Three levels of Math

Question

This is my first post on Mathematics Meta, I hope it is appropriate and not a duplicate.

I do want to ask why there are only 2 levels of Math as MO and MSE but not a third one.

MO is interested in research level of Math, and it is wonderful.

MSE can be reserved for questions above upper division math classes. So that people there will be interested in more on theory/ideas/interesting questions rather than standard homework questions.

Now on MSE, almost major part of questions are homework questions of calculus classes. [As far as I observe, this also varies by time when there are exams.]

And there can be a third one where I believe on the long run it could act as a place where students are solving their homeworks all together. I believe it could even be better for students:

• Some students will learn a lot by answering their friends questions. They are usually discouraged to write answers on MSE since usually language and notation is less formal.
• Discussion between them might be more helpful, then a discussion where one stays very formal.
• They will put more effort on questions, since usually on MSE even a challenging/tricky questions gets a hint immediately.

On the MSE side, I cannot see any disadvantage of such division.

Answer 1

I think "levels" is a red herring. There is a classification (the boundaries are vague):

$$ \begin{array}{c|c} \text{questions about low level math} & \text{low level exercises} \\\hline \text{questions about high level math} & \text{high level exercises} \end{array} $$

The goal of the proposal, I think, is to move the top-right corner off of MSE and onto another site. Splitting on levels would also get rid of the top-left corner.

The problem, however, is that the top-left corner consists of questions we'd really like to keep around on MSE. Or, at least, I think they're great for MSE; I'm presuming others who reject the top-right corner would agree.

If a proposal like this is to go through, it would be better to separate the columns — to move exercises off to another site. This would move the high level exercises elsewhere... but I think that's still a win, we want to be rid of high level exercises too.

IMO, the value placed on "high level" questions is not because they're high level, but because they're less likely to simply be exercises.

Answer 2

I do want to ask why there are only 2 levels of Math as MO and MSE but not a third one.

It has been previously discussed that conceiving of MathOverflow and Math.SE as a dichotomy is an oversimplification for both practical and historical reasons.

In any case I will address the issue of "a third one" (or a fourth, fifth, sixth...).

StackExchange has a mechanism for adding new sites called Area 51. Proposals for new sites go through a three phase process (define, commitment, beta) to assess the prospects for a viable Community around the proposed site.

The elements of the proposed site I read above are not IMHO auspicious:

[A] third one... could act as a place where students are solving their homeworks all together.

This does not sound to me like the curation that StackExchange intends to collect excellent content. But those with sufficient enthusiasm could use the Area 51 process to see how much support there is for a new "math homework" site.

Answer 3

This problem has caused a lot of disagreement over the years, and lately the tension has become, IMHO, intolerable.

I asked for suggestions from moderators of other SE-sites in a network wide mod only chatroom. I also tried to ping people from SE to come here and explain why they turned down the Area51-suggestion from suomynonA. I did get a couple of suggestions, and I was referred to a few blog posts by Joel Spolsky (the CEO of StackExchange). Namely this and this.

Quoting a few passages. Necessarily somewhat out of context, but I don't think I am distorting his message too much.

• (discussing the fate of old usenet groups) Otherwise, the basic questions would just get asked again and again, and the old timers would grow bored and leave. The quality of the newsgroup would then deteriorate to approximately the level you would expect if seventh-graders were left to themselves, in other words, Lord of the Flies.
• Jeff (Atwood, founder of SE) and I talked about this. What did we think of newbie questions? We decided that newbies had to be welcome. Nothing was too “beginner” to be a reasonable question on Stack Overflow… as long as you did some homework before asking the question.
• To novices, the long bureaucratic rigmarole associated with asking your first question on Stack Overflow can feel either completely unnecessary, or just plain weird. It’s like Burning Man. [snipped stuff] A lot of the rules that are important to make Burning Man successful are seemingly arbitrary, but they’re still necessary.

Listing these as I find them relevant here, guiding us towards a successful site, and also giving a glimpse of what SE strives to be.

Quoting also comments/suggestions from mods of other sites (their personal opinions to some extent, but also people who have been around SE for a long time):

• SE was specifically designed for users of all levels. The requirements being showing effort in asking a question.
• If you want to hear my two cents: This sounds like an even worse idea than the ELU–ELL split.
• If you are unhappy with what is happening with homework questions right now, impose strong rules on how they are to be answered and enforce them.

Ok, so what does all this suggest to me:

1. It is unlikely that SE will allow a separate site for lower level math. Granted, there is a precedent for something similar in the ELU-ELL split. I didn't study the history of that, but it is easy to see the die-hard linguists getting sick of the questions from foreigners learning English. That is not actually too far off from our situation in that confused high schoolers / calculus students are not that different from learners of a new language. But, remember that those high-browed linguists don't have their counterpart of MO!
2. If we try to split the site in two, it must be planned carefully. The attempt from suomynonA was, to put it mildly, half-baked. The new site should basically have similar guidelines we have now. IOW context requirement. IT CANNOT BE A DUMPSITE. THAT WILL NEVER BE ACCEPTED. I would rather call it MathTutoring.SE as that might have a better chance of getting the nod. Alexander Gruber has drafted a proposal, and we could try and use it. But, even if launched, it is unclear whether it would work as intended. Some mods of other sites expressed doubts whether the homework askers/answerers would bother taking their business to the new site anyway. That is a valid concern.
3. This leaves us with the option (I'm afraid it may be the only option) to begin to enforce a homework policy. Strictly. As the newbie askers will need guidance (read: a chance to edit their question into shape), the enforcement focus needs to include the answers as well. My proposal would be to delete the existing answers to questions in violation until the questions have been fixed. Nothing short of this will work. We have too many askers on throw-away accounts. They have zero interest in curating the question after they saw an answer, if ever so briefly. There is ample evidence of this. The answerers, OTOH, have invested more. Both in the math they produced as well as in the rep points (the relative weights of the two objectives vary from one user to another).
4. This would NOT be unprecedented. Physics.SE does exactly this. They delete all the answers to homework questions because they have a strict policy. True, they don't have the counterpart of MO either.
5. But, this would be a change in site dynamics. A big change. We have several users who have not internalized the need for context in the questions. I see comments like "PSQs fit well in the chatty Q&A mode of SE, so why should we care?". To such commenters: read and reread what Spolsky said about the Burning man. Why it is necessary that the participants themselves pick up all their garbage etc. That's why!
6. Anyway, if we go this way I guess we need to have a new discussion about the details of the policy. Basically to hear more voices. And make sure that lesson "A post consisting of good math is not necessarily good for the site" sticks.
7. I don't cherish the prospect of having to enforce such a policy. I don't know if my fellow diamond bearers cherish it either. But, whatever we do, we need your support.
8. Unfortunately this may have become necessary. The way I see it the alternatives are either to unleash the bloodhounds from C.R.U.D.E. or, the ostrich way.

In principle we have already agreed on a policy to require adequate context. The strain on the moderators, both the diamond bearers as well as the regular users participating in community moderation, for maintaining/enforcing that standard is very high. It takes too much energy that would be better used for positive things. The problem is, as we all know, that neither askers nor answerers will abide by that policy. I think this due to lack of education and also lack of firm enforcement.

Answer 4

I disagree with the proposal for the simple reason that I believe low level math should, and often does, add great value to the site.

Answer 5

At first I voiced my opinions only in private communication channels. But as many members of the the MathSE community have reacted very positively to this proposal (including some of the moderators), I thought I would add a few comments here. To a large extent this is spiritually similar to Jyrki's post.

In short, I claim that a NoviceMathSE site would be doomed to fail, and such a separation would not solve the underlying problems facing the site.

To explain my point of view, we need to examine more closely the arguments in favor of NoviceMathSE.

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HWMath.SE as stated in the proposal is not appropriate for the SE model

In the proposal itself, the goal is stated to

act as a place where students are solving their homeworks all together.

• Some students will learn a lot by answering their friends questions. They are usually discouraged to write answers on MSE since usually language and notation is less formal.
• Discussion between them might be more helpful than a discussion where one stays very formal.
• They will put more effort on questions, since usually on MSE even a challenging/tricky questions gets a hint immediately.

Encouraging lots of discussion between students solving homework together is a mixture between subjectivity and localization, two things SE tends to avoid.

Maybe someone could create a tool where a school/college/university course would have a SE-like forum/Q&A allowing students to work together on a SE-like framework. This style of tool is used already in some MOOCs to facilitate learning environments (especially since the ratio of students to instructors can be enormous). Some MOOCS reset the forums each term/year to foster additional rounds of student involvement. I don't know if this sort of tool already exists (if not, then maybe someone should go make one).

This sort of tool belongs there, not on the SE network.

But I think much of the positive reaction to the proposal wasn't for exactly the same proposal as in the OP, but instead for the thought of adding a lower-level Math Q&A.

For this reason (and because certainly SE would not want to be explicitly viewed as a place where students go to get their homework done for them), I refer to the potential site as NoviceMathSE instead of HWMathSE. (I note that Jyrki has suggested calling it MathTutoringSE, which is also better than HWMathSE).

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Levels of math on SE

The proposal asks about "a third level of math site". Implicitly stated in this proposal is the distinction between Math.StackExchange and MathOverflow as being a difference of the level of the question. But this is not an accurate description of the differences.

MathOverflow is not an ordinary member of the StackExchange network. MathOverflow is run by a non-profit organization which has an agreement with SE to host their site. It did not start through the typical experimental-beta-public StackExchange model, and does not have the same culture (or even all the same rules) as the rest of the StackExchange sites.

It is more appropriate to compare MathOverflow with PhysicsOverflow, which is separate from the StackExchange network.

In essence, MathOverflow has content that is interesting to research mathematicians. This consists largely of research level mathematics, but sometimes it also consists of essentially basic questions that are of interest to mathematicians. This is exactly how MO was founded (it's older than MathSE).

It is not true that once a question hits a certain level of difficulty, it should be asked on MathOverflow instead of MathSE. Instead it is the audiences that are different.

With this in mind, it is not appropriate to think of creating another math site as something making a three-step trinity of NoviceMathSE, MathSE, MathOverflow.

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Can we isolate the signal from the noise?

The goal makes sense. Right now, most of the noise on MathSE comes from low-level questions. The major intent behind this proposal is to raise the ratio of signal to noise on MathSE by removing most of the noise.

But this cannot hope to work, because we cannot achieve consensus on how to distinguish "signal" from "noise". There are already endless disagreements on what is on-topic or off-topic. It is unreasonable to expect MathSE to be able to draw a clear line on what is on-topic and what is off-topic now.

I cannot begin to imagine the moderating headache that would come from attempting to identify and close these questions amidst the various sources of ensuing community backlash. It would be one thing if MathSE had consensus on the various choices facing it, but this is not the case.

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Dumping bad questions

More worrying to me is that this proposal seems to be supported most strongly by users who want to dump bad questions somewhere else. (It is possible that I am misinterpreting this, but I don't think so.)

Such a site is doomed to fail. It would indeed be full of noise. There would be fewer experts there because there are fewer interesting questions, and novices would often prefer to not post there because there would be fewer experts there. Users want good answers, and depending on novices to help other novices is more appropriate for peer-learning environments than a SE Q&A.

One of the major reasons the SE model has been effective is that each site is created to be a place with very high quality content, where experts want to answer interesting questions, and where people looking for good answers can find good, accurate information.

Yes, migrating lower quality questions to NoviceMathSE from MathSE might improve the condition of MathSE, but the signal/noise ratio of NoviceMathSE would almost certainly spiral out of control towards 0 and the site would fail.

We cannot expect to migrate all the lower-quality content (assuming we could even identify what that means) to another site. If the goal is to remove lower-quality content, then the appropriate course of action is to try to find a way of identifying and removing it. Why bother trying to find somewhere else to dump it?

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We want to create a site for them, to solve our problems

Many of the comments and posts in favor of a NoviceMath.SE seem to want it to exist in order to solve problems of low quality content on Math.SE. It is unreasonable for a group of us to try to create a site for some other group. That is, it doesn't make sense for a group of MathSE members to decide on a site that other people should go and populate.

If a group of people want to make NoviceMathSE (or some variant thereof) happen and be a part of that new community, then it would be a good idea for them to step forward and begin establishing what they want and what they're missing from Math.SE. This is how new communities are established. Too much of the discussion essentially concerns ghettoizing low quality questions. This is against all principles of self determination on the network.

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Proposals for other ways to improve site quality

But I think there are some other ways to improve the quality of MathSE that don't rely on fragmenting the community.

1. Implement a Triage queue here. StackOverflow has a special review queue called "Triage". The goal is to quickly sort potentially problematic posts into categories that can be routed elsewhere. In short, questions are sorted into three categories: Looks Ok (where it goes to the front page), Should be Improved (where it has limited visibility on the front page and goes into a help and improvement queue), and Unsalvageable (where it goes to mod review or a close/delete queue).

2. Consider creating an Ask a Question Template (like the one being experimented with on SO). It is a hard question to determine what someone might put into a question template, but it may just work.

3. Improve awareness of the ability to favorite and ignore tags, and to hide questions from ignored tags. Did you know that you can not only favorite tags, but you can ignore them? And did you know that you can hide questions from ignored tags? This seems to be little-known, but the fact is that every additional method of filtering towards content that you prefer is better.

But I should note that these come with caveats. The Triage Queue is resource intensive. SE has declined to implement it on other sites in the past because it requires tweaking lots of Machine Learning algorithms (i.e. lots of maybe continuous work) and it requires many people looking at review queues to identify questions quickly. As noted here, triage was tailored to the needs of StackOverflow. This doesn't preclude its use elsewhere, but that's a discussion which needs to be had separately. Fortunately, triage makes sense on the largest sites on the network, and Math.SE certainly fits that bill (second largest on the network).

An Ask-a-question template is somewhat complicated, since there are many different questions that can be asked. But in the AB testing on StackOverflow there has been some success. I think it may be beneficial to try to develop a template on Math.SE and proceed with some AB testing as well. (The worst that happens is that it doesn't work, right?).

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_{This is in fact the third in a series of posts that I've written describing some challenges facing Math.SE. The previous two (Challenges facing community cohesion and Ghosts of forums past) appear on my website but are not necessary for this post, where this will also appear.}

Answer 6

The concept of retaining an 'expert' group for 'experts' by starting a 'learners' group has been tried before: have a look at English Language & Usage vs English Language Learners.

The experience there has been that the ELL (learners) site is less visible, possibly because the EL&U site has the depth and history to draw 'learner' traffic to itself rather than to ELL.

The result has been ongoing frustration about 'low quality questions' on the EL&U site, with recurring calls to (re)merge the two and explanations about why that isn't going to happen. Meanwhile, learners still post their questions on EL&U. Some questions are migrated to ELL, creating another problem: the ELL community (largely made up of the same people who answer questions on EL&U) wants to have high-quality learners' questions on its site; it doesn't just want all the questions that EL&U users deem to be of low quality.

Furthermore, it's a noble intention to have learners learn from each other, but the reality is that learners seek answers from experts. In the end, those with the skill and the inclination end up visiting both sites anyway. And if the learners can't quickly find answers from other learners, they would likely end up on the more visible 'expert' site.

The experience with trying to hive off the learners is that creating a 'learners' site doesn't accomplish the objective of preserving the 'expert' site for 'experts'.

Answer 7

I made a proposal here. Interested to see how much support, if any, it garners.

Edit: Stackexchange does not approve.

Answer 8

A site for "questions we don't want here" isn't possible, because that doesn't create a community -- I see someone tried that and it was already rejected. Math.SE needs to decide what questions and answers are acceptable whether or not there's a different site that could absorb them.

However, I think there could well be a niche for a site actively focused on simple questions and answers designed to be accessible to beginners. Not "pls do my homework", but "How do I do X", but focused on questions too basic for math.SE and answers that are more patient and detailed than math.SE needs, but with all the usual stack exchange principles, of finding examplar questions and removing duplicates.

But it would need a community of people who are actively excited to participate in that site, of guidelines for how it would be valuable, etc,

Answer 9

I have to disclose that I support the creation of a "third pole", say hwmath.stackexchange.com.

I am not one of the eldest users users here, but I believe that since a while MSE is suffering. The average question quality considerably dropped in the last year and many great contributors (at least in the fields I am more involved into, i.e. advanced integration techniques and special functions) started not to contribute so much. The main page is often flooded by Calculus and pre-Calculus questions, with many of them having serious issues: poor formatting, no context, cheating attempts.

I believe the majority of low-quality questions is salvageable, but moving them into a dedicated place would be of great help in tidying up MSE. The underlying philosophy is not "to send the trash elsewhere", it is to differentiate math questions belonging to fairly different universes (say low/high level questions). The purpose is to become more efficient in managing both types of questions, both deserving their own place, without them suffering from a forced co-existence. I also support the migration of accounts from MSE to HWMATH for the users requesting it. Of course, there are many delicate points which need to be properly discussed. Among them, a change in the MSE manifesto, since MSE might become a place for people studying math at many levels (rather than any level).

1. Where to draw the line between questions better suited for MSE/HWMATH?
   Keeping it simple, homeworks go to HW. Maybe together with extremely basic questions and low-level PSQs. According to Hurkyl's diagram, I am talking about relocating the whole top-right corner and part of the top-left corner. Answers to low-quality questions may have a great mathematical value: I agree with this statement, so the boundaries of the common room still need to be discussed;
2. Who will be the moderators of HWMATH?
3. What will be HWMATH's manifesto?
4. Will HWMATH accept bare PSQs / homework questions with no context at all?
   Will there be suggestions for writing a good question or requirements?
5. After the creation of HWMATH, will old MSE questions, better suited for HWMATH, be relocated there? What will happen to the reputation points of the involved askers/answerers?
6. Will HWMATH manage its own user-contributed-and-reviewed blog/wiki about basic/elementary Mathematics?
   That would be immensely helpful to so many students and math amateurs worldwide. And it would be very efficient in addressing the concerns of HWMATH and MSE users.

[work in progress, feel free to suggest further points or improvements]

Answer 10

I have not read all of the relevant meta, so likely this has been stated elsewhere but I feel I should still add this as a personal observation:

There are certain problems where the OP could greatly profit from hint-like answers leading him along the way instead of "complete" answers. Some people explicitly ask for hints and that is a great thing. Others do more or less state a problem, inviting an exhaustive answer. Often the latter sort of questions fails the criteria for "good questions", but this is not always the case, for example if the OP also includes a good description of his failed attempts and where he struggles.

I have found myself trying to figure out how to give a "good hint" inducing the OP to work for himself in a direction that will likely approach solution, only to see the question had already been answered exhaustively when I was about to post. I will admit that out of some frustration I have also recently posted pretty complete answers when for pedagogical reasons I better should not have.

There is also a problem inherent to the SE concept that asks for "actual answers" to questions such that hints are technically not meeting the criteria for answers unless the OP explicitly asks for them.

I don't know if a "NoviceMath.SE" with an explicit preference for hints could solve that problem. It might instead help to somewhere state a policy, that certain textbook or homework-like questions should be preferably answered in a way that guides the OP to find the solution on their own instead of outright serving it to them.

While I observed that giving hints in comments is already a practise folowed by many users, there still remains the technical problem that SE by concept asks for "actual answers" thus discouraging hint-answers.

Please note again, that I am a new reader to the meta and have not been active on MathSE for years. If I am missing important points or have a wrong impression of things, please leave a comment and correct me, also links to relevant meta are highly appreciated.

Thank you!

EDIT: As became evident from a comment, the connection to the OPs topic was not clear from what I have written, so I will add some clarification:

A third level of math could IMO make sense if it could encourage an answer style more based on giving hints as I described above.

As an argument in favour of an extra SE site, I would see its possibility to have its own policy on answers that could explicitly encourage a tutoring style. However I have reservations on whether that would fit in the overall SE concept.

Alternatively, "lower-level" math learners (highschool to first university years or students of subjects other than math having to learn some methods) could be helped more optimally by making it more explicit what kind of questions should be answered by tutoring / hints. I have no concrete suggestion on how to get there, ultimately some means of encouraging a tutoring culture for certain questions would have to be found.

The bottomline could be that a dedicated third-level of math could help create a more beneficial learning environment for its audience. On the other hand the community could also focus on how to encourage tutoring behaviour withing the range of the current MathSE.

Answer 11

Delete reason: problem addressed in this post.

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Maybe (just maybe) the right place to draw the line between what belongs to MSE and what belongs to another site (maybe also in the SE network) is not the level of the question but the intention of the asker. I would differentiate between:

• "Do you want to understand the math behind your question?" (on-topic on MSE), or
• "Do you just want your problem to be solved?" (off-topic on MSE).

As a site about math, I feel that we really should focus on the first kind of questions. Homeworks or cheating attempts often fall into the latter category anyways. An asker reformulating its question to be on-topic is most probably interested in the underlying math, because he must have put at least some thought into the problem formulation.

This dichotomy is intentionally vague. It should give new users a rough feeling for where they should go, and us a rough feeling for where a question belongs (what about that: new users on MSE/MO should go through a tiny quiz [like a decision diagram] to redirect/hint them to where they actually want to be). Also it kind of includes the "you should have thought about the problem before posting" policy.

In this sense, I somehow think that a third math side might be a good idea, because it would us provide with a place to migrate questions to, rather then just closing the question and leaving these people without help (they might find help on other places though, but is/should this be our concern?). But I also see the problem that such a side might not really be in the sense of the network.

In my understanding, the posts that adding value to the side are those which ask curious questions, independent of the level. In this way, I cannot see that we loos much by banning the second kind of questions from the side (either by closing or migrating). By this (risking downvotes) I express my strong feeling that we need a "we are no homework-solver"-close reason. Not only would the askers understand what seems to be the actual problem with his post (off-topic, missing context, etc. is often not helpful, and just a nice/subtle way to say exactly that, leaving new users puzzled what went wrong), but also might this change the target audience of MSE over time, seeing banners like "closed because of homework" etc.

Answer 12

Many results are proven in a single line by an experienced mathematician which would take pages of work for a high school student. Moreover, the compact proof is often inaccessible to the less experienced student, since they simply have not yet acquired the more sophisticated tools which may a require deeper understanding, a higher level of abstraction or a wider, more general form of some theorem.

When the range of abilities is too great, this leads to a dichotomy in what constitutes a "GOOD" answer. MathOverflow provides a place where the most compact, efficient answer using the most sophisticated tools will frequently be the best answer.

On MSE however, these would frequently be terrible answers - of no help whatsoever. I think this wide variation in our abilities is one of the main sources of frustration - to some degree for lesser mathematicians, but more so for the experienced ones, as it makes what constitutes "GOOD" content, an imprecise question.

Arturo Magidin's comments to me make a recent case in point:

...it’s not hard to show that such a group exists (at least, an abelian one) using a transfinite construction by starting with your favorite abelian group $G_0$, then Construction $G_1$ by taking $(G_0×F)/N$ where $F$ is free on the underlying set of $G_0$, and $N$ is the subgroup generated by all elements of the form $(g,−x^2_g)$; and then repeating the construction until you get $G_∞$. But start with $ℤ_n$ for different n, you get different groups.

Because this is a relatively throwaway comment to Arturo, he doesn't realise that these two sentences have probably saved me 6 months of fruitless research. But he probably doesn't also realise that it will take me a month or so to even learn what it means for a group to be "free" over a certain set, what a subgroup generated by... looks like and consequently he probably doesn't feel like he's helped me that much or that I've taken on board his comment.

But as frustrating as this may be for both of us, this is also the beauty of MSE. There's no way I would have received such an insightful answer that takes me straight to the heart of the matter in such a skilful way, on a site restricted to mathematicians of my level.

After all, the most skilled have the most to give to the least skilled, and the least skilled have the most to learn, from the most skilled. That's what we're all here - for the transfer on of the knowledge which somebody previously transferred to us.

So my ha'penneth, for what it's worth, is that we should preserve the dichotomy of abilities within a single site, but we should be constantly redoubling our mindfulness that we're dealing with people having a wide range of abilities and remember that what may be obvious to one of us is not always obvious to the other.

Answer 13

I think there is a valid idea here. Since some comments have very valid points, I thought of putting to light some advantages and what I think are some misconceptions.

First of all, I will address the "We don't need a "do my homework" for me stack-exchange" (paraphrasing the opinions in comments).

Yes, we don't. This idea doesn't propose it. In fact, it would arguably be better and more effective to reinforce a no-"do my homework" policy in a site which aims its content at homeworks. Why? It is much easier, homogeneous and fair to implement the LACK OF ATTEMPT => CLOSURE, because we know it is homework. That is the principle of the site. The controversy surrounding this in MSE is due to (among other reasons) the fact that many of us (me included) think it is not optimal to close questions which are not homework because of a "lack of attempt". This controversy seems to exist from times immemorial. This might be one idea to solve it.

One counter-argument against the above is that "lower-level" is not the same as "PSQ" (or homework, for that matter), an argument which is implicit and explicit in comments and answers. This is a good argument, so before addressing it satisfactorily, I need to elaborate on how would be a division which makes sense (for me).

We have, essentially, two communities here. The ones who don't want to work with Mathematics, but want to occasionally have fun with some problems, and the ones aiming to be researchers (or that are indeed researchers). This creates a heavy dichotomy on the types of questions and are two communities with entirely different needs and objectives. And one is hardly useful to the other, and coexisting really does no good. Curiously, I've listened to directly contradicting facts of people I know on my university when I asked for the reasons not to use MSE: ones answer that it is filled with "low-level" questions, and others with things they cannot understand. This sets the tone for the site: an undefined one. "People studying mathematics at any level" seems defined, but is so broad that in practice this does not narrow down any identity for the site.

It would, imho, be better for everyone to separate both. And I think it would be quite simple to tell where (even more simple than telling where we separate MO and MSE). The target-public for each platform would be something like:

• Mathoverflow - Researchers
• MathStackexchange 1 (for lack of a better name) - "Researchers-to-be"; people studying or who studied once with the prospect of becoming researchers who are actively involved with mathematics in their research (e.g., mathematics students in universities, physicists etc)
• MathStackexchange 2 - People who do not wish to be researchers actively involved with Mathematics, but need to do mathematics courses/homeworks or simply want to have fun with what they learned on them.

The associated on-topic questions at large would be:

• Mathoverflow - Questions found during research/Research Level.
• MathStackexchange 1 - Questions found during study/Math's specific curriculum level.
• MathStackexchange 2 - Homework on classes such as calculus, precalculus, basic geometry etc/"Lower"-level. Precisely, the complement of the above.

Note that the slash above is NOT to say that those things are interchangeable, which is where I come back to address the argument that I left untouched. However, they have a very high correlation. And the right one is a precise term, whereas the left one is what we would hopefully expect. If we intend to apply an effective way of dividing content while minimizing headaches and disagreement on subjective interpretations, it seems reasonable to cope with the fact that those are not the same and use the fact that they are heavily correlated. This is how MO separates itself from MSE: it abuses the correlation between research-level questions and questions found on research. And it has been quite effective.

Answer 14

A question what about Junior mathematicians like me who want to solve hard problems? Look at my profile for examples? I do support hwmath though. But I am afraid if people like me who are very junior at mathematics would be signposted to that site (hwmath).