What is Math.SE?

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

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

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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 contour-integral 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.

Answer 4

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.