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    I don't think this is suitable for MO and wanted to start a thread to keep comments brief.

    By analogy, suppose I posted an RSA public key to MO and asked for its factorization. The specific answer would not be interesting, only the process and fact of its discovery by another. Of course, Doron probably had to work harder to get his answer than multiplying two numbers together, but I don't think it changes the spirit of things.

    Here is a link to the actual question in case you got here by accident.


    Based on reading his Opinions, my guess is that he is using the question to make a point about ultrafinitism, or something along those lines. I am not sure if we should be encouraging such things.

    • CommentAuthorgilkalai
    • CommentTimeJul 24th 2011 edited
    Qiaochu's view is very problematic. We should not take the OP's opinions into account when judging a specific question. This is a wrong attitude and in addition it is discriminating in favour of anonymous users and people who do not express their opinions or have no opinions. Also encouraging or discouraging something based on a "guess" by Qiaochu (as by any other user however prominent he may be) is very problematic as well.

    Regarding the question itself. This is Doron's first MO question, it is a bit unusual but quite puzzeling, so I thing we should allow it.

    I agree with the closing. On one hand, the answer is already known in a certain sense, and stated in the question. So the difficulty seems to be only in doing the actual numeric computation. The question does not explain why that should be of interest to research mathematicians.

    The question might be interesting if the answer was serendipitously a small integer such as 124. However, the ways to split a googol into at most 60 pieces include all the ways to split it into 2 pieces, and there are on the order of 10^99 of those. So the answer is going to be quite large. The question doesn't state any motivation for choosing a googol compared to any other number; presumably the reason for a large number is to make the computation more difficult.

    Given those points (the fact that the method is well known, and that the answer is not likely to be broadly interesting), I think the question is "too localized" as it is currently written.

    By comparison, I think that the following question that I asked on math.SE would be acceptable here: how do you show that e^(e^(e^79)) is not an integer? . The thing I am looking for there is a reference for a general method, and the exact number I chose is not really of interest. The reason I have not asked that question here is only that it seems to be open. The difference between the question about partitions of 10^100 and the one about e^(...) is that the partitions question is focused only on the numerical answer, which is in a certain sense trivial, while the question about e^(...) is about the general method, and the particular example is just an illustration of the motivation behind the question.

    I think that the question on partitions might be able to be reworded to bring out a more general question. At the same time, to make the question suitable for MO, it needs to be sufficiently mathematical, rather than philosophical. The FOM mailing list would be a better place to discuss foundational or philosophical questions.

    • CommentAuthorquid
    • CommentTimeJul 24th 2011

    I voted to reopen (the informal votes seem to cancel, as André's first against closing got in fact ignored). As Gil Kalai said this is Doron Zeilberger's very first contribution here, and I am in general of the opinion that first time user should be treated more generously than regular ones. If in addition it is clear that the person knows what s/he is asking, this is even more true.

    As the monetary prize came up: I mean, come on, to assign some minor monetary awards to problems, this is a good, or bad if you like, playful tradition in certain parts of mathematics, since decades (it seems Erdős might well have been banned from MO). And, on MO there is even a question asking for a list of problems with (higher) monetary awards. So, it is not that money is off-limits for MO in general.

    That being said, of course the question is not the typical MO-type question, an if somebody would start asking this type of question on a very regular basis, this might be a problem. But, it is this highly-qualified user's first question, so let us be a bit generous and more welcoming.

    I'm going to agree with quid: In principle, I don't like such questions, and if there were 10 of them, then that might be a problem. But the OP is a known quantity- a provocative, original mathematician, whose strange questions seem to have a history of turning out to be rather interesting. I think we should make a one-time exception to the rule, in deference to somebody we would very much like to see asking and answering questions, and reopen the question.

    I come down on the side of not reopening this question. If this question had been posted anonymously, there is no doubt in my mind that it would have been closed within minutes and with zero regrets. So it would seem that the overriding reason for wanting to reopen this question is that it came from Doron Zeilberger, and that we'd be pleased (presumably) to have him hang out at MO.

    But what is this question about, really? Obviously one cannot give a human-based conceptual solution (except perhaps in broad outline of method) -- what is required is a powerful computer and maybe excellent programming skills. The solution will be a number with 99 or more decimal digits, and then: so what? What does that prove? Where on earth is the interest in such a problem?

    I think the only one who can provide the motivation or say why this problem is interesting is Doron himself. Lacking such an explanation from him, it is natural to wonder (as Qiaochu did) why he wants to post it. [My own speculation is that it definitively shows the helplessness of humans in the face of such problems, and that human mathematics is immeasurably poor in comparison to computer-aided mathematics. Not that such speculation is a proper reason for closure -- I agree with Gil on that point.]

    If, for the sake of keeping Doron here, we reopen the question, then I would hope that it's made clear that such computer challenges (with known answers) are not considered a proper use of MO, that this type of question will be tolerated this time but not again, and that we'd really like to hear his reason for asking. Please read "how to ask", etc.


    I don't understand why the question got reopened and has, at the time of writing this, a net count of 9 upvotes. It is unmotivated, the OP seems to know the answer, the answer is not interesting mathematically in any way (the question was not about efficient algorithms),... The question fails pretty much all my criteria for a good question. It's not even Latexed. I am sure that if it came from an anonymous user, it would not only be closed but would also have attracted several flags. At the same time, a much better motivated question, to which the OP doesn't know the answer and to which the answer would be helpful to the poster (unlike in the case under discussion), gets closed. I am with Joe Silverman on the assessment of both these questions. As we know, one off exceptions don't work well on this site: new users will come to MO, will look at the highest voted open questions and will draw the wrong conclusions about the mission of MO.

    • CommentAuthorquid
    • CommentTimeJul 24th 2011 edited
    Todd Trimble, it seems to me you just helped making the point Zeilberger (possibly) wanted to make.

    Alex Bartel, how can you judge the question is not interesting? Is knowing that x^n + y^n = z^n for n>= 3 has no natural solutions interesting or not? Would it be trivial if the range of n,x,y,z would be restricted to very large ranges? Do you consider any question on partitions as not interesting?
    • CommentAuthorgrp
    • CommentTimeJul 24th 2011
    It is amusing to see the variety of attitudes expressed within the community about how to treat the first question of a poster, and how dependent the treatment is on the supposed reputation of the poster. (Test question: would I get better treatment if I started posting under the name Perelman or Vietoris?)

    The answer seems clear to me: whichever part of the community wishes to encourage the poster, they should edit question, explain the reasons for the edit, and if the revised question meets community standards, lobby to reopen the question either via community or via moderation. Further, some others could follow the poster to help maintain the quality of their participation.

    My opinion is that DZ's contribution requires editing before it becomes acceptable in this forum. If someone asks, I will suggest three kinds of revisions to be made.

    Gerhard "Ask Me About System Design" Paseman, 2011.07.24

    @quid: maybe I did, but only Doron can say for sure. (I take it you meant the point about human mathematics being so impoverished.) And if that is the point, then so what? It's hardly a reason to keep the question open -- it merely succeeds in making the question seem rhetorical.

    • CommentAuthorgilkalai
    • CommentTimeJul 24th 2011
    Dear Todd, in my opinion, there should be a different attitude to anonymous users compared to people who sign by their name. Users who sign by their name put, to some extent, their reputation on the line. (I mean real-life reputation not MO reputation points.)
    Dear grp, what are the 3 revisions that you propose?

    Gil, in that case I'm happy to sharpen my assertion: the question would still be closed within a few minutes if someone used their real name but didn't enjoy such a reputation as DZ has in the world of professional mathematics. And based on the merits of the question as currently written, quite rightfully so. So clearly the reason this has been reopened is on account of DZ's name. One can debate the justice of this, but let's be clear that this is what happened.

    • CommentAuthorgrp
    • CommentTimeJul 24th 2011
    Revision number one is purely to put the question in a more acceptable framework for MathOverflow, while preserving the initial intent. Something like: "I am doing the following computation and desire independent verification of a particular quantity. Is there someone here who can help or knows who is willing to help? For bizarre reasons, my grant permits me to pay precisely one person $100 for such assistance, but by a certain deadline ..."

    This version can be improved, and is better because future questions of a similar nature may have the same answer ("No, go away", or "Try this web search", or "Yeah, I know a guy....") which means those future questions may be answered by referring to this post.

    A version which reveals part of the motivation (let's presume ultrafinitism for example, thanks to Qiaochu) is; "I have money riding on a discussion with this person about the philosophical meaning of large numbers. In particular, do numbers exist before we can write them down? How should this affect perception of the validity of proof? As a test case, I am supposed to show that the partition function exists, and one certificate for existence is to break a googol into at most 60 parts ..." followed by a similar request for independent verification and promise to split the spoils, etc.

    This version is better because motivation is revealed which may suggest to the community how to best answer the post instead of answering the question itself. Answering the post may have utility to those with similar motivations.

    Another version is to focus on computational aspects of the problem. To wit: "I am providing a series of benchmarks for evaluating CAS performance. As well as raw performance, I am interested in algorithmic efficiency, especially in terms of remote address (pointer) evaluation. To simplify the discussion, let us focus on the partition function. I want to know various ways of evaluating p(googol,60) and observed as well as theoretical bounds for resource usage. To ensure sincerity and correctness, I ask that posters provide the actual result as well as an analysis of the algorithm and resource usage...", followed by whatever words to justify the $100.

    This version is better because it leads to interesting aspects of mathematics not often considered by people other than Zeilberger: how can one improve on the production of mathematics by human and computer, as measured by some resource consumption. Having p(googol,60) as a focussing test case now seems like a worthwhile academic endeavour rather than a (in my opinion of the question and not the questioner) single crass challenge of who can compute the fastest.

    Others more skilled than I can refine these examples or provide others to make them suitable for MathOverflow; the point is not just to entertain us (and others to come) but to edify as well (especially the others to come).

    Gerhard "Ask Me About Question Asking" Paseman, 2011.07.24

    I cast the final vote to reopen the question. I did it partially out of respect for Doron Zeilberger, from whose "opinions" I have learned a lot, and because I suspected (because of his work) that he was trying to make an interesting point (e.g. that there was a clever algorithm behind this, or perhaps something about computers versus humans). In addition, I thought it would be unfortunate if he decided to leave the website if his first question was closed. In short, my reasons were similar to those of Daniel Moskovich above.

    • CommentAuthorvoloch
    • CommentTimeJul 24th 2011 edited
    Removed earlier comment made moot by the fact that the question was answered.
    • CommentAuthorquid
    • CommentTimeJul 24th 2011 edited
    reponse to voloch, deleted

    @Akhil: thanks for saying so. Yes, Professor Zeilberger is an interesting guy obviously, and his presence could be a real boon to MO provided he shares his insights, not so much his opinions (which is something he does on his well-publicized website).

    Sorry for so many comments, but I want to add that the purpose of MO is not to provide a venue making interesting points about computers versus humans (which could verge on "subjective and argumentative") -- it is for the exchange of precise knowledge and mathematical insights. Nor would it be appropriate for the main point of a question to be: hey, I've got this really cool algorithm -- there has to be an actual question if the thing is to be at all legit. So, the darn thing could be legitimately closed as "not a real question". I feel strongly about this.


    Since the question has been answered and the answer has been accepted, I believe closing as "no longer relevant" is appropriate. This would prevent spurious new answers from appearing.

    <strike>I am tempted to do this unilaterally, but I would prefer community support since there has been so much debate around this question.</strike>

    Since a spurious answer has appeared, I decided to unilaterally close the question.

    • CommentAuthorNilima
    • CommentTimeJul 24th 2011
    My comment is now moot, and contributed nothing to this thread. The question has been answered, and now closed after I started composing this response.

    Is the precise objection that the answer to Zeilberger's question is 'just a number'? Or that he offered money?

    If the former, that seems rather rigid. Such questions have a way of provoking at least a certain number of mathematicians:

    I wonder if any of the questions in the 100-digit challenge would have been considered legitimate on MO. Maybe not, but they certainly spurred a lot of activity and interest.

    Certainly Zeilberger's question is as scientifically interesting and precise (or not) as, say 'how to referee a paper' or 'colorful language in mathematics'.

    I must now confess my defeat in trying to understand what is, or is not, a good question on MO, after 5 months of trying. Staring at, one must conclude that the most valued questions are what I would consider soft. And yet Zeilberger's (admittedly quirky) question doesn't fit the bill?

    MO is a vibrant community that is working on a truly novel experiment, and I wish you all well. I just don't understand the principles behind it, and must therefore step out.

    Is the precise objection that the answer to Zeilberger's question is 'just a number'? Or that he offered money?

    The precise objection (at least, my objection) is that Zeilberger already knows the answer, and therefore isn't interested in the answer. The offering of money, along with other peculiarities of the question, suggest that his motivation for asking the question lies elsewhere, and why should we have to guess what that motivation is? There is a certain dishonesty to asking questions like this which I do not think is in the spirit of the MO enterprise.

    Staring at, one must conclude that the most valued questions are what I would consider soft.

    I strongly disagree that vote totals (in the tail region, above 20 votes or so) are anything like a measure of value of questions. The most valued questions, in my mind, can't be anything except precise mathematical questions that occur in someone's research that they don't have the background to solve, but that they suspect someone else does. There are several reasons why such questions don't garner the most vote totals:

    • If you don't have the relevant background, it's hard to judge the quality of the question. Thus vote totals are partially a function of how accessible the question is. But part of the point of MO is precisely that it is an efficient way to get answers to inaccessible questions.
    • CW/big-list questions, by their nature, attract a lot of posts, hence views, hence votes. I think many people view them as a necessary evil: people always want to collect math jokes or math stories or whatever, and to some extent this is healthy community-building activity, but ultimately it should not distract excessively from the main purpose of the site.
    • The community attitude towards CW/big-list questions has also changed over time: note that many of those high-voted questions are now closed. In the past we were more lax with such questions, so they were allowed to stick around and garner many votes. Thus for CW questions, vote totals partially reflect the age of the question.

    Is the precise objection that the answer to Zeilberger's question is 'just a number'? Or that he offered money?

    Neither. Reading the discussion, the main objections were that the question was not well motivated and that it wasn't really a question since Zeilberger already knew the answer. The 'just a number' issue did come up, but the consensus appears to be that if the choice of numbers was well motivated there would be no issue at all. The money issue also came up, but did not cause much of a stir.

    Staring at, one must conclude that the most valued questions are what I would consider soft.

    Soft questions are very popular and for good reasons. Such questions are welcome, but only in small quantity. Department seminars are sometimes on soft topics too, but this is rare. Department tea is also an important part of mathematical life, but it is only a small part of it. MO is much the same.

    I just don't understand the principles behind it...

    The how to ask page offers a lot of advice and insight on the basic principles that make up a good MO question. Let us know if you find this resource lacking.

    • CommentAuthorgilkalai
    • CommentTimeJul 24th 2011
    grp: "Test question: would I get better treatment if I started posting under the name Perelman or Vietoris?"
    Dear Gerhard, we may get suspicious to see a signature
    " Leopold, exact sequences get as long as you wish, Vietoris"
    • CommentAuthorblahped
    • CommentTimeJul 24th 2011 edited
    This is not DZ's first question.

    google: zeilberger unregistered inurl:mathoverflow

    to get


    Maybe the point of his question was as a memory test.
    • CommentAuthorNilima
    • CommentTimeJul 24th 2011
    Qiaochu, I defer to your reading of Zeilberger's motivations, the question itself seemed interesting if off-beat. I also, like you, value specific, research-level questions on MO. However:

    a) reputation helps identify 'those who know what they are talking about' (from the faq),
    b) votes provide reputation.

    I infer from a and b that people with higher reputation, and questions with more votes, are assigned some value by the community itself. Otherwise the voting/reputation business is pointless.

    Francois, the how-to are ample. The FAQ don't elucidate (for me) how choices are made between soft or off-beat questions. However the majority of MO users seem to understand how this works, so the lacuna in understanding is mine. I find departmental teas excruciating, since there is much socializing which occurs.

    The issue of providing motivation and background is also addressed in the how-to. Questions in some areas are pressed for more background than in other areas. This is an artifact of the research expertise present at the site. However, this also presents barriers for those (such as myself) who work in other sub-disciplines.

    None of this is intended as criticism, just observations.
    • CommentAuthorblahped
    • CommentTimeJul 24th 2011
    How many other questions on MO are pretend questions that the poster knew the answer to, but not obviously enough to raise any eyebrows ? Or at least others were too polite to raise them, but just played along ?

    How many questions are there that the poster could have answered themselves with a few minutes on google ?

    How many questions where the OP didn't really care what the answer would be, but just enjoyed playing the MO game ?

    a) reputation helps identify 'those who know what they are talking about' (from the faq),
    b) votes provide reputation.

    Votes on CW questions and their answers don't provide reputation precisely because of your point a).

    • CommentAuthorquid
    • CommentTimeJul 24th 2011
    Nilima, I am slightly longer active on the site than you, but not by too much. Still, I am (too) fairly frequently surprised by the collective behavior of MO. At the start, I guess before you were around, I too asked some questions related to it. One thing is, there is a considerable randomness to certain aspects (somewhat inevitably, as hundreds of people collectively shape the site, their opinions on what is 'right' or 'wrong' differ, and depedending on who happens to be active at a given time things develop). And, though not too much lately, there were somewhat fierce discussions between long-time MO users, which questions are or are not 'good'; conclusion: there is no real conclusion.

    My personal solution: eventually, I gave up on trying to understand some explicit or implict rules in detail, and within broad boundaries, act according to my own rules. Indeed, I believe this is what 'everybody' does, and I guess this is also true to the idea of a community moderated site, and so it really should be like this.

    One thing is, there is a considerable randomness to certain aspects (somewhat inevitably, as hundreds of people collectively shape the site, their opinions on what is 'right' or 'wrong' differ, and depedending on who happens to be active at a given time things develop).

    This is an important point. Community moderation is SE's solution to the problem of how to moderate the site without taking up too much of any one person's time, and while it scales quite well it has the unfortunate drawback of being somewhat erratic. Barring a significant restructuring of the software I do not think there is too much we can do about this, although we should certainly keep it in mind.


    From Nilima's comment above:

    I infer from a and b that people with higher reputation, and questions with more votes, are assigned some value by the community itself. Otherwise the voting/reputation business is pointless.

    Well, it's important to keep in mind that the way the voting/reputation works in practice can be very different to what one might consider 'logical', and one shouldn't take the whole business too seriously. Just speaking for myself, some of the answers in which I poured a lot of effort and personal insight have gotten very few votes, whereas others that I more or less dashed off without much work were upvoted far, far more. It can sometimes be surprising.

    My own suspicions are that people tend to vote up questions and answers that they think they understand. So if a question or answer is on the esoteric or somewhat demanding side, then you probably won't see much voting up. But a snappy answer that most graduate students can understand will tend to attract a lot more upvotes. Rule of thumb: as long as it's a decent answer and doesn't make too many demands on the reader, expect a decent number of upvotes.

    For the same reason, a soft question which is understandable and easy to read (hence one making few demands on the reader) may also get upvoted a lot. This phenomenon is, you understand, independent of what theoretically makes a good MO question "according to Hoyle" (e.g., the faq and how-to-ask).

    It is most important to keep in mind that you have no idea who is doing the voting (unless they say so, of course), and with thousands of onlookers, the voting patterns will reflect sort of the "average" intelligence, taste, and so on of the community, and not that of the "ideal" discerning MO user. Or, they may reflect collective tendencies that run counter to what one might think of as "good". Voting is after all as easy as a click of a button, so you can expect that a lot of it might not be based on deep reflection, but on more spontaneous reactions, and maybe even reactions to reactions.

    So it's best to not take all this reputation stuff that seriously. Those who have the highest reputations are not necessarily the most respected and accomplished mathematicians in the world, right?

    • CommentAuthorNilima
    • CommentTimeJul 24th 2011
    Todd and quid, thank you for your thoughtful (and helpful) comments, these certainly shed light on aspects of MO which puzzled me.

    Perhaps this is moot since the question has been closed, but I'd like to point out that it is rather strange (to me) to offer a monetary reward for a computation that can be easily done in a widely distributed freely available CAS. I think at MO there is an expectation that a person asking a question think about it for a bit before posting, and it seems like Zeilberger didn't do his homework in this case.

    This question in particular was rather egregious. Once you know that power series expansions of rational functions satisfy linear recurrences, you could ask a nearby linear algebra student to take the (10^100-n)th power of a matrix for some suitably small n.


    Upon further reflection, it seems to me that people who are experienced with generating functions (e.g., Zeilberger) may be quite familiar with this property of rational functions, while those people who do not study generating functions are likely to find it obscure. In other words, people who specialize in fields near his own may be able to come up with a solution method immediately, while people further away may not. I no longer think that this is a problem of Zeilberger not doing his homework, and in fact I am now quite confused about what his motivations for asking the question might be.

    • CommentAuthorquid
    • CommentTimeJul 25th 2011

    What I am confused about is: why all this drama?

    Somebody for whom it is a very save assumption that he knows what he is doing asks something, which admittedly is not in the form of a typical MO question, but then still a mathematical question. Whether it was meant somehow seriously, as a semi-joke, as a joke, as a mildly unfriendly act, or whatever, so what? Why couldn't it simply stay open in the first place? That after all the discussion, and the answer, and the spurious answer, it now got re-closed, alright, I understand this. But what would have happended if it just would not have been closed in the first place. Nothing 'dangerous' ... much simpler for everybody. (And, this "nothing 'dangerous' " is key for me, and the main reason why I would not argue like this if an anonymous user, or also some non-(well-known)-mathematician under real name, would ask the same thing. Because in that case it is not clear what would happen if one let's the question stand; in the sense of potentially numerous follow up questions of a similar type and so on.)


    quid: I think the answer is simple. Doron Zeilberger posts a question which, based on the merits of the question alone, was deservedly closed (I don't know the official reason for the first closure, but one could say it was not a real question since actually there was no question, was there? and anyway DZ knew the answer to his problem). The "drama" was simply over the fact that it was after all a well-known mathematician who might otherwise be a real boon to MO, and nobody really wants to shoo him away by closing his question summarily without accompanying discussion and explanation.

    Edit: there is of course the issue of setting bad precedents if this type of question is allowed to stand. In the interest of fairness, and in the interest of not having to split hairs based on some community assessment of who does or doesn't pose a "threat" based on their standing, it is in fact much simpler to judge the question itself, not the man/woman.


    But what would have happended if it just would not have been closed in the first place. Nothing 'dangerous' ... much simpler for everybody.

    As Todd says, it sets a bad precedent. I am sure you are no stranger to arguments of the form "I don't see why my question should be closed, since Question X looks very similar and after all you kept it open" on meta.

    • CommentAuthorquid
    • CommentTimeJul 25th 2011

    Qiaochu and Todd, yes as soon as one starts discussion things get ever more complicated. If you press me for a definition, along the lines what I said in my first comment, I would accept from everybody who demonstrates in some way to be a mathematician, e.g., by linking to a relevant website in the user profile [and let's say this includes students], a first somewhat off-topic question (in particular, only one). Well, and if the person is not a mathematician, and the question is not obviously off-topic, as said, I would also be generous and welcoming (again for the first question, or more generally very early contributions).

    In short, welcoming to (essentially) newly arrived users and strict to regulars; not the other way round, as it seems to be the wider spread opinion.


    quid, I think it is possible to be welcoming while still closing a question if it is off-topic. Is it so hard to say "Welcome to MO! Unfortunately, questions of this type are a little off-topic. Please see the How to Ask page"?

    • CommentAuthorquid
    • CommentTimeJul 25th 2011

    Qiaochu, no it is not hard to say this, I just do not find it welcoming. For example, I would prefer if people were told, in borderline-cases, something along the lines "You might not have known this and that, for the next time please keep it in mind."


    In a situation like the present one, where we have someone as obviously well-known as DZ, it might be nice to first suggest modifying the question before moving to closure. That's fine.

    Last I checked, Professor Zeilberger hasn't responded to anyone except joro in his answer. I thought there were a number of polite openings and welcoming gestures from people where he might have responded a little more. It would be nice to hear from him.

    • CommentAuthorgrp
    • CommentTimeJul 25th 2011
    In response to gilkalai's
    Dear Gerhard, we may get suspicious to see a signature " Leopold, exact sequences get as long as you wish, Vietoris"

    Touche. I really thought the living/nonliving distinction would be a tipoff, but behaviour would be even more so. Even so, I am not fully convinced that the poster is Professor Zeilberger, but find it convenient to assume so.

    Gerhard "No, I'm The Other Gerhard" Paseman, 2011.07.25
    • CommentAuthorquid
    • CommentTimeJul 26th 2011
    Todd, I agree on both points.

    Gehard, since e-mail correspondece was mentioned and not contradicted by joro, it seems very likely.

    I'm also baffled by why Doron posed this question, so I don't have any insight to add there. But I want to mention something that doesn't seem to have been mentioned yet. Jan Hendrik Brunier and Ken Ono recently came up with a new formula for the partition function (as a sum of certain algebraic values of weak Maass forms) that I think gives a faster algorithm than the obvious one using the generating function. (Though I don't understand their work well enough to be sure.) I thought perhaps that Zeilberger's challenge had something to do with seeing whether the ideas of Brunier and Ono could be extended to computing partitions with a bounded number of parts. But since Zeilberger's challenge was met using classical methods, I guess I'm barking up the wrong tree. Still, this could have been an interesting question if phrased this way.

    • CommentAuthorgilkalai
    • CommentTimeJul 26th 2011
    The reason I like Doron's question is that, although I am in this field, I did not know the answer. (Namely I did not know, certainly not off-hand, how to solve it with a computer, and I certainly cannot do it myself.) It was not obvious to me that this is feasible and I was interested to see it is. (Also Scott's comment above is a bit too cryptic for me to be very useful.) I am a little disappointed that even with the answer I still dont know precisely what is going on.

    I think it's an unusual but reasonable problem to leave open no matter who asked it.

    A lot of issues were raised. E.g.,

    a) Is it ok to ask a question you know the answer to when you think that the question and answers can educate our community? I think its ok occasionally. (I dont know if Doron figured out the answer before asking.)

    b) Is it ok to offer money. (I dont have a strong opinion about it.)

    c) Is MO is only it "for the exchange of precise knowledge and mathematical insights". Well, once you talk about insights you may get away from "precise knowledge". (And when you think of it it is hard to get more precise than Joro's answer.) I like Bill Thurston attitude "I enjoy questions that seem honest, even when they admit or reveal confusion". In any case, I think we should tolerate various approaches.
    • CommentAuthorgrp
    • CommentTimeJul 26th 2011
    I think we should permit "Bad" MathOverflow questions occasionally, if only to serve as an example of how not to ask a question. I can tolerate the occasional bad question as long as it is not succeeded by a long line of other questions of similar type.

    There have been many threads on meta discussing what is a good and what is a bad question, and the notions have changed somewhat along with the community. ( Among the ideas suggested is that a good answer does not change the quality of the question. ) If we are to consider MathOverflow as a resource not just for the present but for the future as well, we should exercise more care in what questions we encourage.

    I think the question is more "Bad" then "Good" primarily because of how it is worded and because of lack of motivation of a nonmonetary type. I would not like to see MathOverflow become a site of computational challenges of the form "compute this number first: win a prize". However, for every such question, if it could modified to include issues of mathematical interest (cf an earlier post of mine for some suggestions), then I would welcome similar challenges from Prof. Zeilberger, whoever she may be.

    Gerhard "Ask Me About System Design" Paseman, 2011.07.26

    Dear Gil: I said "precise knowledge and mathematical insights", which on ordinary reading means that each on its own should be considered important. I didn't say that all insights are precise knowledge -- and nor would I, because that's not something I believe. (E.g., some of my own answers are more at a level of intuition than precise proof. That's a perfectly ordinary event at MO.)

    Moreover, this quotation was really taken out of context (from comment 19, if you care to count); here is a fuller extract:

    I want to add that the purpose of MO is not to provide a venue making interesting points about computers versus humans (which could verge on "subjective and argumentative") -- it is for the exchange of precise knowledge and mathematical insights.

    The context was some speculation as to what the motivations were behind Zeilberger's post; Akhil Mathew suspected "...that he was trying to make an interesting point (e.g. that there was a clever algorithm behind this, or perhaps something about computers versus humans)."

    I agree that we should tolerate various approaches. Of course! But I do not agree, I don't think, with the idea that MO could be used as a soapbox (e.g., if someone were to make a point about the relative poverty of purely human mathematics in comparison to computer mathematics, a common theme in DZ's Opinions page) -- again this should be read in the context of what Akhil speculated.

    • CommentAuthorMariano
    • CommentTimeJul 26th 2011

    (Todd puts in evidence the fact that this forum, which tons better than's meta, does not make referring to previous posts in a discussion easy at all!)

    @Gil: I think cash offers are fine, why wouldn't they be? As it happens, I personally offered $.50 and a Sprite (and am still fully prepared to honor the offer for a reasonable answer) here:

    But I want to mention something that doesn't seem to have been mentioned yet. Jan Hendrik Brunier and Ken Ono recently came up with a new formula for the partition function (as a sum of certain algebraic values of weak Maass forms) that I think gives a faster algorithm than the obvious one using the generating function.

    Brunier and Ono's work does not, to my knowledge, apply to partitions where the size of the parts is bounded above. The generating function in this case is rational rather than modular-formy, and so much easier to deal with.

    Perhaps a mathematical point is worth clarifying here.

    • There is a well-understood procedure for reducing the computation of the nth coefficient of a rational generating function to the computation of entries in approximately the nth power of an associated matrix. Using binary exponentiation (and perhaps the Chinese Remainder Theorem), there is an efficient algorithm for doing the latter computation.
    • Given the focus of Zeilberger's research, he is almost certainly aware of this.

    So, as others have noted before, Zeilberger isn't asking this question because he doesn't know how to compute the answer, and I don't think it sets a good precedent to allow such questions unless the alternate motivation is clearly spelled out.