Formulae for the Number of Partitions of n into at most m parts(Using the Quasi-Polynomial Ansatz)

Generally, there is no reason for posters to feel stigmatized when their questions are closed.

You may claim that there's "no reason" to feel stigmatized, but remember that all people feel a little embarrassed when they are publicly shamed, no matter how trivial the transgression.

The only effect of closing a question is to prevent further answers from being added. There are many legitimate reasons to do that. (Albeit, the stock reasons that the software provides are not always self-explanatory.) Generally, there is no reason for posters to feel stigmatized when their questions are closed. Moreover, closing should never be used in a punitive manner -- such inappropriate actions will be notoced by the moderators who will then take appropriate measures. (Downvotes are the appropriate way to express disapproval of a question or answer.)

On the other hand, deletion is a much more drastic measure that should be used with great care. Worse still is deletion by way of flagging as spam/offensive, which comes with an additional 100 pt penalty to the poster. Needless to say that this should be reserved for extreme cases.

I (third?) the thanks for you sending email directly to DZ, which, in light of the resolution it brought, is the most productive contribution anyone has made to this thread. I'm also very grateful to Nilima for the original suggestion.

Gerald Edgar, it might be a bit ironic, but if you read the meta thread and study the timeline you might notice that it is you who is to a considerable extent responsible for the reopening. Since I consider the final turn of the discussion, for various reasons (whether the question is open or not is a detail), as quite fortunate, I am (at least in retrospect) also grateful for your contribution.

The precedence-issue is certainly something to keep in mind, but then I think one also should not overdramatize this risk. For one thing, as François Dorais mentioned a while ago: C'est l'exception qui confirme la règle.

Looking back at the discussion I can see points where I could and should have been less confrontational. I appologize to those negatively affected by this.

I think the heated nature of this conversation has given you a too negative impression of how the process works. Usually most questions are closed with justified reasons (by the way, to vote to close you only need 3K). In addition, anyone can open a meta thread to keep a question open (a very recent example is this one. Finally, deletion is quite rare, I have never voted to delete one, and even in this case most people disagreed with deletion.

After all, the question is now open, even though many people (myself included) think it is not an appropriate use of MO (Of course, as Professor Kalai rightly pointed out, it is a subjective opinion).

The article he will write might asymetrically hurt MO's reputation more than say 100 open questions with negative votes where cranks give clearly wrong proofs of famous conjectures.

The strength of MO lies in its ability to answer (not too difficult) technical questions reasonably well, since getting stuck is such a frequent experience in our life. If it keeps doing that job, it will be quite hard for an article to hurt its reputation, even if it is written by someone of Professor Zeilberger's stature and reputation in the mathematical community.

In addition you can't technically stop a motivated crank because at least of (open) proxies and one time accounts.

is rather besides the point. In regards to crank the moderation of the community should aim at effectively stop not completely stop. If it means the moderators having to play whack-a-mole for a few weeks, so be it.

(This also reminds me of an after-dinner chat at a workshop a few years ago, where from the shared experiences it was revealed that mathematicians are often automatically washed from serving jury duty because prosecutors know that mathematicians and physicists tend to confuse beyond reasonable doubt with absolute certainty and 5-sigma level of confidence respectively.)

state of the art: the current stage of development of a practical or technological subject; freq. (esp. in attrib. use) implying the use of the latest techniques in a product or activity.

I guess Noah is correct, though the phrase is frequently used to mean something stronger.

Anyway, I don't think this question if reopened will attract much more attention. It already has an accepted answer, so it won't pop up to the main page very often.

Also, I think that Noah's edit reads a bit much into Zeilberger's explanation: there is nothing about the "state of the art" in what Zeilberger wrote, it looks like he only wanted to know whether computing p_60(10^100) was doable using known methods.

Perhaps I was mistaken, but because of Nilima's statement

"One should ask them outright, if their thoughts are of interest. No, queries on meta don't translate to asking outright - it is conceivable that he does not wish to get embroiled in this rather public discussion."

I assumed that the word "outright" (as used by Nilima) meant a direct query by email, phone, or in person. Perhaps you thought the bit "queries on meta" was meant to be interpreted as distinct from queries on main MO, and I think that's a reasonable interpretation, but probably not what Nilima meant (was it?). Probably it's not worth worrying about too much.

I think this thread has served some really useful purpose. Next time we are in this situation this one can be used to remind us that: 1) Some preemptive editing of controversial questions could be really helpful; 2) Most of the drama could be our own creation; 3) A simple solution like what Will did could save a lot of troubles.

Can I say one more thing: Storkle, thanks for your kind words, they made my day!

I appreciate that there is an acknowledgment, if indirect. I offer my services to Prof. Zeilberger to rewrite any question he wishes to present in a form suitable for MathOverflow.

Gerhard Paseman, 2011.08.11

The question that was meant to be asked was: "I have a new technique for computing X, and I'd like to know how it compares to known techniques. How fast is the current state of the art." Is there any objection to my editing the question by inserting something saying roughly that? (I wouldn't remove any of the current content.)

Well, Storkle, you're asking me outright right here, aren't you? The answer is: yes. I assume he read the comments. He is under no compunction to respond (just as no one is compelled to respond to email), but since there were repeated requests in the beginning, I think it would have been a nice gesture to do so. Don't you?

Although I've had very brief email contact with him (in response to one of his Opinions, which he gracefully acknowledged in an addendum), I don't feel I know him well enough to email about anything that's taken place here.

I agree. There seems to be a culture clash here that is causing some confusion: some regular users are upset that DZ has been somewhat opaque about his motivation for asking and does not respond to queries publicly here or on the main site, while others (you and me, for example) are dismayed by the resulting complaints and uncharitable speculation about his motives, as we do not see that DZ has any responsibility to respond to questions posed on public threads.

I also agree with GK's perception that reactions to this question are based as much on DZ's other opinions (and Opinions) as the question itself.

one should drop him a note to clarify what he means. Second-guessing a colleague's thoughts is not productive. One should ask them outright

He was asked outright. Very early on. I wish he had responded, before the discussion had gone so far.

In the interest of making a positive suggestion: Gil, as a friend of DZ, would you be able to find out what his purpose was in posting? I think you tried to ask something similar in the comments; would he be more responsive in email do you think?

Would we speak to any colleague like this, in person, face-to-face?

One should ask them outright, if their thoughts are of interest.

DZ was asked in the comments, and he didn't respond. I don't think the analogy to face-to-face conversation holds water: in a face-to-face conversation, my first response would have been "why do you want to know? Aren't you quite familiar with techniques for solving such problems?" and none of this would have happened.

I agree that this discussion could have been more professional, and I bear part of the blame. I apologize for that. I was trying to respond to what seemed to be unprofessional behavior on DZ's part, veiled in such a way that people not familiar with the subject (and with DZ's own credentials in that subject) would not see that there was an issue. Perhaps I should have chosen my wording more carefully.

If I can turn the conversation into "amusing" mode, then I am happy!

More seriously, perhaps my point was simply: questions like these are unlikely to make the site more harmonious (largely due to our own shortcomings), so we should avoid them.

"...the drama that follows was largely our own creation." Agreed. I don't see that DZ has done anything remotely resembling trolling MO---to me, someone who is not involved at all in the controversy over this question, all the heat is coming from the discussion of whether the question is appropriate for MO, and mostly from those against. In this context I found your previous comment "This thread presents (to me) a convincing reason that we should not encourage questions like this." quite amusing!

Having said that, I don't think we should delete the question. Although many of us, including me, believe that this question is not appropriate for MO, the drama that follows was largely our own creation. So it is a bit unfair to delete the original question. Eventually everyone will calm down, and this matter does not really deserves that much attention, and I hope we will all come to that conclusion.

@quid: to be fair, I think both sides overreact here. I agree that some of the comments following Joro's post on page 2 were unnecessarily harsh. Probably things blew up because people have been quietly discomforted by this discussion.

How does this saying go: if you point a finger at somebody, four point back at you.

I generally agree with Gil's comments on meta, and I've mostly stayed out of this discussion because I figured there was too high a chance of Gil being right and me being wrong. But I'm quite baffled about why you're still defending DZ's actions. DZ's behavior seems to me to be clear abuse of the site and disrespectful of everyone using it.

If he would acknowledge requests about how he presents himself on MathOverflow (even if he were to say explicitly "I want to do it my way."), I might change my feelings about how he might participate. For now, to me he is as likely as not to acknowledge (much less respond) to any request put to him on MathOverflow.

Gerhard "Responds To Responsibility of Responding" Paseman, 2011.08.10

The question you mention as written is, yes, sort-off a career question. However, I cannot help but feel that the main point was to draw attention to the thesis itself. The link to it was posted as an answer not even only a comment despite a explicty request beforehand not do so.

And there is also http://mathoverflow.net/questions/71979/flat-lie-algebras where the last two lines (the link to the authors work) at least do not seem inevitable for the question. And, if the questioner has a paper on arXiv since years, what's the point of the other question? Why not ask the coauthor or other people involved in the thesis?

Perhaps there are good reasons for this, and even if not, as said, I do not see a big problem.

I agree that case is borderline. Here are some differences I see: first, he didn't ask a question of the form "can you solve this problem: 'prove that...' " which I have seen posted by others, with the implication that OP knows how to solve it and is offering it up as a challenge -- this type of thing indeed gets closed very quickly. The question by amine was more a piece of asking for career advice, with little reference to the actual content of his thesis. As 'advertisement', I think it's pretty mild and unassuming.

Second, amine seems actually responsive to the issues that people have to some of his posts, both the PhD assessment one and the cross-posting one. I suspect this is what has irked a lot of people here: that DZ has refused to engage with anyone on issues of the social norms of this site and concerns about the form of the question. I believe, for reasons given by Noah, that there are real concerns here, and it's not hard to see why such resolute refusal to engage comes across as, frankly, pretty rude, or at least antisocial. (BTW: I've had brief email contact with DZ in the past about other things, and there he didn't come across as rude at all; in fact, he was very polite. So I'm trying not to draw any absolute conclusions here.)

With regard to "it is hard to imagine for me that this would be discussed if the question would have been asked by sombody not well-known (with whose views some people here seem to have a problem)." Yes, precisely. I'd bet a good sum of money that such a "question" by someone not so well-known would have been shut down, and perhaps deleted, with dispatch and with little to no discussion. The fact we are discussing this case at length actually betokens a measure of professional respect for DZ. (But I think I'm repeating myself here.)

It's very important that MO not become a place for people to advertise their own results. (Ask some question, get attention, and then say "if you like this question you should read my new preprint which has the answer!")

I'm not sure if deleting is the right way to make that point though. It might be, but another option would be adding a section to the FAQ about not advertising (both by asking questions you know the answer to, and by bringing up your own work in situations where it's not relevant), and then editing DZ's question with a link to that FAQ entry.

To put it mildly, this seems excessive to me! And, it is hard to imagine for me that this would be discussed if the question would have been asked by sombody not well-known (with whose views some people here seem to have a problem).

I would invite everybody who thinks about deleting this question, first to check the list of question sorted by votes and have a look at the end what type of things stay undeleted on this site, and second, and more importantly, to read the question and its answers/comments and to see whether some interesting content accumulated or not.

ADDED: One more point to note, Doron Zeilberger was now (actually already to days ago, not sure why just now this discussions needs to restart) answering in a comment a question asked in a comment by Gil Kalai. To me this makes all insinuations about self-promotion even more strange than they would be no matter what.

Using the Maple package PARTITIONS, soon to be posted in a joint work with Andrew Sills, typing restart: read PARTITIONS: t0:=time():qmn(60,10^10000): time()-t0; gave 3.121 seconds. If you want to actually see the 589838-digit integer, ending in 71918678375357 it took 3.932 seconds.

This appears improvement to his other comment:

Shalosh can do it in two seconds once it found the quasi-polynomial expression for p_60(n), and it found it in 400 seconds. So Shalosh does first symbol-crunching then number-crunching. -Doron Z.

Note that the first timing is for 10^10000 while the OQ is for 10^100.

Thank you for the example. I am not sure it is comparable to our situation. As far as I know, question of the type "I do not understand a point in this paper/book, please explain" is widely accepted on MO. Also, the timing/topic of the question may contribute to how fast it attracts enough people to vote.

But perhaps Noah is right, this debate may no longer be productive.

Best regards,

EDIT: In light of Professor Kalai new evidences, I would like to withdraw the word "faster" from my original post. Perhaps a better choice would be "closed without much opposition". Please accept my apology.

Long

If you would kindly suggest a more respectful way to phrase the term "..it seems to me that the most charitable interpretation of the question is..", I would gladly change it. It was my honest impression after reading the thread, but frequently I find it difficult to express myself well in English. I used the word "charitable" since it has been used in the thread. Please help me here!

As for the other points, I respectfully disagree (but would be happy to be proven wrong).

Best regards,

Long

I am actively in favor of "bending the rules" for new users that are mathematicians (well-known or not). [And, although Doron Zeilberger apparently once answered a question more than a year ago, I think he is in essence a new user.]

For example, one main criticism of the question was that the questioner (seems to) know the answer. However, where is it documented that one should not know/must not know an answer to a question one asks here?

In principle, one could well imagine a Q&A site where people also (or even mainly) challenge each other with carefully selected questions. This site is not like this, and I do not wish to suggest any change, but how does one know this if one just arrived? (I just had a glance through the FAQs and did not see it anywhere, but might have overlooked it yet at least it seems to me it is not prominently written anywhere.)

Secondary point and subjective: overall, in agreement with Gil Kalai, I believe Doron Zeilberger had no advantage from his off-line reputation here; rather to the contrary.

Reading the thread, it seems to me that the most charitable interpretation of the question is the OP wanted to demonstrate the power of his method over the usual approach. While the new approach itself might be very interesting mathematically, I am not sure we should encourage such things on MO. Most of us can ask a few questions which no one can answer better than ourselves, so open a door to such questions is not a good idea, in my opinion.

To bend the rules for a well-known expert is not right, for reasons others have pointed out. But it is not even beneficial. By doing so we may actually discomfort many quiet observers, among them might be a) other top experts, b) people who will become top experts in the future.

There are many brilliant mathematicians on MO whose behavior has always been respectful and professional. I (and probably many young people) learned a lot from how they carry themselves as well as the actual mathematics. Fortunately for us, there seem to be many of them around.

And, thanks for the link to the Colman paper!

I do agree with you that it would be nice if DZ had entered the discussion (and I still hope he will). But I wouldn't necessarily attribute this to arrogance or anything like that; he may well have his reasons, based on long past experience. I think it is fair to say that his general point of view is dissenting from the "mainstream" mathematical culture. And so I would imagine that he "chooses his battles" carefully. This may be one of those times where he decides to spend his time and energy elsewhere.

First I don't remember any such case. Any examples?

It might take me a while to dig up an example, since I've forgotten specifics. (I'm not sure I'll get around to it, because I'm busy with other stuff.)

Suppose that somebody had asked a question: what is the best known upper bound for the number of groups with n elements. And then after people will mention what is known he will mention in a comment an even better bound that he discovered.

That would be completely appropriate. I would have been much happier had Zeilberger approached the matter in something like that manner.

Although it was claimed that DZ's question had been closed if he was not a well known mathematicians many of the arguments in this thread goes the other direction and represents bias against known mathematician.

I don't think so. I think it would be great if DZ became active here. I think Qiaochu in his response has expressed some of what I find problematic about the question itself.

Second, I am not sure it is an improper way to use MO. Suppose that somebody had asked a question: what is the best known upper bound for the number of groups with n elements. And then after people will mention what is known he will mention in a comment an even better bound that he discovered. I would see nothing wrong with it, in fact it will be quite welcome. Suppose you have reasons to believe that he actually is quite familiar with the known upper bounds but really wanted to announce his new result. Frankly, I would see nothing wrong with it either. (And always he can be surprised by a result he did not know.)

This would be more than fine if, in the end, the OP explained how she obtained her own answer (in a way that someone not familiar with the technique would be able to follow), which Zeilberger has thus far not done.

suppose you disagree with me and do think that there is something worng with such a behavior and vote to close the question based on your speculation on what the OP knows which is based on his mathematical reputation. This would be inappropriate since it discriminates against known mathematicians.

I think "discrimination" is the wrong word here. If this question had been asked by a random user, I would have wondered several things: why is the user offering a cash prize? Does the user know the standard techniques for solving such problems? If not, why isn't the user asking about those techniques? If it came out in the comments that the OP was unfamiliar with standard techniques, somebody would have posted an answer explaining them, and everything would be fine.

I can skip that step with Zeilberger because I am positive he is aware of the standard techniques (as evidenced by his explanation of how Shalosh solved the problem). That's not discrimination, except insofar as it's the use of extra information in a special case that isn't available in the general case. Based on what I know about Zeilberger, I can guess at his actual motivation for posting the problem, and that guess is problematic.

Of course it can be argued that we should give new users, especially prominent new users, the benefit of the doubt. I suppose that's fine. At the beginning of this thread I was hazarding a guess, not arguing that we should definitely be making decisions based on that guess.

Maybe I should bow out now -- I've done enough talking. Myself, I would have preferred your suggested rephrasing, or something along those lines [it could still be fun!].

a. I was informed, or rather reminded, how to compute this fairly efficiently (joro's solution)

b. I was informed that there is a different way (Zeilberger's solution), the details of which are not yet clear to me, but perhaps they will appear eventually on the site, or I could follow up on it elsewhere [perhaps not yet if the thing should be very new, but eventually it will be on his website, I suppose].

The fun part is that this unfolded in a playful way. Some strangely particular request...noone knows what the purpose is...but one could be essentially sure there is something 'hidden' and...eventually it was (partly) revealed.

Now, the fun part is fun IMO if this happens (very) rarely. If every other question would be of this form I would certainly find it quite annoying; and I can even understand that one does never find this type of thing funny, but still I do (sometimes).

The question was: Can you/one compute this (fast/efficiently)?

And, an answer or answers to this question can even be useful to somebody who knows a method or even methods to do it him/herself. Because others could have different ideas; or even just carry out the same idea more efficiently.

One possibe rephrasing could be (I am not sure if this was the intention): I have a (new/not widely known) method to compute p_60(n). [Explanation or not.] I would be interested in knowing how it compares to known/standard methods. Thus, I would be interested in the time it takes others to compute p_60(10^100).

But it would be much less fun this way.

Personal note: for completely unrelated reasons I will be off-line soon and not too much around in the days to come, sorry in advance in case I should not follow up (in a timely manner).

(Edit: By the way, where was the question?)

Todd, this seems an uncharitable interpretation to me.

In any case, while I (of course) do not know either what was the intention, I found this in various aspects admittedly unusual question interesting and fun. In short, I liked it. But, I can see how one might not like it.

I can't be 100% sure this is what he's doing, and since Prof. Zeilberger has been resolutely silent with regard to queries, we will probably never know. But this is how it looks to me. To make matters worse, it's just this raw boast without any attempt to share knowledge or insight. I just don't get it.

Joro did a great job, but still it took his computer two hours. Shalosh can do it in two seconds once it found the quasi-polynomial expression for p_60(n), and it found it in 400 seconds. So Shalosh does first symbol-crunching then number-crunching.