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    • CommentAuthorquid
    • CommentTimeSep 7th 2011 edited

    Reently JSE posted a well-received question (though meanwhile with one vote to close)

    Mathematical habits...

    More recently, Gerry Myerson

    Unmathematical habits...

    which is not so well-received (3 votes to close in half an hour)

    In any case, since in particular the latter might cause some discussion I create this thread.

    The mathematical habits question has been a very useful one. I have learned that we are a far more supportive bunch than most other academic communities, that mathematicians are very good at disagreeing with each other in a productive way, also mathematicians have a knack for seeing what is pertinent to the discussion, and mathematicians seem to be better about ignoring the disagreements of last week and focusing solely on the problem at hand, in addition to which mathematicians seem to be able to take positive action quickly in these discussions rather than getting disheartened by the difficulty of the problem at hand. What's more, we know how to break a problem down into easier pieces, and disagreements among my math colleagues tend to be much more about issues, among math ed colleagues things tend to get personal. One of us observed, "the math groups I have been with are much more social," and mathematicians tend to be better at asking and receiving help.

    Is there *anything* we can't do?

    Hence, my question.
    The first question has generated some interesting (if not very original) answers. The second question seems to me only fair if you're going to entertain the first one, and at least equally interesting if not more (no answers yet so it's hard to say how interesting the discussion will be). I don't have a voice in closings, but if I had, I would vote the same way for both question (probably for closure, since the questions are too discussion-y for MO ).
    As one of the people who posted an answer to the first question I felt I should come say something here. First, I fully expect both questions to be closed. There is simply not enough mathematical content (really none at all) to keep them open. Still, I figured before it got closed I'd throw in my 2 cents. I get into discussions about topics like this all the time (e.g. when I argue that we should have required math courses at my small liberal arts college where math is somewhat looked down upon), and the answers to this question may give me some list items I wouldn't have thought of otherwise. Of course the answers are not very original...we are all mathematicians and we all know what types of thinking we're good at! Anyway, for the same reason I'm interested in answers to the second question - these are likely the counter-arguments I'll face. I hope some good answers get posted before it gets closed.

    Now, all that being said, I really don't think the tone in Gerry Myerson's post above is appropriate. I'd hate for meta to turn into a place where people go to mock posts on MO, and I really hope the second question was asked out of curiosity rather than just to point out how the first question doesn't belong on MO. I'd be curious to hear whether or not Gerry Myerson wants the questions to remain open or get closed. Certainly if the first is closed then the second should be closed. If he wants both to be closed, why post the second one at all? Why not just vote to close and start a meta thread for discussion like we always do?
    • CommentAuthorEmerton
    • CommentTimeSep 7th 2011

    I don't agree with the characterization of JSE's question as being self-congratulatory. In his question JSE explained that he is writing a mathematically-themed piece for the general public, in which he wanted to explain some advantages, outside mathematics, of a mathematician's perspective on things. Presumably mathematicians have flaws as well, certainly individually, and no doubt as a collective tendency as well. This was not what was asked about, though. Knowing JSE's writing style, I also doubt that his actual piece, when it is written, will be of a self-congratulatory nature.

    In any case, he gave a sensible and well-articulated justification for his question, and I think that it was an appropriate use of MO.

    I don't have a strong opinion on Gerry's question, although I don't think the motivations are spelled out as clearly as in JSE's question.

    @David: Actually, the sarcasm in Gerry's question made it immediately endearing to me, in a way that a more conventional wording probably couldn't achieve. I guess there's no accounting for tastes!

    In all seriousness, I don't advocate making fun of other questions in general, but if we can't make fun of ourselves occasionally, then we are *really* in danger of becoming self-important buffoons...
    • CommentAuthorquid
    • CommentTimeSep 7th 2011

    In brief: in my opinion, both questions are not MO questions by usual standards as they are highly subjective (and thus argumentative).

    One can (and perhaps should) sometimes make an exception to usual standards. I agree with Emerton that JSE had in some sense the 'better' motivation (which is why I wrote 'very little' and not 'no' in my first comment); though I wonder were the people are that typically send such questions to blogs. Still, I think Gerry's question would have been a nice counter-balance. While JSE question itself is perhaps not self-congratulatory, in my opinion some of the contributions are (to a certain extent this is perhaps inevitable) and this at least needs a counter-balance.

    So, now that the one is closed, I voted to close the other one; as subjective and argumentative.

    Finally, I second Thierry's second paragraph.


    Although I agree these aren't really MO questions, I love Gerry's question and hope it stays around for a while!


    I agree with David White that the tone of Gerry's question is off-putting. Not only is it a little off-putting, it's also clearly argumentative. I'm not a huge fan of JSE's question, but it is clear why the question is being asked (to help with writing a journalism piece) and it's although it's certainly phrased in a way that's "subjective" it does a good job of avoiding being "argumentative." In short, JSE's question is a "big list" question while Gerry's is more of a statement of opinion.

    Finally, I would be inclined to close followup soft questions because they run the risk of compounding and causing too many soft questions on MO.

    • CommentAuthorquid
    • CommentTimeSep 7th 2011

    Noah, one could start a lot of arguments on the math-habits. Just a small example: the alphabetic ordering thing right a top of the comments, plenty to argue here whether this would make sense in some other disciplines (and even if it is optimal in math), or the arXiv-posting; even for math some people think it can be not a good idea (cf. the closed MO question and the subsequent discussion on your blog). Actually, on the other one there is IMO much less 'to argue' as it is conceived in a more playful way.

    Now, not to you specifically: Perhaps this episode is a great illustration just how good mathematicians are at being self-critical, and of course also humble.

    • CommentAuthorWill Jagy
    • CommentTimeSep 7th 2011
    I'm curious to hear what Jordan has to say on this. If I were writing a piece for a somewhat pro-mathematics readership, I might be content to catalogue virtues of mathematicians. If, however, I were writing something for the general U.S. population, most of whom hate us based on a bad experience with middle school algebra, I might well want to present a realistic picture with positive and negative aspects. It is somewhat better to be disliked for what one actually is, as opposed to a collection of stereotypes.

    Put another way, I'm not sure why Jordan did not also ask about our bad habits in his initial question.
    • CommentAuthorJSE
    • CommentTimeSep 7th 2011
    I am writing for the general US population, but the subset of that population which reads the stuff I write tends to start from a somewhat pro-mathematics position. So Will is right on both counts.

    As for my question: in retrospect I can see that it's a boundary case for MO, and I won't throw a fit if it's closed, but on balance I am happy with it. My earlier question of this kind (about misapplied mathematics in the real world) got tons of very good, substantive, responses, which was what induced me to post this one. I agree that answers to this question (as to my earlier one) will inevitably be subjective. On the other hand, I think the question falls well inside the line of "questions which professional research mathematicians are uniquely well-qualified to answer well" -- in that sense I think it fits in with, e.g., ethical questions about hiring, collaborating, and graduate advising, which tend to stay alive here.

    I apologize if the question came off as self-congratulatory. To clarify my own view: "The mathematical community has many bad habits that we must work hard to correct" and "The mathematical community has many good habits which others could learn from" are not at all in contradiction, and I strongly endorse both assertions. This question was about the latter. I think the former could be a good question too -- indeed, I read Gerry's question as essentially asking this, not as any kind of mockery of me or my question.

    Finally, regarding self-congratulation; I DO concede that the pieces I write in newspapers and magazines tend to emphasize the positive side of the mathematical enterprise. I don't think it could be any other way; when I pitch a piece about math to an editor, they expect me to tell them why the subject material is interesting, important, and of use to their readership. So I end up writing about the successes of mathematics.

    I disagree with Will on the utility of this kind of work, I guess -- I think that "math is generally disliked for good reasons" and "math is generally disliked for bad reasons" need not be the only options.
    • CommentAuthorWill Jagy
    • CommentTimeSep 7th 2011 edited
    Jordan, works for me.

    On utility, it would be nice if more people were a bit more understanding, and reaching out is probably a worthwhile activity.

    On the theory that MO and the eventual article are distinct, voted to re-open Gerry's question, although accomplishing that seems the harder slog.

    I've cast the 3rd re-open vote (my first ever re-open vote).

    • CommentAuthorquid
    • CommentTimeSep 7th 2011

    Mainly out of general interest: is the to be written article about the self-perception of mathematicians/the math community or about actual recommendations based on mathematicians/the math community?

    @David, you ask whether I want the two questions open or closed. I'm tempted to reply, in which topology? but I'll try to be serious instead. I could have voted to close the 1st question, but I didn't, so, no, I don't want the questions closed. That said, it would be fully consistent with (parts of) MO history to close both questions, and I wouldn't shed any tears if that were done. I take your point that I could have started a discussion on meta, and I appreciate quid for taking that step.
    @Emerton, I don't think I characterized JSE's question as self-congratulatory (and, if I did, I apologize to JSE and to MO as a whole). I do so characterize many of the responses to JSE's question. I believe I am in agreement with quid on this.
    @Noah, My question is Community Wiki. You are permitted, nay, encouraged to edit it so as not to appear as a statement of opinion.
    • CommentAuthorEmerton
    • CommentTimeSep 7th 2011

    Dear Gerry,

    I'm sorry for conflating your opinion of the answers to JSE's question with your opinion of the question. Also, I enjoyed your topological joke.

    Best wishes,


    • CommentAuthorgilkalai
    • CommentTimeSep 7th 2011 edited
    I edited Gerry's question so it includes two questions:

    The first question is

    What habit of thoughts in other areas can be of use in mathematics.

    The second question is:

    What habit of thoughts in mathematics should be avoided (even by mathematicians) outside mathematics.

    (Gerry asked the first question but his proposed examples were to the second. Both questions are of interest.

    I propose to leave both JSE's and Gerry's questions open. They are untypical to MO and have a strong "discussion" flavour but I think they are of interest.

    In the past, we've left open "soft questions" in the spirit of Jordan's and Gerry's when, among other conditions, they satisfied the property of being best answered by research mathematicians. For example, I imagine it would would be hard for a non-mathematician to describe precisely what it is about how a mathematician thinks that would prove advantageous in other contexts. On the other hand, it would take only a mildly non-comatose person to identify inadequacies in the sort of mathematician that Gerry portrays in his question. I'm also not sure mathematicians of this sort exist, making Gerry's question at least mildly vacuous. So while I enjoyed Gerry's question (to an extent -- it was at least mildly offensive to mathematicians), I vote to close it and leave Jordan's open.

    • CommentAuthorquid
    • CommentTimeSep 8th 2011

    Cam McLeman: several people said similar things as you. But I cannot see this point at all; to the extent that I started already to wonder whether JSE plans an article completely different form the one I at first assumed. More precisely, I do not understand why a research mathematician would be particularly well placed to answer what "would prove advantageous in other contexts." Of course, they are uniquely well-placed (essentially by definition) to answer what they believe would prove advantageous in other contexts. But this is something quite different.

    Indeed, I would go so far as to say that to get good answers on JSE's question (in the interpretation most seem to have) one should rather ask people close to mathematicians that are not mathematicians. While for Gerry's answer one could say the mathematicians collect together what they individually learned in there interaction with non-mathematicians.

    Genral: My personal stance is that both are sufficiently far from the usual standards that any detailed analysis which one is more/less on/off-topic is a bit pointless, but still since it came up repeatedly I wanted to point out that even this is perhaps not so clear as some like to make it look.


    quid: "Of course, they are uniquely well-placed (essentially by definition) to answer what they believe would prove advantageous in other contexts."

    I don't understand. Mathematicians don't have to speculate as to what might prove advantageous were they to ever find themselves in a non-mathematical context, since the vast majority of their lives are thusly spent!

    • CommentAuthorquid
    • CommentTimeSep 8th 2011

    Cam McLeman: The question is a bit what precisely is to be understood by 'contexts'; at least some of the answers go into the direction of other professional contexts. Yet, even in general, I maintain an individual/or a group is not particularly well-placed to judge their own ways of operating.

    By analogy, if you want solid information on the merits of the programme of some political party, do you think that representatives of that party are the best source for this? Or would you rather ask somewhat neutral people that are only familiar with said party but not directly involved?

    In particular, I observe that so far it seems nobody came up with a real-life 'success story', that is a situation where they made a math-habits suggestion and somebody later or immediately said this was good advice; that is something I would consider interesting. For the opposite phenomenon there are examples. And, on the other question there is an individual success.

    • CommentAuthorCam McLeman
    • CommentTimeSep 8th 2011 edited

    quid: I think your interpretation of the question seems as unforgiving as possible, in a similar vain to that insinuated by Gerry's question, that mathematicians think they know better and would gladly suggest how historians/bankers/etc. are not doing their job as well as they might have had they been inclined to think like a mathematician. To the contrary, the actual wording: "Which habits of mathematicians would you recommend that non-mathematicians adopt, at least in certain contexts?" is much less imposing, asking mathematicians to brainstorm things that they do that they feel could be of occasional benefit to others.

    I find your analogy a little disingenuous, kind of like asking "If you wanted solid information, would you prefer an opinion or a fact?" Of course a fact is preferable, but such as is with like well-informed neutral parties, they need not necessarily exist. But if I had a choice between a biased expert answer, and an not-particularly-informed neutral answer, I would choose the former. In any case, the topic of "general strategies for conducting one's day-to-day business" falls, to my mind, in the "very few facts exist" category.

    Here is (what I would interpret as) a "success story": academic departments/colleges/universities very frequently have to spend much time debating the precise wording of rules and regulations for various bodies (undergraduates, transfer students, professors on leave, visiting professors, etc.). I have not infrequently noticed, in line with Emerton's top-rated answer to Jordan's question, instances of wording ending up significantly clearer because a mathematician (or similarly-minded individual) testing the proposed wording against the extremes of the definitions involved. (e.g., "The worst-case scenario is a transfer student who has taken X classes here, leaves for Y years, and then files for a z% financial aid award. Our proposed procedure would have have us borrowing money from her!", or some other such thing.) I don't think it's particularly hubricial* to believe that this mode of thinking can lead to an objectively better state of affairs.

    *: sadly, not an actual word

    I did not view JSE's question as being self-congratulatory; I think that the answers, *especially taken out of context*, would definitely appear so. I think we all know to take everything with a grain of salt when reading those answers. Even if we agree with them, we are keenly aware of the limitations to any stated upside. Someone who is not so familiar with mathematics and mathematicians, on the other hand, might not. I think Gerry's question, in that context, provided a nice balance.
    • CommentAuthorquid
    • CommentTimeSep 8th 2011

    Cam McLeman: As I said earlier I do not have that much of a problem with the question. And, yes, as collective brainstorming, and I assume it was perceived as such, it can be useful for the OP and perhaps some others. And, of course, if I were to write something on mathematics/the math community for some general audience I would also emphazise positive aspects, so that as a consequence if i'd prepare for it I'd ask for this. And earlier I even acknowledge that to some extent there is a certain inevitability to make this (the outcome of the collective brainstorming not the piece written based on it) look a bit self-congratulatory.

    Yet, the problem is with some of the answers and comments. Also, 'problem' is perhaps to strong a word, but I don't particularlly like them. Because they precsiely suggest that 'mathematicians think they know better.' For example, they seem to 'know' that one should order authors alphabetically. In which context or for whom is this a useful suggestion? In any case, it seems to be of immense importance (with 50 something upvotes for the comment). Perhaps this is an unforgiving interpretation, but the main (only?) message here seems to be that 'we mathematcians' are such a nice egalitarian community while others are not. And, with slightly less assertive formulations, IMO this could have been avoided.

    I am willing to admit to a bit of silliness in insiting on precise formulations, and each contribution alone would be fine, but the collection creates a general tone that somewhat annoys me. But, perhaps I am also over-sensitive here.


    quid: Yes, I am not blind to the irony of defending the in-principle non-imposingness of the generic mathematician in the wake of some at-least-mildly-presumptuous comments/answers. I think your point distinguishing between between the individual comments/answers and the collection as a whole is very well put. For example, I myself upvoted the alphabetical-author comment early on, partly because it's mildly a mathematician in-joke and I know Mariano to make light-hearted humorous comments, and concede that with 50 upvotes it obtains an air of "Everyone else does this stupidly." So to me, this is not what the question was after: while I'll admit to strongly preferring this mechanism -- I've never had to have an awkward discussion with a coauthor about naming priority, and colleagues in other disciplines cannot say the same -- I wouldn't presume to tell people in another discipline that our method is better for them. So it sounds like we're in relative agreement (if I'm not presuming too much...): The phrasing of the question admits a variety of interpretations, some in the spirit I was hoping for and some in the spirit you were worried about, and so a tightening of the language in the question to coax answers towards the former would not be misplaced (if it is even salvageable now).

    • CommentAuthorquid
    • CommentTimeSep 8th 2011

    Cam McLeman: I agree with the relative agreement. Thanks for the interesting discussion!


    JSE's question has been closed, and now has a few votes to reopen. I would vote to reopen but don't want to cast a moderator vote; maybe if I see it at (4).


    Sorry to steal your final vote, Scott. I cast the fifth before I saw this.