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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.
No, clearly it should be, "Who is the last mathematician who understood all of mathematics?"
I've voted to close as subjective and argumentative.
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.
@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?
@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.
@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.
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.
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.
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.
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:
Disclaimer:
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).
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).
[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.
@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.
@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.)
I cannot wiki someone else's question. If you want me to be able to, vote for me in the upcoming MOderator election!
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.
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.
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