\Bbb R$ is really countable, and questions about the best diet for doing non-commutative algebra.

I’ve no doubt that for some users Math.SE is first and foremost a place to do mathematics, asking questions as they arise and helping others with theirs when they can; indeed, I’ve spoken with such users in Chat. Moreover, one can see some evidence of this in the available user data: one user, for example, has asked $106$ questions and answered $114$; another, $94$ and $122$. And of course as they arise is flexible enough to cover the possibility that for some users they simply don’t arise, so in some sense this description could fit just about anyone here. However, it’s very clear from the user pages that for many users Math.SE is primarily a place to ask questions, and for many others it’s primarily a place to answer them. Here, for instance, are some statistics from the first page of users sorted by all-time reputation:

$$\begin{array}{cccc} \text{Rep in thousands}&\text{Nr. of Users}&\text{Answers}&\text{Questions}\\ \hline 150\text{+}&3&14380&2\\ 100\text{ - }150&2&4795&55\\ 70\text{ - }100&6&15469&114\\ 50\text{ - }70&7&8981&77\\ 30\text{ - }50&18&18296&284\\ \hline \text{front page}&36&61918&532 \end{array}$$

Of those $36$ people six have asked no question, $17$ have asked fewer than five each, and one person accounts for a little over $20\%$ of the questions asked by these people.

For me Math.SE is primarily a place to teach mathematics, and the data above suggest that I’m not alone in this. The doing is part of the teaching and often contributes to my enjoyment, depending on the problem, but producing what I think is a good explanation or hint brings a pleasure that is independent of the mathematics involved. It is secondarily a place for me to learn mathematics: sometimes in order to answer a question, occasionally from another answer to a question that I’ve answered, and once in a while from an answer to a question that simply caught my fancy.

Given both the Question & Answer format of the site and its explicit openness to questions at all levels, it’s inevitable that teaching (as distinct from providing more or less collegial assistance) will be seen as one of its major functions, both by those who want to teach and by those in search of teaching/tutoring. And in practice teaching is one of its major functions: answering this question is teaching every bit as much as answering this one, this one, or this one is. (I might add that it’s by far the easiest place to teach on-line that I’ve seen: its technical platform makes it especially attractive to those of us who have taught on-line in straight-ASCII environments like the Usenet groups alt.algebra.help and alt.math.undergrad, the Topology Q+A Board, or the Math Forum @ Drexel.) That is, your second possibility describes not only my view of what Math.SE ought to be, but also what it actually is.

Finally, I don’t think that your first possibility really exists. One could of course establish and enforce rules that would reduce the scope of Math.SE by greatly reducing the amount of explicit teaching, but the result would in my opinion no longer be a place to do mathematics at all levels: it would substantially favor the higher levels. Math.SE would become a sort of Junior MO.

• A follow up question to your answer then is what constitutes teaching/tutoring and what constitutes doing students' work for them. – Alex Becker May 12 '13 at 3:13
• @Alex: The two are not mutually exclusive: providing a complete answer is still teaching to anyone who learns from it. Sometimes it’s even the best choice, though this is easier to judge in person than here. I tend to give hints, especially for low-level questions, but my hints tend to be on the larger side: it took a while, but over the years I’ve learned that problems are very often harder and hints less illuminating than one thinks. And getting a student to fill even a small detail is definitely teaching. – Brian M. Scott May 12 '13 at 3:32
• I'm glad you brought up USENET groups. I was about to post an answer explaining that I would like Math.SE to be a modernized version of sci.math with the noise from cranks and trolls moderated out. I visited alt.algebra.help occasionally, but didn't like it. – Jyrki Lahtonen May 12 '13 at 7:25
• I’ve learned that problems are very often harder and hints less illuminating than one thinks - as a student I think this is something most answerers don't realize. I see the kind of stuff some of my class mates struggle with. Lecturers don't even dream the kind of stuff students don't know. – Git Gud May 12 '13 at 10:41
• @Jyrki: I stopped reading sci.math over ten years ago, I think about the same time that Ilias Kastanas mostly stopped posting. I first ran into Arturo in the two teaching groups that I mentioned, probably at about the same time. – Brian M. Scott May 12 '13 at 15:38
• The table isn't really comparing apples to apples, since there are generally multiple answers per question, and greater reputation gains for answers. – user14972 May 12 '13 at 21:33
• @Hurkyl: If you’re talking about my data, I’m not comparing questions with answers; I’m looking at the observably different practices of different Math.SE users. At the other extreme you’ll find numerous users whose use is largely or wholly confined to asking questions. It is very obvious that some of us are here primarily to answer questions, others are here primarily to ask them, and yet others are here for both reasons. The User front page was an easy place to find members of the first group and incidentally to demonstrate their value to the site. – Brian M. Scott May 12 '13 at 21:43
• @GitGud: I realize that "lecturers don't even dream the kind of stuff the students don't know". I've been lecturing for twenty years and seen my share. More often than not the root cause of a student's plight is not with the current material, but gaps in their understanding of some more elementary material. Granted, such a student will not benefit from the best of hints. But giving a solution to the problem at hand is not going to help such a student understand either. Math.SE is relatively ill fitted a tool for filling in such gaps. Hints work much better with more advanced students! – Jyrki Lahtonen May 13 '13 at 6:01
• @JyrkiLahtonen but gaps in their understanding of some more elementary material. Granted, such a student will not benefit from the best of hints. I agree with (almost) everything and I'd like to emphasize that part. I also agree that giving a solution to the problem at hand is not going to help such a student understand either. most of the time, but I still think it's better to give the solution than some hints which the student can't work with. – Git Gud May 13 '13 at 6:16
• @GitGud: My approach to teaching here is under continuous evolution. But I always start by giving hints. On a sunny day that will do it. If not, then I start a dialogue and/or expand the hints. All depending on A) how responsive the student appears to be, and B) how large a time commitment I can make. So I can't do that too many times per day. Also, occasionally it happens that I leave a student stranded, because something else came up, or I got tired. The latter is common, because I'm 7 hours ahead of US East Coast. – Jyrki Lahtonen May 13 '13 at 6:24
• @Carl: Not as far as I’m concerned. – Brian M. Scott Dec 10 '14 at 1:28
• I pulled up area51.stackexchange.com/proposals/3355?phase=definition again, to check that (1) the comparison with MathOverflow was there from the beginning, as was (2) the sense that blatant homework should be off topic – Carl Mummert Dec 10 '14 at 1:31
• @Carl: I don’t doubt you. I also don’t care: it’s quite clear that MSE has evolved in a somewhat different direction and had already done so when I first got involved three and a half years ago. – Brian M. Scott Dec 10 '14 at 1:34
• @CarlMummert There are only a handful of occurrences of "Mathoverflow" in said Area51 link, and they say nothing about MSE being a "Junior MO". fyi: some MSE users view "MathUnderflow" as derogatory. Though it may be used frequently by MO users, it is little used here. – Bill Dubuque Dec 25 '14 at 3:27
• @Bill: In fact I had never seen the term until Carl used it, and Google indicates that it’s rare; a quick look suggests that it was most common before MSE got a permanent name and used mostly by MO folks. – Brian M. Scott Dec 25 '14 at 6:54

## What is MSE not?

To understand what something is, we must also understand what it is not. Some things are obvious: MSE is not a place for Harry Potter questions, nor is it a place to advertise the latest summer fashion trends.

I further assert:

• MSE is not a classroom
• MSE is not a textbook
• Corollary: MSE is not a solutions manual
• MSE is not a factory

And also due to the actual implementation of SE:

• MSE is not a math chatroom
• MSE is not a math forum

While some amount of discussion is possible and productive, the site really isn't well designed for that type of interaction.

## So what is MSE?

I agree with the option

Math.SE is a place to do math (at all levels), asking questions as they arise and helping others with theirs when we can.

However, "learning and teaching" already fits into this description; questions arise in the process of learning, and answering questions gives people an opportunity to teach others how to solve problems and write short expository articles on the topic asked.

• A consequence of the Q&A versus forum versus chatroom distinction that I've realized and tentatively agreed with in the course of writing this answer: this site isn't really the appropriate place for people who are so truly lost they can't even ask questions; MSE simply doesn't provide the right environment to give such people the guidance they need. Making sacrifices to throw such people a bone unlikely to be worthwhile. (and arguably, a bone might actually be more harmful than helpful anyways) – user14972 May 12 '13 at 22:23
• I feel your last paragraph is unnecessary. The best we can do is determine the goals of our policies, and we need to know what the goals are in order to judge the effects anyway. – Alex Becker May 12 '13 at 22:57
• @Alex: I strongly disagree, which is why I have that last paragraph. In fact, I consider what you describe to be the worst we can do while still having noble intent. Before the fact, the best we can do is to actually put in the effort to reasonably predict whether a policy will achieve our goals and anticipate what side effects it will have, and compare and contrast with other policies. – user14972 May 12 '13 at 23:43
• ... however, I think the last paragraph may be better placed as a comment on the OP rather than in my answer (to avoid the "post containing two separate ideas that people might have split opinions on" problem), so I'll move it! – user14972 May 13 '13 at 0:05
• This answer "depends on what your definition of is is". – zyx May 13 '13 at 3:44
• Most obviously, MSE by implementation is first and foremost a particular type of math forum (one for Question & Answer interactions and related conversations), and has a chatroom. So it's not at all clear what it means to say it is not either of those things. MSE is not exclusively a forum or a chatroom, just as it is not exclusively a textbook, solution manual, factory or classroom. But it is, in part, every one of those things, and rightly so. To arbitrarily choose some as the what-it-is and others as the is-nots is to pre-empt the entire discussion (pending further explanation). – zyx May 13 '13 at 3:47
• @xyz: MSE is not a forum in the conventional sense, since it does not support back-and-forth discussion. (Or, rather, it supports it only in a very awkward and deliberately limited way.) Yes, it's possible to extend the meaning of "forum" to cover Q&A sites like MSE, but I'm pretty sure that's not what Hurkyl meant by that word. And while MSE indeed has a chat room, it itself isn't one -- the chat room is just about as disconnected from the main site as it can possibly be while still maintaining some degree of official association, and most MSE users probably don't even realize it exists. – Ilmari Karonen May 23 '13 at 17:55

My personal opinions below, I speak not for any other member:

1. Math.SE is a place to do math (at all levels), asking questions as they arise and helping others with theirs when we can.

Of the three, I think this is the most appropriate descriptor, but it is incomplete. Math.SE is a place to do math. It is a place to solve problems and to seek solutions to problems. But it is also a place to seek alternative ideas, to experience new branches of mathematics, and a place to hone problem solving skills. As a Q&A site, by nature this must involve multiple parties: at least one to ask, and another to answer. To me, this means that Math.SE is an interactive utility. Both the asker and the answerer are jointly responsible for doing math. A necessary component of making/keeping Math.SE as a place where people can do math is to ensure that this interactivity is upheld.

2. Math.SE is a place to learn and teach math, in addition to doing it.

I disagree with this. Math.SE is not a crowd-sourced tutor, although it can sometimes be used as such (and that's OK!). Learning and teaching are individual objectives. It is not the duty of the community to impose these objectives on its users. Some may be here to teach. Some may be here to learn. Some may be here just because they want to show the world that they're the best and fastest solver of problems with the tag. If the focus shifts to teaching/learning, then we adjudge questions and answers entirely within that framework, and that would be wrong.

3. Math.SE is a place for anything math and math-related.

No. Math.SE is for asking legitimate questions and seeking legitimate problems. This is too broad. Math.SE is not designing to be a cumulative solutions manual for the world's most popular textbooks. It is not designing to be a skeptics forum whereby we do the world a duty by debunking every crackpot. Math.SE does not exist to attempt to convince the countless number of individuals that no, in fact your "novel" concept of "tiny numbers" does not disprove $0.99999\ldots = 1$.

If Math.SE becomes for anything math and math-related, and we fail to enforce controls, then the site runs the risk of being the go-to source for everyone who has found a three line proof of the Riemann hypothesis.

Questions, and answers, should be self-contained and have a clear goal.

• +1 for the part assessing the actual question. As for the part of your answer on PSQ, I don't think this is the place for it. I liked your answer better when the last section wasn't there yet (regardless of my (dis/)agreement with it). – Lord_Farin May 11 '13 at 15:07
• @Lord_Farin I wasn't really sure if the question could be taken with or without the background material separated. So I branched it off into separate sections. Take from it what you will; the original question is very broad, and these points, by their inclusion in the OP, are still germane to "What is Math.SE?" – Emily May 11 '13 at 15:40
• Do you have a moral obligation to call the police when someone is robbing (or rubbing) a liquor store? Who is the police in this scenario, the lecturers? the university? the moderators? Do you agree that giving a ride to someone who just robbed a liquor store is against the law, assuming that you know what they did and they are not forcing you to help? – Asaf Karagila Mod May 11 '13 at 15:44
• I would prefer that answers not address PSQs because there are already two very well-exposed questions specific to them. I included PSQs to motivate the question, so people wouldn't ask "why should I care?" and "where is this coming from?" – Alex Becker May 11 '13 at 15:52
• @AlexBecker Very well; I rolled back to my original answer. – Emily May 11 '13 at 16:03
• Learning and teaching are no more (though also no less) individual objectives than is wanting to do mathematics in a more collegial fashion. And a question plus an answer in themselves constitute an interaction, irrespective of the quality (by whatever yardstick) of the question. – Brian M. Scott May 11 '13 at 23:11
• @BrianM.Scott I respect that view, but I disagree in the sense that teaching and learning are more specific objectives. A metaphor: sometimes I want to go to the driving range to hit golf balls. This is not teaching/learning. This is just doing. Sometimes, however, I go to learn how to hit my fairway woods. This is doing and learning. If the driving range was just for learning, I would not be allowed to just go and whack at balls when I wanted to. – Emily May 12 '13 at 14:03
• Going to the driving range and hitting golf balls is learning. It may be undirected learning, and you may be learning bad habits, but it’s still learning. More important, I don’t see that desire as any less specific than a desire to learn how to hit your fairway woods better. It simply serves a different end — fun, or working off steam, or whatever. Finally, no one has suggested that this ‘driving range’ should be just for learning. – Brian M. Scott May 12 '13 at 15:46
• In my mind, the key point is that this is a site to do math, not a site to do math homework. The main challenge with homework is that the askers are often not doing math in the sense I understand the term, even if they are doing their math homework. – Carl Mummert Dec 10 '14 at 1:33
• @CarlMummert So what precisely is your distinction between "doing math" and "doing math homework"? – Bill Dubuque Dec 25 '14 at 3:49
• @BillDubuque I am not Carl Mummert, but I would wager that one is done for a grade in a class and prescribed by an instructor, one is not. This is among the least challenging distinctions to make. – Emily Dec 25 '14 at 3:50
• @Arkamis Are you aware that some professors (e.g. JDH) encourage their students to use sites like MSE for assigments? – Bill Dubuque Dec 25 '14 at 4:08
• @BillDubuque Yes, I am. And I encourage many students that I advise and tutor to do the same. And yet I encourage them to use the tool as a collaborative platform by expanding on the knowledge they have, and being clear about the knowledge they lack. I do not advise them to use the site just an exercise in re-typing the questions they have been given. – Emily Dec 25 '14 at 4:10
• @Arkamis So, to you, there is indeed, more to the distinction between the two than what you said above. Hence my question to CM. – Bill Dubuque Dec 25 '14 at 4:13
• @BillDubuque Not really. It's still pretty clear: one is assigned by an instructor, one is not. – Emily Dec 25 '14 at 4:14

Math.SE is a place where users are willing to teach. Math.SE (along with StackOverflow) helps virtually anybody, sometimes to newbs without any hint of clue. Our people won’t engage in pointless quibbles and use high-rep privileges to debase authors of questions (although answers, certainly, require competence). Contrary, people help these, sometimes clueless, authors to make their content eligible. Also notable, this meta site doesn’t have a tradition to shut legitimate issues up, as far as I observed, unlike most other ones in SE system.

Many other StackExchange sites have a spirit of “elitism”. Sometimes it is substantiated by actual expertise of active participants. Sometimes it doesn’t rely on anything but a couple of enlisted celebrities (such as Gerard t’Hooft and Peter Shor at physics.SE), who cover up generally awful and amateurish level of discussions. AFAIK any of “elitist” sites hasn’t professional-level achievements remotely comparable to ones of MathOverflow. IMHO superiority attitudes common at many such sites will eventually undercut their usefulness for anybody but a narrow circle of “professionals”, actual of self-perceived. At math.SE it will not happen.

• Sorry to hear about your lack of success on other SE sites. – user147263 Dec 9 '14 at 9:38
• @Behaviour: you can’t refute my point about professional-level achievements, and hence resort to ad hominem arguments ☺ – Incnis Mrsi Dec 9 '14 at 9:40
• I have not been uniformly successful in participating in other SE communities, but I'm not sure what the gist of your "point about professional-level achievements" is. Of course Math.SE benefits from the participation of many accomplished mathematicians and graduate students, without (IMHO) discouraging participation by "non-professionals". If that is your point, then I agree with it. Rather than bemoaning "a spirit of 'elitism'", it seems more constructive to advocate for meritocracy as a community value. – hardmath Dec 9 '14 at 15:41
• @hardmath: if you make an address to the community, then you certainly can find better (i.e. more prominent) spot for it. If you intend to talk to me, then what do you know about me, Incnis Mrsi, that give me en.wikipedia-linked word “meritocracy”? Do you know why did I prefer Q&A sites to Wikimedia projects? Of course, you are not interested in it, as well as I’m not interested in arguments about nothing. I expressed my view. It wasn’t accepted, but nobody blocked me for dissent, shut me up, or something alike. No offense taken. – Incnis Mrsi Dec 9 '14 at 16:04
• @IncnisMrsi: I did intend to talk to you, hoping to better understand your post and how it addresses the Question. No, I do not know those things about you, and I'm glad if no offense was taken. I was not a downvoter, and my words were an attempt to outline some possible agreement with you. – hardmath Dec 9 '14 at 16:13
• Even "serious" questions theoretically oriented or focussing on the mathematical justification and meaning of steps used in physics are not welcome to PSE, as, for ex., the comments under this, and the need felt by professional physicists to establish Physics Overflow, show. A pity when a physics site that could be so useful gets into the hands of high rep. users that do not understand that a calculation has to be proved to be mathematically justified... – Self-teaching worker Mar 1 '16 at 12:21
• @IncnisMrsi +1, i also think MSE is more forgiving than others but that does not make other sites or their users bad. – A---B Jul 5 '16 at 15:30