Maybe I should elaborate a tiny bit: I see three possibly answers here:

- History questions are not welcome in general;
- History questions are welcome, but the question in question (!) is not good and should be closed.
- History questions are welcome, and this question is a perfectly good such and should not be closed.

I feel only marginally competent to decide between alternatives 2 and 3, but at least I don't think I am in favour of alternative 1.

]]>MO seems like a good place to answer such a question definitively. It is similar in genre to a question recently asked by Greg Kuperberg that tries to straighten out the facts about a particular widely circulated urban legend.

However, after seeing several discussions here on meta about non-technical questions, I get the impression that a sizable number of regular participants don't want questions like this on MO. Should I pose it or not?

]]>http://mathoverflow.net/questions/82024/pythagorean-quadruples-with-a-fixed-d

http://mathoverflow.net/questions/82021/how-to-find-diophantine-integer-solutions-to-a-sphere-for-large-spheres

which Noam found out was

http://projecteuler.net/problem=360

I would like to repeat my claim, from an earlier such episode, that P.E. problems are intended to stay within that sphere of people, and not posted on MO. One of the askers pointed out that P.E. was intended to be a learning experience, so I suggested that he read some books. Meanwhile, they are not particularly mathematics problems as such, and are certainly not research mathematics, rather an invitation to computer programming. ]]>

However, I had a long conversation with Felipe Voloch in the comments to my version, which I'd like to be able to refer to if there is further discussion about Arul's question. So I am archiving it here with Felipe's permission. I don't have anything more I want to say, but certainly Felipe can feel free to get in the last word here if he wants to.

This is not MO level. Factor and compute the Galois group. – Felipe Voloch 56 mins ago

@FelipeVoloch It seems to me there is a lot to say here. I was going to leave this in an answer, which is taking some time to write. Basic points: – David Speyer 53 mins ago

Although factorization of polynomials over ℚ is rapid, computation of Galois groups is not. Testing whether a Galois is abelian should be much faster than running a general Galois computation algorithm on something abelian. – David Speyer 52 mins ago

Once you know that the Galois gorup is abelian, finding the cyclotomic field is tricky. Matt Emerton started to write out the details here math.stackexchange.com/a/36664/448 and didn't give them all. – David Speyer 50 mins ago

Before calling GAP (for example) to compute the Galois group, there are some obvious Frobenius element plausibility tests which will allow us to reject almost all f. – David Speyer 50 mins ago

"rapid" was not specified in the question. If you want something faster, you can compute the discriminant and narrow down the choice of cyclotomic field, or a number of other things, depending of exactly you want. But that won't make it research level. – Felipe Voloch 48 mins ago

Calegari-Scott-Morisson arxiv.org/abs/1004.0665 have some interesting results when the root is small. – David Speyer 48 mins ago

It is research level in the sense of a computational problem which can reasonably come in research and which a graduate student shouldn't be expected to know how to do. (Agreed that it is not research level in the sense of something you could publish a paper on.) – David Speyer 47 mins ago

When someone asks "how to decide" something, I think it should be taken as the default understanding that they mean in practice. – David Speyer 45 mins ago

It seemed to me more like a random question than that the person actually had a number that he/she needed to decide whether it was cyclotomic. I don't think it's up to you to revive and/or reinterpret the question. If a downvote caused them to delete the question, they don't need the answer that badly. – Felipe Voloch 41 mins ago

I mostly revived it because I was annoyed that I had 80% of the below written out when the question disappeared. I wish the question had had more context (and wish the close-voter had requested some), but otherwise I think it is a good example of the sort of question where experts in computational number theory (not that I am claiming to be one) could quickly help someone who is doing reasonable research in a different field. – David Speyer 39 mins ago

I originally started writing the below in the form of a comment asking for the question to get more specific but, as often happens, it didn't fit in the comment box. Note also the bolded comments as places where an expert (like Felipe!) could probably say something better. – David Speyer 37 mins ago

@FelipeVoloch "It seemed to me more like a random question than that the person actually had a number that he/she needed to decide whether it was cyclotomic" I do have some numbers I want to decide to be cyclotomic. If they are not, then I would know either some natural limits of my technique or the known bound is loose (with relevancy to a problem I am working on). – Arul 9 mins ago ]]>

I want to make my query specific. This question, http://mathoverflow.net/questions/133597/what-would-remain-of-current-mathematics-without-axiom-of-power-set, is only the latest in a series of many questions (it seems to me) questioning the validity of transfinitism and nonconstructivism. Any trained mathematician knows that these controversies have been around for a long time. So my question is: why now? Has something happened in the world of mathematics or math education that is causing what seems to me a rethinking on this?

I saw one comment that jokingly suggested it was Wiles' fault for solving FLT, with the cranks moving on to Cantor and the like. More seriously, though:

1) Is the rise of computer science and coding in importance driving any of this? Specifically, does anyone actually involved in CS see examples of educators opening suggesting/calling for finitist teaching universally? I know of some examples, but how widespread? I realize that theoretical CS deals with essentially finite objects, but why now the urge to shut down the rest of the mathematical world?

2) It strikes me that finitism and the like is a claim that we should restrict knowledge, since finitism and constructivism are perfectly fine subsets of classical mathematics. If you a writing a computer program, what you are doing is necessarily computable. But why restrict the exploration into the non-computable? Again, I'm looking for examples from the practicing mathematicians here of examples they see where this idea of pedagogy is taking hold. I can understand how much of this is non-intuitive at first, but a key part of math education is learning to follow the logic wherever it leads. Why now the urge to suppress this?

I ask this because I am not a practicing mathematician or an educator (I have an MS degree, and use math in an applied field; but I am thoroughly classical in outlook). Perhaps I'm just seeing things that aren't there. Perhaps increasing interconnectedness just amplifies some voices beyond their actual influence. But I sense that it may be more than this, and since I don't actively deal with the research and educational community, I'm interested in their views. I'm wondering if some more grassroots in education is happening.

Speaking only for myself, calls to restrict exploration into acquiring knowledge is profoundly anti-scientific and anti-mathematical. As I saw one wise contributor suggest, if some area doesn't interest you, study something else. But why the desire to shut off other discussion? I'm talking about non-crank motives--we'll never reach them. In particular, why teach impressionable students to not be curious and chase knowledge wherever it leads? Again, not here to discuss philosophy, but is anyone here seeing this urge in some area of teaching, and if so, what are their stated motives?

Thanks in advance! ]]>

I had problems with a question (closed in 9 min, 10 down votes and finally deleted) about mathematicians,

neurosis and all common stereotypes among non-mathematicians on that.

I warn you that I'm not talking about severe neurosis as schizophrenia (John Nash...), it's not at all my point.

My point is about mild neurosis, allegedly widespread (by non-mathematicians) among mathematicians.

I think it's an extremely interesting question (also sensitive...) and a good idea that the mathematicians could respond freely on that.

But after this bad experience, I dare not open a new question on this topic ..., and I prefer asking you directly:

Is it possible to post such a question on mathoverflow ? how ? what would be an acceptable shape ?

What is the red line not to cross about questions on mathematics and psychology ?

I apologize once again.

Sebastien ]]>

Remark: The typical pattern for using CW mode in this way is:

- Have a
*simple*question, e.g. a statement of the original bound, a link to the original paper, and a statement of goal. - One
*accepted*answer with the main info: the latest known improvement and a timeline of earlier improvements. - Possibly additional answers with auxiliary information.

In my opinion, cramming everything into the question text is a rather confusing use of this site.

]]>Besides this question being generally problematic, it also strikes me first as unansawerable (in completeness) as well as, and most importantly, rather pointless. In addition to having already create a quite aggressive exchange in the comments.

If the questions would at least ask how *to avoid* accidentally picking a journal of questionable reputation I might consider this as an *in principle* reasonable question (which does not necessarily mean it should be on MO).

Of course, theoretically, having a completele list of all these journals (leaving matters of subjectivity in some cases aside) would allow one to also answer the question I raise. However, first, a complete list is unlikely to be compiled (as there are many, new ones appear, and so on ) and, second, it seems a most ineffficient way to me to approach the (practical) question I mentioned.

However, it seems to me the distinction between the two questions 'create a complete list' vs 'how to avoid them' is not made in a sufficiently (IMO) clear way by various contributiors in the discussion (in already twenty comments). One could consider this as harmless or even irrelevant yet it [the lack of this distiction being clearly made] appears to me to be a main reason for a already quite agressive exchange in the comments.

(Further note on this exchange: I cannot know if I saw all comments and I know some where (self-)deleted, with good intentions, but I was active in the exchange, in trying to calm it down, with at first some success or so I thought, but quite limited success in the end it seems. From what I saw, and circumstantial evidence, it seems to me that the accusation, not directed at me to be clear but at somebody, that there were 'racist hateful comments' as quite exaggerated and/or incorrect thus the claim seems insulting; that being said a comment I saw, while in my opinion intended as playful [which I tried to convey and thought had achieved, thus everything related to this is gone], reasonably could have been read as insulting, too, which explains the reaction, yet still 'racist hateful' seems very exaggerated and/or incorrect, from what I saw.)

In any case, I would appreciate if this question was reclosed (I have no interest to partcipate in another open/close conflict) and best deleted as soon as possible. Or at the very least the question could be reformualted and the comment thread cleaned.

ps. I thought about handling this via a flag but then since the situation is complex for 140 characters I decided for this way of raising the matter (besides it is in my opinion also somewhat typical and thus possibly of wider interest than the specific case at hand, but this really only in parenthesis). [Added: It occured to me I could raise a flag in addition, which I did, referring to this.]

]]>I think there is a pattern of closing questions too rapidly. That something sounds like it might be an exercise, and was posted at about the same time as someone else posted a few exercises, doesn't mean it is one. Of course, maybe I'm just missing some trick for solving this type of problem... but then perhaps it's worth saying what that trick is. There is a recursion based on the number of bins. Inclusion-exclusion leads to a recursion, too. Neither of these recursions looks simple to analyze. I vote to reopen. ]]>

If it's appropriate, I'll migrate it here as soon as the bounty is expired (and of course, if there's no answer in MSE).

]]>http://mathoverflow.net/users/18465/luke

His questions are typically answered quickly, sometimes with comments to the affect of my sentence above. He's been posting questions of this variety for several years now, so it's hard to imagine these are actually homework problems but they're certainly not research questions.

I thought I'd mention this quirky trend.

]]>I have studied Dilworth's Lemma (I'm not a student, just hobby). But I couldn't make an analogy.

Then the problem is closed. Actually, I didn't know the difference between MO and math.stackexchange. I have learnt it from one of the comments.

Then, I edited my question as it is closer to the definition of Dilworth's Lemma. And I mention where I am stuck.

I think the latest form of my question is now similar to the other question at MO. How can I make the question reopened? ]]>

has been closed. Let me try to explain my motivation for asking and hopefully convince someone for reopening.

Clearly there are two edge points:

1) Applications are "driving force" for many research directions in nowdays mathematics (especially information theory,

numerical algorithms).

2) Some areas quite successfully developing without connections to applications.

But seems main body of iceberg is in the middle.

The aim of the question is to shed light on that.

"Applications" can be different, some leads to direct usage in industry, some are "nearby".

So hopefully the person answering can specify what kind of application he is talking about.

There is some part of "subjective and argumentative" but I do not agree that

is so serious that can be a reason for closing. ]]>

Cf. this older question, though I acknowledge that was back in the Old Days.

I was under the impression when MO started that it had a place for questions one honestly ran into, which one thought an appropriate "expert" or "specialist" would know about.

(Disclaimer: I have met the OP and think he is a serious researcher. This of course colours my judgement.)

]]>In doing so, I note that a line is drawn between math majors and non-math majors. This led me to wonder about applied math majors. I checked the website of my Alma Mater in New Zealand and saw that these days, they offer the possibility to major in pure mathematics, including taking a first course on proofs, or majoring in applied mathematics, which does not appear to require taking such a course. Since the original question seemed primarily about North American universities, I wonder if this situation also exists in North America.

It is tempting to ask the spin-off question whether applied mathematics majors should have a separate course on proofs, and whether they should be classified under maths majors or non-math majors, but I suspect that such a question would be perceived as argumentative. The word "should" is probably a warning sign.

I am also sensitive to the point of view that that separating mathematics into pure and applied is somewhat artificial, although at times useful.

I would much appreciate your thoughts on whether this question can be turned into an acceptable non-argumentative question. ]]>

I want to get an overview of the subject of irrational and transcendental numbers (most important ideas, methods and theorems - and especially what ideas are possible to push further).

Is it ok to ask about that here?

Here is what I know about so far, but I didn't study the details of it all yet:

* logs (easy) and roots (Gauss)

* existence of trancendental numbers: Cantor

* construction: Liouville

* e: series

* pi: Lambert, Niven, Apery, Flint-Hills

* e^pi: complex analysis

* reciprocal fibonacci constant: André-Jeannin

* Erdos-Borwein constant

* Thue-Morse constant: Dekking

* Euler: zeta(2n)

* Apery: zeta(3)

* Wadim Zudilin: zeta(5),zeta(7),zeta(9),zeta(11)

Theory:

* Dirichlet, Kronecker, Weyl equidistribution, Markoff-Lagrange spectrum

* Mahler measure

* Lindemann-Weierstrass, Gelfond-Schneier, Baker's linear forms in logarithms

Open:

* pi + e

* Catalans constant

* Euler-Mascheroni ]]>

I request this question be edited and reopened. A suggestion for more acceptable wording is: "In my studies I came across the following binary operation table on a three element set. The resulting operation is not associative, so the related structure is not a group or even a semigroup. What kind of structure is it, and where can I find out more about it?"

Put the table somewhere below this paragraph. Also, another paragraph giving more context and motivation would be welcome. I recommend the reference-request and general-algebra tags forthis question. The title wording might be changed to replace semigroup with structure.

When it is reopened, I will post a reference to Joel Berman's catalog of such structures, and mention the references he provides for this structure.

Gerhard "Ask Me About System Design" Paseman, 2013.01.27 ]]>

It is a reference request regarding data what numbers people name when asked to name some number.

It was closed quickly and has now three votes to reopen. The main (only?) objection seems to be it is not a mathematical question.

Personally, I somehow like the question but can see why one might not consider it as mathematical enough for MO (although this would be a debate to be had, but I can see why somebody would say so).

It was closed and now has three votes to reopen. (I did not yet vote to reopen, but am considering it.)

]]>(Aside: This leads into a more general question of mine about the use of representation theory as a generalization of modular forms. My question is the following: I understand that a classical Hecke eigenform (of some level N) can be viewed as an element of L2(GL2(Q) GL2(AQ) which corresponds to a subrepresentation. But what I don't get is why the representation tells you everything you would have wanted to know about the classical modular form. A representation is nothing more than a vector space with an action of a group! So how does this encode the information about the modular form?)

I'm thinking of this in part because Yemon Choi wrote in a very recent comment that he thinks it would be a good question. However, I'm already wondering whether I should have asked the original question in the first place (something I did more than 2 years ago, when I knew less, and when MO was much different, I believe). So that's one reason I'm not even sure about asking this new question.

I think this new question, while certainly appropriate for MO two years ago, fits into the following category. It is perfectly clear to someone who understands the representation-theoretic point of view of modular forms quite well. However, it might be a legitimate question (and this depends on what the nature of MO is) for the following reason: the answer to the question is NOT "just go read a book on automorphic representations." Why? Because the question speaks to a confusion that I believe a number of students first learning the subject face, one that will be hard to remedy by reading books on automorphic representations, which just give the definitions without explaining why we generalize them in the way we do.

Then again, shouldn't the answer just be "read Kudla's Chapter 7 of Introduction to the Langlands Program" (though he doesn't address my question explicitly, except arguably at the bottom of p.147). ]]>

It seems like a good question on its own. But I feel like it's coming directly off of the question above, which got 17 votes. So it's basically like "this question had an answer with a counterexample, so is there another counterexample if we add more restrictions?" ]]>

Since it is not very visible let me mention that it was already closed and then reopened. For details on who vote what see the revision list of the question

My opinion, in brief, is that this question is either going to be argumentative or irrelevant. Personally, I consider most existing answers as off-topic and/or of poor quality. [Added Jan 2nd: it is still quite mixed IMO, but at least meanwhile there seems to be a reasonable number of reasonable answers.]

The arguments put forward in the comments are somewhat the 'usual' do not imped subjective disucssions calls. I have no great interest to debunk the comments one by one but still some remarks:

First it is in my opinion not true that most people on this site are professional mathematicians (for example, there are plenty of students on the site), second there is a difference between discussing something subjetive somewhere (even in public, though most of the mentioned examples even refer to typically non-public things making the argument even weaker) and here on MO, third in most democratic communities there are, say, speed-limits on roads that are enforced without this being generally perceived as undemocratic, oppressive, dictatorial, or whatever.

]]>Is there some reason for the two votes to close this question? ]]>

I started to vote to close this as off-topic for being sub-research level. But the FAQ says (I'm paraphrasing from memory) that questions are on-topic when they're the sort of thing you'd ask when reading graduate level math books. By that criterion, this seems to me to be on topic; it's a natural question to ask when reading a graduate level algebra book, the natural counterexamples requiring more topology than many such readers are likely to have encountered. In particular, I don't think it would be embarrassing for a second-year graduate student to ask this question in the coffee room. So instead of voting to close, I answered it --- but it was a close call. I'm wondering what others think. ]]>

(ps. I do not wish to personally get much involved in the discussion as some of the involved users, I believe, have some general problem with me; but still I want to say that Peter Samuelson's comment is essentially precisely my opinion.)

]]>In my opinion in its current form it is completely unsuitable as an MO question; but some modifications seem more reasonable, so please those in particular OP that want this question, perhaps you could at least modify/clarify it a bit.

First, I am not completely happy with the way of closing, but I can see why this happened like this (since with a link to a comic as its only reference, its timing, and its general form it does not come of as serious question even), since at least to me the closing reason misses the point a bit, or at least it can be understood that way.

Second, my problem with the question is that it is extremely lazzy to the extent of being actively harmful to the success. To say something specific, what is the precise role "Navier--Stokes equation" plays in this question. Some scenarios:

OP actually wants to know

**only**about Navier--Stokes.OP would in fact also be interested in answers involving

**any PDE**and Navier--Stokes was just an example that came to mind.OP would in fact also be interested in answers involving

**any type of (advanced) maths**.

Moreover, it is all but hard to find something on this on the web; a minimal amount of preparation and to at least make clear what the actual goal of this question is seems more than desireable.

]]>http://mathoverflow.net/questions/63221/ideas-on-how-to-prevent-a-department-from-being-shut-down ]]>

In response, I want to ask a question about whether etale and *other* fundamental group functors (e.g. motivic, Tannakian in general) can be viewed as left adjoints.

Both, I might want to ask about the existence of such things in multiple cases and if there is any generality to such a construction. ]]>

I'm wondering whether it would make sense to have some kind of discussion on Mochizuki's recent purported proof of the ABC conjecture. Maybe something so that experts could give ideas about what ideas are in the proof? A discussion of when people might know enough to seriously judge the proof? Some other kind of discussion? ]]>

I have 60 or 70 mathematics monographs & textbooks for sale (in general: asking 1/2 amazon new price + shipping). It is appropriate to make a post advertising this on mathoverflow?

Thanks,

David ]]>

http://math.stackexchange.com/questions/167498/is-this-function-decreasing-on-0-1

So far it received 17 upvotes but remains unanswered. I was thinking of asking it on mathoverflow too. Would it be acceptable? Perhaps it will result in interesting references and comments...

Thank you,

Malik ]]>

I do feel, however, that I am unsatisfied by these answers. On the other hand, I am also not sure what answers I am looking for... I was wondering whether or not it would seem reasonable to post this into MO (despite not knowing what answer I am looking for)

]]>Clearly the question is somewhere on the border of acceptable questions.

But hopefully can generate goods answers.

I am against closing such questions.

There is opinion that it should be closed:

"HW: On further consideration, let me also add that this question is really absurdly broad. Group theory is an enormous subject; at least a little motivation would be helpful. Does the OP want to start research in the area, or is he/she teaching a course? In either case, what's his/her background? I'm voting to close. – HW "

PS

Obviously should be done "CW". ]]>

I may have misread the question, but it seems to me like something known but non-trivial. That is to say, I think I know the answer, and in the discrete case I do know the answer, but only because this is a calculation I've seen in a few papers. On the other hand, rereading the OP's comment, it is not clear if the question I am thinking of is the question he or she is thinking of.

Anyway, would be interested to hear other people's thoughts on this one.

]]>If it is acceptable, I'll post the problem in MO when the bounty expires in MSE.

]]>For me, it was mostly the hit-and-run approach of the OP. There is a fine comment somewhere on Meta by Bill Johnson, I do not know how to find it, something about "It is inconceivable to people of my generation that someone write a question and then just go away for hours. If you don't have the time, don't ask the question."

edit: three votes to reopen as of 1:51 pm Pacific. ]]>

http://math.stackexchange.com/q/148710/2987 ]]>

I was thinking about posing to mathoverflow a question designed to collect the various typesetting conventions that lead to more professional looking LaTeX output, given that most mathematicians (such as myself) did not have any formal training in typesetting. The type of conventions I had in mind were things like the following:

* Use \langle, \rangle instead of <,> for inner products

* use \ll, \gg instead of <<, >>

* use \lvert, \rvert for absolute values, and \lVert, \rVert for norms

* use \mid instead of | for the "divides" symbol

* Use \operatorname for various operators such as Hom, End, etc.

* Use \colon when declaring domain and range of functions, e.g. f \colon X \to Y

* Use \dots instead of \cdots, \ldots for most ranges

* Use -- instead of - for page ranges and for joint authors (e.g. Cauchy--Schwarz)

* etc.

Also I wanted to collect not only the conventions themselves, but the justifications for them. For some of the conventions above, for instance, I can see why they are preferable to the alternatives, but for others all I know is that professional typesetters seem to all agree on the rule. But I am not sure whether this question is actually appropriate for MathOverflow as it is (a) not a mathematical question, and (b) would be a big list or community wiki rather than a question with a definite answer (unless, perhaps, someone provides a link to a style guide that has all of these sorts of things, but I have not been able to find a definitive such guide in my own searches). So I was wondering what other users felt about such a question. ]]>

One possibility is that I do not mention the paper, but then it may be difficult to appropriately "motivate" the question.

An input would be appreciated,

- Micah ]]>

These are all questions of interest to many research mathematicians. (Of course, most things of interest are also of interest to research mathematicians, but these are of interest to research mathematicians as a particular part of being a research mathematician.) These seem to fall into a grey area in the FAQ---the FAQ says "MathOverflow's primary goal is for users to ask and answer research level math questions", which doesn't include these, but also includes various categories of explicitly forbidden questions, none of which include these.

Perhaps there's simply been a decision about how to handle these questions (though if so, I'd suggest that the FAQ be updated to include that, since the comment threads don't reflect an existing consensus on the issue). But if not, perhaps there should be.

These questions seem to have been more accepted in the earlier days of MO, and of late there seems to have been a turn against them. I admit that my motivation for bringing this up is that I'd like to see such questions explicitly allowed when they fit other criteria for being good questions. (Given the danger for some such questions devolving into discussions, or being stalking horses for starting a discussion, they might appropriately be scrutinized more closely than clearly math questions.) But I think such questions are beneficial to many users of the site (in as much as most users are research mathematicians), and (when appropriately tailored to be primarily about mathematics, rather than academia in general) good for the site (in that they may attract mathematicians in subfields underrepresented on the site, who might then start asking questions about their areas).

That said, if the conclusion is that such questions not be allowed at all, I think we'd still be better off reaching a decision on that, instead of rehashing the dispute every time someone asks such a question. ]]>

I was hoping to prefix it with:

I for one would definitely like to read Andrew Wiles' one. The fact that he was in tears in a youtube video upon dawn of illumination really moved me and also I would like to read the "AUTO"biography of Perelman. Some more contenders would Szemerdi, Milnor or Sir Atiyah(among the Abel prize winners)...

Please advice! ]]>

My impression based on earlier responses is (1) there is no appropriate way to mention a publisher's promotion. Fair enough. I probably should have realized that. (2) In the future, if I'm not sure whether something will be considered appropriate, the place to ask is here, not there. (3) Without the bit about the discount, the question might have been tolerated as "barely appropriate" but might also not have, as it is not a "specific and appropriately focused research question." (4) Even without the bit about the discount, the question probably would have been received as "unacceptable self-promotion" and a better approach would be along the lines suggested in Gerhard Paseman's first comment (which is the model for the current version).

Is this about right?

I admit that my motivation for posting to MathOverflow about this is two-fold. On the one hand, I do want to find out about and write corrections for all of the errors that people have found. And, on the other hand I want to help people who have the book and think they may have found an error in it find the errata website. I guess that's still a bit self-promotion-ish, but it seems like it would have some value to a segment of the MathOverflow community. (I was motivated by http://mathoverflow.net/questions/84451/moderate-growth-and-maass-raising-operators). So I would like to find out if there is a right way to go about it, and go about it in that way if there is.

On a somewhat related note, is there are right way and a wrong way to reference one's own works in answers? For example, for this answer http://mathoverflow.net/questions/89761/restriction-of-irreducible-representations/89776#89776 there are lots of good references, but for our book, I can tell you exact page numbers... if you have access to our book. So, was that helpful, or was it gauche?

I appreciate any guidance. ]]>

http://mathoverflow.net/questions/92337/ts2-and-s2-x-r2-not-homeomorphic-as-topological-spaces-closed

asks whether the tangent bundle to the two-sphere and the trivial plane-bundle over the two-sphere have homeomorphic total spaces. The question's been closed, but it seems to me to be a perfectly fine MO-level question (though, of course, I might be overlooking something).

I'd vote to reopen it except for one thing: The poster says he's trying to prove that the two spaces are not homeomorphic, as opposed to asking *whether* they are homeomorphic. This suggests that he already knows the answer, which in turn suggest it' s a homework problem.

So I guess my twin questions are: 1) Am I wrong in thinking this question is a perfectly good MO-level question? And 2) Am I wrong in thinking that the wording suggests homework and that this is sufficient not to reopen it? ]]>

Suggestions are welcome, especially why the question does not add up.

]]>I voted to close the question because it seemed a little ridiculous to me. No journal of any repute whatsoever would not accept submissions of papers that were posted to the arXiv. It would be impossible for them to publish anything!

What do other people think? ]]>

It seems to me that this question is a duplicate of the Meta.MO thread "Where to keep track of MathOverflow success stories," so I would advocate for closure of this question. Also, the FAQ clearly states that "MO is not for questions about MO." Joel commented that having this question on MO rather than Meta would make it periodically pop up to the front-page whenever someone adds to it, so the whole community would be aware of another MO success story. That's true, but because the Meta thread is already sticky you can always just check meta and see when that thread was last modified. So I don't see the benefit of having what should be a Meta question on the main site. I agree with quid that it sets a bad precedent. ]]>

Some exaples (to be added later):

http://math.berkeley.edu/~gbergman/grad.hndts/ has several "developed as a series of exercises" writings.

http://math.berkeley.edu/~gbergman/grad.hndts/nonEucPID.ps "A principal ideal domain that is not Euclidean, developed as a series of exercises."

http://math.berkeley.edu/~gbergman/grad.hndts/quad.recip.ps "Quadratic reciprocity, developed from the theory of finite fields as a series of exercises."

(quotations taken from the webpage)

(Thanks to Arturo's comment at: http://math.stackexchange.com/questions/108766/luroths-theorem)

Should each of these be in a separate answer, even if they are at the same webpage? or should people post the first URL, which points to them (as a "resource")? I think the first choice is better.

I also know about some wonderful exercises (in Spanish), which guide the reader through some of the equivalences of AC, while introducing concepts such as towers and the principle of recursive definition. (Based, I think, on Munkre's "Topology")

At the beginning of times, MO was open to this kind of CW, big-list questions. Is it still appropriate?

Is "Guided exercises" the right wording in English? Some searching seems to suggest "Guided exercises" is too general and includes those meant to review a recently learned topic, which is not what I mean. In Spanish, "Ejercicios guiados" would be the fine. ]]>

My instinct is the same as Theo's; namely, that once the question is stripped to its essence, it is just asking for some trivial linear algebra. But since no one else has voted to close, I thought I'd bring it up here to see what other people thought before I did so. ]]>

There are neither down votes nor comments and not even closed ?

What will be the fate of this question ? Please feel free to criticize it . ]]>

Note that similar issues were discussed in this thread.

My opinion is that this question is fine, for roughly the same reasons as I gave in the previous thread.

]]>http://mathoverflow.net/questions/87491/definition-of-hessian-with-respect-to-connection

but I do consider this to be too elementary for MO. Am I wrong? ]]>

Thoughts?

]]>http://mathoverflow.net/questions/9921/equality-of-elements-in-localization-via-universal-property-unsolved

was not clear enough; Tom Leinster wrote a long comment as an answer, not really answering my question. Then I cast a bounty and since nobody else replied, the answer by Tom Leinster was accepted automatically. Of course this means that other readers don't pay any attention anymore to this question.

Today the question is still unsolved. Is it appropriate to start a new thread with basically the same question and some more explanation? What do you think? ]]>

If it is acceptable I will refine or expand it further.

Thank you. ]]>

http://math.stackexchange.com/questions/101456/does-the-concept-of-predicativity-need-to-be-formalized-to-go-beyond-feferman-sc

Althoughy I am planning on a bounty, I believe it'd generate more interest here. ]]>

I searched for questions which had answers and were deleted by the owner. I found 91 such cases, but I don't know what to do with them. I guess I'll post them here so that 10k+ rep users can have a look at them and vote to undelete them if appropriate (in the next comment because of the character limit). Note that 10k+ rep users can also see what questions have the most undelete votes by looking at the delete tab of the tools menu.

I welcome any ideas about how to better deal with this issue. Ultimately, humans have to look at the deleted questions to decide if they're worth undeleting, but perhaps there are better criteria I could use to narrow down the search space. Maybe I should even be widening the search space to include questions that don't have any answers, but do have "substantive-looking" comments. How would I programmatically look for such things?

Also, is there a good way to filter out questions that (somebody has verified) really should stay deleted so they don't add noise to the sample every time I refresh the list?

]]>1+5 3+5

1+7 3+7 5+7

1+11 3+11 5+11 …

1+13 3+13 5+13 …

1+17 3+17 5+17 …

. . . …

. . . …

. . . …................... 79+83

1+89 3+89 5+89 …....79+83 83+89

1+97 3+97 5+97 …... 79+97 83+97 89+97

The columns of the map contain numbers of presentations in the following sequences:

24, 23, 22, … 3, 2, 1.

Because of this structure of sequences we can calculate the number of presentations within the quantity 10^2 with the formula (f+1)f/2 where f is the number of odd primes>1. And so we have: Number of presentations=(24+1)24/2=300 within 10^2. Because we want to exclude all presentations that are greater than 10^2, for the time being we will accept that half of the number of presentations is ≤100, so Number of presentations 10^2=300/2=150.

The number of even numbers contained in the quantity 10^2, excluding 2, is 49. So for each even number contained in 10^2 we obtain almost three presentations. This does not mean that each even number has three presentations. From the prime number theorem we have 10^n/ln10^n≈f primes so

(f+1)f/2≈10^2n/2(ln(10^n))^2

If n=2 then 10^4/2 (ln100)^2≈236. This result is a close approximation of the actual number of presentations within 10^2, which is 300. The number of even numbers contained in the quantity 10^n, excluding 2, is obtained: Even numbers=(10^n/2)-1 and so we obtain

[10^2n/2[ln(10^n)^2]/[((10^n)/2)-1]=10^2n/[2(ln(10^n)^2)(10^n-2)]

Because we have accepted only half of total presentations are equal or less than 10^n the last result is written 10^2n/[2(ln(10^n))^2(10^n-2)]. The actual number of presentations in the quantity 10^2 whose distinct sums exceed 10^2 is 104 and the actual ratio is (300-104)/49=4 which means within the quantity 10^2 we have 4 presentations for each even number. From the last relation we obtain 10^4/[2((ln100)^2)98]≈2.4 which means 2.4 presentations within 10^2 for each even number. The numerical value of the ratio 10^2n/[2(ln(10^n)^2)(10^n-2)] tends to infinity as n tends to infinity.

All even numbers greater than two can be written as 2m+2 and when m takes values from one to infinity all even numbers are presented. Also the sum of two prime numbers is written as 2k+2. If we prove k takes all values m takes then the Goldbach conjecture is proved.

When p_1=4x+1 and p_2=4x_1+1 then m=[(2x+1)^2+(2x_1+1)^2-2]/2-2x^2-2(x_1)^2

When p_1=4x+1 and p_2=4x_1+3 then m=[(2x+1)^2-(2x_1+1)^2-2]/2+(2x+2)^2-2(x_1)^2

When p_1=4x+3 and p_2=4x_1+3 then m=(2x+2)^2/2+(2x_1+2)^2/2-[(2x+1)^2+(2x_1+1)^2-2]/2.

These three cases cover all the sums of prime numbers. That means k takes as many values as the number of presentations in a given quantity 10^n.

So (k number of values)/(m number of values) tends to infinity as n tends to infinity.

From the above we can show by shear calculation m takes all values k takes from 1 to 100 and from 100 to 1,000,000 and from 10^6 to 10^9 and because the relation of k to m is asymptotic, m will take all values k takes.

My question is, is this form of mathematical induction correct or incorrect? If incorrect, what are the logical arguments to support such an opinion?

If this question is not acceptable as it is, please suggest improvements. ]]>

(This should not be counted as a vote for closure as I don't have the necessary rep.) ]]>

So for me, this doesn't automatically fall into the class of questions which do not admit good answers, although I admit that as phrased it could easily invite a bunch of not very good ones...

]]>http://math.stackexchange.com/questions/98604/topological-space-as-an-infty-1-category

http://math.stackexchange.com/questions/97699/evaluation-and-coevaluation-maps-of-a-tqft

http://math.stackexchange.com/questions/91867/fields-in-stable-homotopy-theory

These are probably really basic questions for current research homotopy-theorists, but it seems that the people that work on such things are pretty much only on MO. Where do I draw the line?

Thanks! ]]>

http://mathoverflow.net/questions/85251/non-computational-software-useful-to-mathematicians

seems to be considered accpetable (being open since a day, with only two votes, one by me, to close so far).

As I pointed out in a comment, the way it is phrased would even admit anwsers like 'a webbrowser'. Now, I am willing to admit that this is a bit of a silly overinterpretation, and OP argues that the examples given should make the intent clear. However, in my opinion, this is not as much of an overinterpretation. Version controls systems are mentioned and an anwer is some syncronisation tool. IMO these are essentially as standard programs, though perhaps less wide spread, as a text editor or a browser.

Furthermore, the notion of software/programm underlying this question is very broad (including such things as OEIS, which IMO is mainly a collection of data/a database which most people I guess access via some web-frontend). So is any useful mathdatabase ontopic or is the criterion that it does have a nice frontend? Say, the Cremona's tables of EC are useful, there are handy ways to access them, so if OEIS is ontopic I guess this would be too.

Or, LaTeX is mentioned as example; I do not want to do some hairsplitting whether LaTeX is a programm, but what I find starnge is that then 'beamer' (a documentclass for LaTeX) is mentioned in addition. So, amsart is also useful, I guess this would count as silly answer; but I guess if I named some documentclasses for creating posters this might count.

Should all this be collected in this *one* question?

In particular, some things are really duplications of existing questions. Which I pointed out, yet OP did not follow up.

Well, in brief, to me this question is an instant close; 'tools' question are always a bit difficult, but if it is as unfocused as this one... Apparently it is not. What am I missing?

]]>I have been wondering recently what other practices other mathematicians follow when deciding whether/how much to talk about work in progress. I have been considering asking a soft-question on this topic, and I would like to ask (a) whether the community feels that such a question would be appropriate for this site, and (b) if so, how could this question best be phrased so as to be useful to the most people (and also to avoid being closed)?

Tentative wording for the question:

Title: Presenting work in progress

At some point in the evolution of a project, one has to decide when to start talking about it in seminars and at conferences. I am interested in hearing about how other mathematicians make this decision. Of course the decision to give a talk on work in progress may depend on the state of the project, on the venue and the audience, and on other factors.

My specific questions are:

(1) At what stage of a project do you consider it to be ready to talk about?

(2) How does the venue (departmental seminar/colloquium/conference/other) affect your decision?

(3) What other factors do you consider when deciding whether to talk about work in progress?

--------------------------------------

I'd welcome any suggestions for improvement. ]]>

If this, in its present form, is not a good MO question, how can I improve it? ]]>

What everybody must/should know achievements in 2010 and around

Quick facts: Closed yesterday without much discussion. Now 3 votes to reopen.

Personal opinion: On the minus side it is really subjective and possibly argumentative. IMO, in case it is reopened people should at least please refrain from expressing their disagreement with nominations verbally. On the plus side it could be interesting.

]]>As I say in a comment: you can consider categories whose objects arise in analysis and whose morphisms have some flavour of continuity. Hence, category theory can be used in analysis. Fin. Or as Paul Siegel says

What I can say is that many interesting and nontrivial categories do arise in certain parts of functional analysis and it is useful to understand the structure of these categories

So I wanted to start a thread where people could try and convince me otherwise.

]]>k_1m^1+k_0=k_2, k_2m^2+k_1=k_3, k_n-1m^(n-1)+k_n-2=k_n.

For m any non-zero positive integer and a_0=1, a_1=0, k_0=0, k_1=1 I was able to predict the result of k_n/a_n. For any other pair of values a_0≠a_1 and k_0≠k_1 the result is unpredictable. Does anyone know if it is possible to predict the numerical value of the ratio k_n/a_n for such pairs?

If the question is not acceptable, how can I improve it? ]]>

It is my opinion that for such a high-profile question it might be better to arive at a consensus or a solution via discussion rather than to send it through various open/close cycles.

My opinion is: It was good it was open for a long time, but now I would prefer if it was/stayed closed.

Here are the reasons.

It seems to me the software is not really made to deal with question with that many answers. I am often on a slow connection with poor harware, it is really difficult to handle this and related questions (on technical grounds).

There is an ever growing risk of duplicate answers and almost duplicates. Which is particularly large as there are only limited ways to structure and or search the answers (for the latter one could use google in a targeted way as a work around, but still); cf. the first point.

Finally, and semi-seriously, if a false belief was not added over that long a time it can't be that common.

Afterthought: In case some should really want to keep it open, one solution I could imagine is that one or a group of these users does for this question what Gil Kalai did/does for Fundamental Examples that is make it so that one can get an overview over the already given answers.

]]>Of course, the interpretation of a koan can be varied. Perhaps it will help in a taxonomy of paradoxes?

http://en.wikipedia.org/wiki/List_of_paradoxes#Mathematics

Some examples not on list:

-Is hypergame a hyperghame?

-Quining (computing)

-Can you hear the shape of the drum? (not a paradox but has a koan flavor)

It can a simple question as:

Why is it that any number raised to the power zero is equal to 1 and not zero ?

http://www.calculatoredge.com/math/mathlogic/logicans4.htm

Related:

http://en.wikipedia.org/wiki/Hacker_koan ]]>

k_1m^1+k_0=k_2 k_2m^2+k_1=k_3 k_n-1m^(n-1)+k_n-2=k_n.

For m any non-zero positive integer and a_0=1, a_1=0, k_0=0, k_1=1 I was able to predict the result of k_n/a_n. For any other pair of values a_0≠a_1 and k_0≠k_1 the result is unpredictable. Does anyone know if it is possible to predict the numerical value of the ratio k_n/a_n for such pairs? ]]>

What is the main goal of a paper really?

Quick facts: closed couple days ago. Now edited with the idea of reopening. 3 votes to reopen.

Personal opinion: I voted to close the original version; my opinion stays essentially unchanged by the edit.

]]>http://mathoverflow.net/questions/82499/what-is-the-step-by-step-procedure-for-classifying-a-new-data-point-with-an-rbf-k

one of which is mine. ]]>

It is currently closed but has a vote to reopen, and some dicussion is developping, thus a meta thread.

Personal comments:

I am not among the voters to close, but I can perfectly understand why one would vote to close this. Depending on various unspecified circumstances any among the listed four options could be advisible. So, this is not a 'real question'. (As documented, one can still answer something useful of the form, if this than do that, but still I do not think this is a suitable MO question.)

That there are some questions on MO that are similar, as was pointed out, is not much or any reason to not close this one.

]]>Note that most of the votes to close were submitted before the question was edited, when it made less sense. I think it's an acceptable question now, and since I have spent some time myself puzzling over the Getzler--Kapranov article, I think I could submit an OK answer. (Although maybe not in the next few days which will be very hectic.) ]]>