What is the purpose of math.se; to learn to provide nice answers or just to get them?

Hello to all,

I am a relatively new math.se member, and I have a question about the site.

First of all I must say, that I have found this website to be completely amazing. No other related site that I have ever seen can even compete with it. I am astounded by the quality of answers provided here, and how much work people put into them (especially with Texing everything).

However, now and then, when some question I am capable of answering pops up, I do not wish to just type down my immediate thoughts and post my quick answer. I instead choose to think for a while to make sure what I write makes as much sense as possible. In addition to this, I am not the fastest typer.

Due to this, I don't think I was ever the first person to submit an answer, there's always someone quicker. So here are my two questions:

Is it frowned upon if I submit a second answer, that is very similar to the previous answer? Of course, I do not mean to ask if I can copy the previous answer.

Secondly, I have noticed that the experienced people answer questions that must be very simple for them. By experienced I mean either people that have a very high reputation (although that need not be proof), or professors, postdocs etc. Isn't this a place for people to practice their way of explaining? I've seen professors provide answers to $1^{st}$ year undergrad questions. These answers are very nice, lucid and most of all, correct. But as soon as such an answer is provided, I don't think another undergraduate will attempt to provide another answer himself. This is the position I find myself in.

So is this a site for asking questions and getting a nice answer or is this a place to develop something of a teaching quality? I have found it mostly to be the former.

Thanks.

• One small remark: typing in LaTeX is almost second-nature to most people who have been writing mathematics for any length of time, so don't be too impressed by this! – Matt E Jan 31 '11 at 4:27
• I'm not saying it's hard to Tex, just that people put in a lot of effort, and I find joy in that. – milcak Jan 31 '11 at 4:33

Hello milcak,

Welcome to the site. I think your question is a fantastic one: there is a tension between two worthy goals: of having a site with the best (including quickest) possible answers, and having a site which actually develops people's answering skills.

I agree that the focus at present seems to be on the former, but I think that the latter is also important and more emphasis on that -- if possible -- would be a good thing.

Here on math.SE though we have people who have answered literally hundreds of questions and asked literally none, and indeed most of the high rep users have asked very few questions. I wish it was otherwise. I have asked only two questions here myself, but I'm thinking about how to improve in that regard. (I do admit that because I have a high rep on MO, there's much less chance that a borderline-too-elementary question that I ask there will get closed, so it's tempting to throw out questions to a community of mostly research-active mathematicians. But I think that there must be plenty of questions that I could ask here and get just as good an answer to, especially since there is a lot of overlap between the answerers here and the MO people.)

I think you're absolutely right that the reputation system has a way of drawing people in -- that's pretty much the genius of the stack exchange platform as I see it: sublimation of the natural urge to exhibit your intelligence and quickness into a socially beneficial outcome -- and getting them to answer questions that they could just as well leave to someone else. I personally have tried to make a point to only answer questions at the advanced undergraduate level or above. I totally agree that "How do I do this integral?" is something that an undergraduate math major is equally qualified to answer, and such a person probably has more to learn about writing and explaining mathematics to a general audience than I. (I don't always adhere to this rule: just today I wrote out a complete solution to a simple recursion problem, for the not very good reason that the way the problem was posed confused me for almost a day, and I finally wanted to get it out of my system.) Or, if a question gets a few answers but not the one I was expecting to see, I may chime in at a later point.

Anyway, I'd be delighted if we could have a larger discussion of these issues. Is there some way to leave room for people at various levels to answer questions? Is there some way to encourage PhD mathematicians to ask questions on this site? Do we dare admit that we do not know it all, not even everything relatively close to the ground? :)

• Actually, some rather eminent mathematicians have asked questions on MO that got closed as being too elementary. It would be nice for both sites, if there was a stronger culture of PhD mathematicians asking questions here. I could certainly swamp this site with completely elementary question on model theory, say, and would get excellent answers from Andres Caicedo and other experts in the field. – Alex B. Jan 31 '11 at 11:41

If your answer has anything that the posted answer does not have (goes over some point you find or found particularly troublesome, expands on something, adds something), by all means, add the answer. I would only abstain if my answer is completely and totally subsumed by another answer already posted, but this is unlikely to happen.

I can tell you that there are topics in which I find it very hard to speak in a way that is actually accessible to the questioner; for instance, I find that I simply cannot teach college algebra courses well. Not because I don't know the material, but because I found the material so clear and easy when I learned it that I just have no inkling whatsoever about what students find difficult. While I can certainly answer questions on this site about material on that level, someone closer to the material, who actually had some issues with it, is likely to give a much more insightful answer, even if it is completely contained in one I give. And this holds for material at a high level too: I like and enjoy algebraic number theory a lot, and know a reasonable amount of it, but I simply cannot give the kinds of insight that someone Pete Clark can, because he knows more and uses it far more often than I do.

• Thanks Arturo for your anwser as well. I think that everyone has some place and purpose in this community, and if all I can do is add some insight, I am sure it will be useful to the person asking. – milcak Jan 31 '11 at 4:45
• you bring up a great point here, that beyond a certain level of knowledge it can be harder to explain some things, because you cannot place yourself in the mental state of not knowing them to figure out what to say. (I made some plaintive comments about teaching induction in one of my recent answers.) This is a good example of how post-PhD mathematicians like us can actually learn from younger people on this site: how do you explain such a topic in a way which actually works to satisfy the OP? – Pete L. Clark Jan 31 '11 at 9:29
• It can also be the case, I think, that answers which look the same to us do not in fact look the same to the student/OP. More than once I have seen someone post an answer after mine and thought, "Well, isn't that almost exactly what I said?" And then I get to look back and see how that's not quite the case. (For me personally, I often find the fact that I've said much more than the other answer to be part of the issue.) – Pete L. Clark Jan 31 '11 at 9:31
• @Pete: Exactly; and I did see your comments in the Induction thread, and it immediately brought to my mind my issues with pre-calculus and below. – Arturo Magidin Jan 31 '11 at 14:06

I have noticed that the experienced people answer questions that must be very simple for them.

In our defense, simple questions can, in various ways, hide subtleties that a more straightforward answer might not address. When I answer simpler questions, I try to indicate some of these subtleties and also point to related ideas and topics that the OP, or anyone else looking at the question, might find interesting. For example, in response to this question about the formula $\frac{\pi}{4} = 1 - \frac{1}{3} + \frac{1}{5} \mp ...$ I indicated the standard proof one might see in a typical calculus course, but also sketched a completely different proof related to some nontrivial number theory (of all things!).

Isn't this a place for people to practice their way of explaining?

Well, no, in the sense that the focus of the StackExchange people is really on getting people answers to their questions as efficiently as possible. But I am far from the only active user here who thinks of math.SE as a teaching tool, and as a teaching tool it is just as important to let people practice answering as to get people good answers to their questions. So I agree that this is an issue worth considering.

I think Pete's comment on Arturo's answer is really key here:

It can also be the case, I think, that answers which look the same to us do not in fact look the same to the student/OP. More than once I have seen someone post an answer after mine and thought, "Well, isn't that almost exactly what I said?" And then I get to look back and see how that's not quite the case. (For me personally, I often find the fact that I've said much more than the other answer to be part of the issue.)

The point of the voting system is that answers which are liked by the community are recognized as such, and the voting system works best if it has many answers to choose from. So you can only make the system work better by providing your own answer: if it doesn't get voted up (which will unfortunately happen from time to time) then it is still available but doesn't clutter up the answers (if people view by votes), but if it does get voted up then that means you've provided an explanation of value to somebody. In other words, just submit your own answer anyway. The system is optimized for this kind of behavior.

This site is what we make of it. People with more advanced knowledge (not necessarily smarter, just more experienced) can answer questions that beginning students often can't, so these questions should be answered by the knowledgeable. Simpler questions - those same people might find them less challenging, and so it seems that the only reason to answer them is to boost your reputation points; so all it needs is some restraint on the part of us "old-timers".

On the other hand, if someone answers a question inaccurately, then while some feedback targeted at the answer benefits the answerer, the questioner is likely to be confused. So there is some price of your learning how to answer. But if the community decides that the price is worth paying (since the goal of developing "teaching quality" is also worthwhile), then this practice will not be frowned upon, but rather encouraged. Another advantage when a student answers a student is that the former still remembers the difficulties the latter is trying to overcome.

All of this shouldn't stop you from trying to answer questions. Even if a good answer is already there, an answer coming from you can be closer to the OP's viewpoint, and so more helpful. Whether the community is willing to moderate such "practice answers" remains to be seen.

• I agree with much of this answer, but not with "so it seems that the only reason to answer them is to boost your reputation points." I'm sure there are many other reasons people have for answering questions that are easy for them to answer. But with the point you were making, that we should restrain ourselves to leave more room for the less experienced, I think I agree. – Jonas Meyer Jan 31 '11 at 0:55
• "so it seems the only reason to answer them is to boost your reputation points." Well, my job involves a fair amount of answering questions that I don't find particularly challenging myself, and more, questions about topics that I never found confusing. I answer them because I honestly want to help, and also because it is good practice for me to answer them and try to do so in a way that is understandable and clear to beginning students. This is not always trivial. – Arturo Magidin Jan 31 '11 at 1:56
• Thank you Yuval for the answer. I just wanted to make sure I do not upset anyone by providing a second explanation that might be worse than the one already posted. – milcak Jan 31 '11 at 4:42
• Whether I answer "easy" questions or not has nothing to do with reputation; see my answer. – Qiaochu Yuan Jan 31 '11 at 17:15

While I agree with the sentiments expressed so far, that if your answer adds something genuinely new, then you should post it, I do see it quite often that people repeat almost literally what has been said before them. This has several unpleasant consequences: it bumps the question to the top, thereby detracting attention from questions that are still waiting for a good answer, it takes up the readers' time without offering them any new insights in return (and it sometimes transpires rather late into the post that there is nothing new). It also leaves the unpleasant after taste that the answer has been added as part of a reputation hunt, rather than in an honest attempt to help the OP.

You have asked a question that nobody seems to have addressed so far:

So is this a site for asking questions and getting a nice answer or is this a place to develop something of a teaching quality?

Although this site is what the users make of it, I would definitely say that at the moment it's the former and I personally very much hope that it will stay that way. If you ask a question that you want to know the answer to, then you will not be so enthused by answers from people who may be slightly confused themselves, and who deepen your confusion even further, instead of clearing things up. My point is that the askers don't normally ask questions to test the other participants' teaching skills. If you want to practice your teaching skills, then I would recommend that you do it with your class mates, at the black board. If you are writing an answer here, then you should aim to help the OP and not to pursue some egoistic aim. That's my personal point of view.

There is one more thing: sometimes you will see people purposefully not giving away the full answer, but rather trying to guide the OP to an understanding that will help him find the answer himself. While in such a situation, it is easy to add something new by posting a complete answer, you should always ask yourself whether that's really the best way to help the OP.

• In other words, an inexperienced user should answer only when they're quite certain that the answer is correct; this of course applies also for experienced users! – Yuval Filmus Jan 31 '11 at 9:35
• Nearly identical duplicate answers can result through no fault of the answerers, since you cannot know what other answers have been submitted while you were composing your own answer. If you are a slow and thoughtful type, then you are likely to appear instead as a "repeats already-posted answers" type, due to the system itself. – Matt Apr 25 '11 at 19:20