Not signed in (Sign In)

Vanilla 1.1.9 is a product of Lussumo. More Information: Documentation, Community Support.


    Question 27881 is raising some debate. I don't think it's that bad, but I'm willing to listen to other people's opinions.

    • CommentAuthordanseetea
    • CommentTimeJun 11th 2010
    I think it's a perfectly appropriate question because of two reasons:
    1. It should interest many mathematicians (it boils down to asking about the development of mathematics in early 20th century)
    2. While as it stands it could be too subjective and argumentative, maybe someone has good references for some of the claims (Hilbert, Von Neumann) - I am sure many have discussed this topic (or variations of it) in history of math journals, so we just need to wait for an expert to give us the references (and it would be a shame to close this question before the expert arrives).

    I have been reading some of the recent debates in meta about how soft questions should be treated, and as far as I could tell there is no consensus at the moment. I think this is a fine soft question; those who downvoted it probably generally dislike soft questions.
      CommentAuthorJon Awbrey
    • CommentTimeJun 11th 2010

    No, clearly it should be, "Who is the last mathematician who understood all of mathematics?"


    I've voted to close as subjective and argumentative.

    • CommentAuthordanseetea
    • CommentTimeJun 11th 2010
    @Harry -
    Nearly all soft questions could be said to be subjective and argumentative. Do you usually vote to close most soft questions?
    If not, I think it could be profitable if you share with us more precise information for why you consider this question inappropriate (other than the catch phrase "subjective and argumentative").
    • CommentAuthorHarry Gindi
    • CommentTimeJun 11th 2010 edited

    Nearly all soft questions could be said to be subjective and argumentative. Do you usually vote to close most soft questions?

    I disagree and could find a number of soft questions that aren't subjective or argumentative (I've made a total of seven soft question posts, none of which could be considered either subjective or argumentative. I'm also very careful about what I call a soft question in the tags, so anything not immediately relevant to actual mathematics is marked as such).

    Well, it's subjective because a.) it requires us to judge someone's understanding of a subject from insufficient historical evidence. b.) requires us to determine what fields we would consider mathematics, and c.) leads people to choose mathematicians within their own fields.

    By c.) above, and since it is very close to the question "who was the best mathematician ever", it seems likely to start an argument.

    • CommentAuthordanseetea
    • CommentTimeJun 11th 2010

    @Harry- I entirely agree with you that "it's subjective because a.) it requires us to judge someone's understanding of a subject from insufficient historical evidence". Undoubtedly very few people can claim to have such broad historical perspective of mathematics that would allow them to answer this question. But if instead of asking people to give their own opinion, you would ask them to give concrete references of competent people dealing with this question, don't you think this would make the answers (if there are any) very enlightening?

    I've closed the question. Although it is conceivable that at some point some answers citing scholarly historical work would appear, it seems unlikely that an authoritative answer is even possible.

    To be honest, the answers I saw seemed to vastly underestimate just how much math was known before 1900. If I had to guess at an answer, I'd pick someone 2000-2500 years older.

    @Scott: +1. The first names that occured to me was first Euler, then Gauss.


    Scott, you said it best in another soft question with similar problems: any answer would reveal more about the ignorance of the answerer than about the question.

    • CommentAuthorVP
    • CommentTimeJun 12th 2010
    On a related theme: who was the last historian of mathematics who would be qualified to answer this question?
    • CommentAuthorHarry Gindi
    • CommentTimeJun 12th 2010 edited

    @VP: +1!

    I don't think that a historian of mathematics could ever answer this question for the following reason:

    We can say what areas of mathematics a person did work in, but it's very hard to say what areas of mathematics that person understood. The only answer we could give is a pretty bad lower bound (Euclid, perhaps, could be said to have understood all of the pure mathematics of his time, but mainly because the field of pure mathematics was miniscule compared to today. However, even this is not a definitive answer, since it's very possible that large amounts of the work done were lost to the sands of time, so to speak.) Further, this depends integrally on our definition of what constitutes mathematics (was Aristotelian syllogistic logic actually mathematics?)!


    I haven't been convinced by the arguments so far, so I'm voting to reopen.

    • CommentAuthorEmerton
    • CommentTimeJun 12th 2010

    Dear Francois,

    I also voted to reopen. I think this is an interesting question in the history of mathematics, and good answers will likely be informative and stimulating (as are some of those already given).


    To complete my earlier thought, I don't think the purported non-existence of experts to answer the question invalidates it. This is for the same reason that an open problem is not necessarily an invalid MO question. In any case, I don't buy the arguments that no such experts exist since you obviously don't have to be a polymath to recognize one.

    I believe the question is a.s. essentially unanswerable for a trivial reason. For most of human history, mathematical centers of activity were widely separated, and mathematicians a.s. would not visit more than one or two in a lifetime. But by the time a single mathematical community could be said to have emerged, mathematics was a.s. too broad to have been entirely comprehensible to any single person.

    There appears to be confusion between the title and the actual question:

    Who is the last mathematician who had an understanding of a large proportion of mathematics (at the time they were alive)?

    I don't think the arguments using the "totality of mathematics" apply to this question.

    I find the existing answers to this question frustrating as there are no actual arguments just bald assertions.

    Qiaochu, my comment on question 21562 was meant as a statement about our collective ignorance, not as an insult to the people who took the time to answer Negative refraction's question. At least, I hope most of the 30+ upvotes came from people who understood it this way. I feel kind of bad now that I see that it could be interpreted as a personal statement.

    Regarding the question under consideration, I feel that if it were revised to reduce the "who was the greatest" tone, I'd be less against it. One could ask something like "at what point in history did it become impossible for a person to understand most of mathematics?" and get information of roughly the same quality.

    • CommentAuthorJeremy
    • CommentTimeJun 12th 2010
    @Scott: I did not interpret that as an insult.

    Also, on speculation about how to improve this question, wouldn't a better way to ask this be: how big is math as a function of time? That would be much easier to compare to how much a person could know, than speculate based on who's your favorite supermathematician.

    I feel that if it were revised to reduce the "who was the greatest" tone, I'd be less against it.

    Same here.


    @Scott: Ah, my mistake. I didn't mean it as an insult, either. It's just hard to have any kind of hard evidence about this kind of question.

    One could ask something like "at what point in history did it become impossible for a person to understand most of mathematics?" and get information of roughly the same quality.

    That certainly sounds more agreeable.


    I have reposted the question in the suggested form (and with community wiki enabled).

    Here's a copy of the disclaimer I left on the new post, which explains why I did this:


    I am asking this question as an improvement to this question, which should be community wiki. This is in line with the actions taken by Andy Putman in a similar case (cf. meta).

    • CommentAuthorEmerton
    • CommentTimeJun 13th 2010

    I don't understand why people think that it is difficult to have hard evidence about this question. It seems reasonable, as a point of history of math, to (a) roughly enumerate all the fields of mathematics at a given time; (b) survey all of a given mathematicians publications; and then (c) see to what extent the topics of their publications cover the existing range of mathematics.

    Naively, this will measure pure breadth, rather than depth, of knowledge, and the question probably requires an analysis of both. But the depth of understanding of a given mathematician can be evaluated, for example, by studying the importance of their papers (say as judged by contemporary and later opinions).

    • CommentAuthordanseetea
    • CommentTimeJun 13th 2010 edited

    [EDITED some time later: I was not aware only moderators can wikify a question; hence I retract most (but not all) of my criticism in this post]

    I am rather baffled by the chain of events surrounding the closing and "reopening" of this question.

    First, I feel it was unfairly closed. I think it may have been more honest of the closers to wait until the discussion at meta was finished; especially since at least two very respected participants have shown their interest in this question; why were everyone in such a rush to close it before all opinions were expressed?

    Second, it had to be community-wikified as soon as possible. Why didn't anyone wiki it? If it had been community-wiki I could (or anyone else could) edit the question so it'd be more along the lines of Harry's "new version".

    Third and most important - Harry, you were so eager to close the original question because it was "subjective and argumentative" but the new question is still subjective and still argumentative and for precisely the same reaons the previous question was*. As I've already stated, when asking "who's the last mathematician to have known all of math?", it's IMPLIED you ask about the mathematical development at the era the mathematician lived in (and if you thought this being implied isn't enough, and that it should be more explicit in the question, you could've edited one or two lines in the original question to make this clear). In fact I see the two questions as more or less equivalent (as evidence of this, Wadim Zudilin, who was probably unaware of the original question, commented on your question right after you posted it: "Aren't you asking about who was the last universal mathematician?"). So why did you open a new question rather than simply edit the original one?

    *On second thought, your "new" question is likely to get more "discussions" and subjective opinions (which is as far as I understand what the closers were afraid of) than the original question.

    Although it's certainly conceivable that one could give hard evidence about this question, the fact remains that there were already 5 answers several with multiple upvotes *none* of which gave hard evidence. If you think this is a good question then I think it'd be better to restart from scratch with stronger guidelines about what sorts of answers are acceptable. I tried to do that (somewhat successfully) with early comments in the "oldest open problem" question, but this question wasn't phrase in a way that would lead to good answers.
    • CommentAuthorHarry Gindi
    • CommentTimeJun 13th 2010 edited

    @danseetea, my hand was forced by the fact that the old version had four votes to reopen. As you can see if you read the comments, I was reluctant to post it at all.

    I would have edited the original question and just reopened it if it had been community wiki, but it wasn't, and the person who asked it did not respond to the calls for it to be made so. I don't understand why you're defending this question when the person who asked it was given every opportunity to fix it.

    • CommentAuthordanseetea
    • CommentTimeJun 13th 2010 edited

    @Harry - I apologize, but I fail to see why you were forced to make a new question, rather than reopen the original one, community-wiki it and change its contents slightly.

    Are you saying it is bad mathoverflow ethics to wiki someone else's question? (I am not being cynical; I am asking this seriously. I'm new here.)

    • CommentAuthorHarry Gindi
    • CommentTimeJun 13th 2010 edited

    I cannot wiki someone else's question. If you want me to be able to, vote for me in the upcoming MOderator election!

    • CommentAuthordanseetea
    • CommentTimeJun 13th 2010

    Sorry, I didn't know that. I thought anyone with 3000+ could wiki other's questions.


    Not even the 10000+ users can. Only moderators have that privilege.

    • CommentAuthordanseetea
    • CommentTimeJun 13th 2010

    Thanks. Well, given this new (for me) information, I retract most of my earlier criticism of your actions; I still think it would have been better if one could've contacted a moderator so he could wiki and re-open the question.


    I flagged the post, but it wasn't made CW, and I decided it was better to rewrite it from scratch than let the non-cw one, which everyone objected to, be reopened.


    Well, according to the rules, three 2000+ users can force community wiki by successively editing the question.