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I'm self-teaching algebraic geometry, and obviously the problems get hard fast (for a hobbyist at least) and I can't be 100% sure if I solved a particular problem. Initially I found Math SE to be very helpful in confirming or correcting my proofs.

But as time has gone on, I've noticed less answers or comments coming in, and I don't know if it's because I'm violating a sort of "etiquette" about asking too many questions, or if it's because the math is getting harder and less people can help. I certainly ask more questions than I answer, but always try to help whenever I see something I can help with.

Thoughts? Is SE an appropriate venue for this kind of thing?

Thanks!

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    $\begingroup$ I can see only 12 questions asked by you, so definitely you are not asking too many questions. Probably it is just because the math is getting a bit harder. $\endgroup$
    – user99914
    May 13, 2018 at 22:41
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    $\begingroup$ This is only my own observation but for what it's worth, I feel like hard questions in algebraic geometry specifically get in general less answers than hard questions from other topics. This may be due to less specialists of that particular topic hanging around. Then again this is just my feeling. $\endgroup$
    – Arnaud Mortier
    May 13, 2018 at 23:30
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    $\begingroup$ @ArnaudMortier thank you so much for you thoughts, that makes a lot of sense. Just out of curiosity, what subjects do you find have a lot of specialists hanging around? Would be interested to perhaps learn a bit more about whatever subjects seem to have garnered so much interest :) TIA! $\endgroup$
    – William
    May 14, 2018 at 1:47
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    $\begingroup$ @ArnaudMortier Indeed, it was observed that algebraic geometry is among the tags with higher unanswered rate: Best and worst tags for % answered rate. As you can see here it is 35.5% all time, 57% last month, 66.2% last 7 days. $\endgroup$
    – Martin Sleziak
    May 14, 2018 at 10:20
  • $\begingroup$ @William There are a lot of topics of high interest in maths that are represented here, but above all, if you have started learning AG, I would surely not like to encourage you to stop. It is a wonderful topic (I can see that even though I'm far from a specialist myself) that has witnessed a surprising and beautiful shift in the second half of the last century. Some topics that may be more represented and will be helpful for you to grasp AG are general and algebraic topology. $\endgroup$
    – Arnaud Mortier
    May 14, 2018 at 11:26
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    $\begingroup$ Maybe using chat in addition to asking on main might be worth giving a try. If you are lucky, you might find there people interested in the same topic. Just today I've seen people discussing in chat possibility of a studying Hartshorne together. $\endgroup$
    – Martin Sleziak
    May 14, 2018 at 11:29
  • $\begingroup$ And since part of the question was whether you are asking too frequently, I will add that there is a limit of 6 question pre day, 50 questions per month. So the Stack Exchange software will not allow you to ask more questions than that. $\endgroup$
    – Martin Sleziak
    May 14, 2018 at 11:31
  • $\begingroup$ Another aspect of it (again, personal opinion) is that questions for specialists tend to get much less rewarded by upvotes (only a few other specialists will read the question, let alone the answers). It may be that some get discouraged from writing long answers that will mostly be ignored (although I personally keep writing alg-top answers). $\endgroup$
    – Arnaud Mortier
    May 14, 2018 at 19:15
  • $\begingroup$ @MartinSleziak some AG users will comment a hint or brief words towards an answer instead of writing an answer, which may bump up the unanswered rate. I agree with the above speculation that answers don't tend to get very many upvotes - over the past 30 days, the top 10 users providing answers per Martin's link receive an average of about 1.66 upvotes per answer, which is fairly low. $\endgroup$
    – KReiser
    May 14, 2018 at 20:34
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    $\begingroup$ If they are ready to study algebraic geometry, someone should not need too much "proof assistance", because by that level they should be able to mostly assess the correctness of their own proofs and identifying the most likely gaps. This is not the same as a student just learning to write mathematical proofs. So rather than focusing on proof correctness, questions at advanced levels should really focus on the concepts involved. This includes graduate-level algebraic geometry in my opinion in addition to other graduate-level topics (the kind that are generally not seen by undergrads). $\endgroup$
    – Carl Mummert
    May 14, 2018 at 23:41
  • $\begingroup$ @CarlMummert Could you expound a bit more on this point? Certainly if my self-study is getting "ahead of itself" I'd like to know. But, it seems to me that the world's most famous mathematicians still need help verifying their own (substantially more complex) proofs. It's hard to know whether I've stumbled into the AG equivalent of proving all triangles are isosceles or that 1 = 2. I'm not worried about proof technique -- I'm worried about the arguments I make and whether I use the theorems I've learned to correctly solve the problem. Thoughts? Are you saying you no longer confirm proofs? $\endgroup$
    – William
    May 19, 2018 at 18:40
  • $\begingroup$ @William: the issue in my mind is exactly that their proofs are substantially more complex. For what are essentially introductory exercises, someone ready to learn algebraic geometry should not need to post here to verify routine proofs - and particularly not very often. Overall (apart from this specific question) I think that "is this proof correct?" questions are often not a very good fit for this site. Better-fitting questions often focus on specific mathematical issues rather than whether some specific proof text is valid. $\endgroup$
    – Carl Mummert
    May 21, 2018 at 19:27

3 Answers 3

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I believe using Math SE as an assistance for self-teaching is a great idea, for the following reasons:

First, I believe it fits the scope of the site very well: This site focusses on math, that is sub-research level (as opposed to MO). Thus problems appearing while self-teaching should fit in very well.

Secondly, the SE concept is about questions being answered in a way that the generated content will be valuable to future readers and not only the OP. While having your proofs verified may appear very specific to your own situation at first, I believe that in fact by asking such questions you are providing excercise material for other learners that are on the same level as you are. A good answer to one of your questions would in general point out problems with applying proving techniques you may have and also suggest improvements in notation.

To elaborate on this consider the following situation: You encounter a problem that can be proven by a standard trick that you however are not yet aware of, so you attempt a different way to prove it. This sort of question directly motivates two sorts of answers: A description of the standard-proof as well as answers relating to your alternative proof, that may in fact be viable, possibly after some corrections.

Having multiple answers and pointing out different approaches to a problem is at the core of the SE concept and thus again, what you are doing fits in very well and generates value for future readers.

Whenever you post an attempted proof this is valuable even if the question remains unanswered, because if anybody with the same problem ever encounters your question, they have a starting point in your proof and may be inspired to retrace your attempt and thus learn from your work. With an unanswered question a good description of your attempt will even additionally motivate people to work through your proof, as they could be the first to answer!

Third and finally by having your own attempts verified you are acting as a positive example: Too often we have questions asking for quick solutions without providing own work. By showing your own work and asking for feedback, you are doing the opposite and you are showing, that learning requires own thought and effort.

In conclusion you are certainly not violating any "unwritten rules". Also you should not worry that you are asking too many questions: This site does not work like a store in the sense that you would have to pay for every answer you are getting with an answer of your own. To stay in that picture, rather think of it as an account with a very wide credit-margin: Once you have gained the expertise you strive for, you may be better able to provide answers on your own and pay back for what you once received.

Also the very sort of question you are asking already constitues valuable content in itself, even if lacking an answer, and you should not be concerned that you are taking more than you are giving.

If you are not receiving any answers it ist most certainly because your questions are hard to answer:

On the one hand, your subject, algebraic geometry, is very specialised and requires a lot of dedication: Unlike basic calculus, linear algebra, functional analyis or stochastics, many students graduate without having acquired a basic knowledge in algebraic geometry. Thus it is probably harder to find somebody who can answer even a basic question about algebraic geometry than to find somebody to answer a basic functional analysis question.

On the other hand, your type of question (verifying proofs) is typically more work to answer than a question that could be completely answered by providing a well-known standard technique. Somebody to answer your question will be required to work through every aspect of your very personal proof and even might attempt to work around and correct some minor errings in order to make your general approach work. If you are self-teaching you may not yet be familiar with the usual ways of presenting the argument in your field of study and your proof may thus be hard to read for an expert. This very nature of your question might thus reduce the amount of persons able to answer even further, as not every expert may have the time that would be required to provide a quality answer.

So please do not be discouraged by a lack of answers and keep it on. I personally am very happy to see self-learners questions and the type of question you are asking provides a strong motivation to me to invest some time in an answer.

PS.: I am sort of sad now that I have quit algebraic geometry after giving it an honest attempt... I have by now forgotten everything I might have ever known about it, otherwise I would attempt an answer to one of your questions now. ;)

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  • $\begingroup$ Thank you so much for your very thoughtful answer. I really appreciate it. Ironically, it's only in later life that I've gotten so enthused about filling my brain with knowledge, and resources like this are so helpful. Also would be interested in why you stopped learning AG? Did you find the results boring? I also did the first few chapters of Hatcher's AT and found that much more "mind-blowing" at first blush, although AG has its own nifty punchlines as well (e.g. Nullstellensatz). $\endgroup$
    – William
    May 19, 2018 at 18:46
  • $\begingroup$ AG appeared as an "all-or-nothing" thing to me - it was so hard for me to follow the lectures that I would have had to specialise there if I wanted to stand a chance: Put in all effort for AG only and do the minimum everywhere else. I was however interested in applied math and did not want to sacrifice these subjects. AG is certainly not boring, it rather had a "die-hard" reputation among us students and I decided to drop it in favour of a broader knowledge in (as I thought then) "easier" fields. I might give it a try again in later life, as you do, though. $\endgroup$
    – mol3574710n0fN074710n
    May 19, 2018 at 18:53
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Absolutely! To be honest if you are even being considerate enough to ask yourself the question, then you're probably fine. As people have said above, it will be the maths getting harder that's causing what you have experienced.

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I've found Math SE most helpful when my questions are on the standard path. It makes sense: there's more people who have been there, and it's easily accessible to them.

Your own proofs, done in your own way, are not the standard path. And as they get harder and more complex, it's harder for people to peer review them.

I'm not sure what the answer is: you could try to follow the standard proofs, but on the other hand, it's great to do it all yourself, without guidance. I guess all you can do is try to make them accessible... though that might not be enough.

Or perhaps you could try to relate your own proof to the standard proof, and if you have trouble, ask that as a question. That might be more accessible; and also give you practice in checking them yourself.

Anyway, I think something like that is the problem, and not that people are boycotting you for working hard on your own proofs and going to the trouble of asking about them!

BTW Although many people here will happily do their best to help people with very specific problems, it's not really the primary mission, at least of the stackexchange websites - which is to build up a resource of good answers to questions that might be of use to other people too.

So perhaps that's another aspect of making it accessible: to whom. Not just to potential answerers, but also to future questioners. Though this may be difficult to apply to your own proofs!

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