tea.mathoverflow.net - Discussion Feed (Who is the last mathematician that understood all of mathematics) Sun, 04 Nov 2018 23:27:57 -0800 http://mathoverflow.tqft.net/ Lussumo Vanilla 1.1.9 & Feed Publisher François G. Dorais comments on "Who is the last mathematician that understood all of mathematics" (6070) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6070#Comment_6070 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6070#Comment_6070 Sun, 13 Jun 2010 10:42:37 -0700 François G. Dorais Well, according to the rules, three 2000+ users can force community wiki by successively editing the question.

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Harry Gindi comments on "Who is the last mathematician that understood all of mathematics" (6069) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6069#Comment_6069 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6069#Comment_6069 Sun, 13 Jun 2010 10:38:11 -0700 Harry Gindi 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.

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danseetea comments on "Who is the last mathematician that understood all of mathematics" (6068) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6068#Comment_6068 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6068#Comment_6068 Sun, 13 Jun 2010 10:36:20 -0700 danseetea 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.

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Harry Gindi comments on "Who is the last mathematician that understood all of mathematics" (6067) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6067#Comment_6067 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6067#Comment_6067 Sun, 13 Jun 2010 10:29:49 -0700 Harry Gindi Not even the 10000+ users can. Only moderators have that privilege.

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danseetea comments on "Who is the last mathematician that understood all of mathematics" (6066) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6066#Comment_6066 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6066#Comment_6066 Sun, 13 Jun 2010 10:25:07 -0700 danseetea Sorry, I didn't know that. I thought anyone with 3000+ could wiki other's questions.

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Harry Gindi comments on "Who is the last mathematician that understood all of mathematics" (6065) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6065#Comment_6065 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6065#Comment_6065 Sun, 13 Jun 2010 10:24:07 -0700 Harry Gindi I cannot wiki someone else's question. If you want me to be able to, vote for me in the upcoming MOderator election!

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danseetea comments on "Who is the last mathematician that understood all of mathematics" (6064) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6064#Comment_6064 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6064#Comment_6064 Sun, 13 Jun 2010 10:19:55 -0700 danseetea @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.)

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Harry Gindi comments on "Who is the last mathematician that understood all of mathematics" (6063) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6063#Comment_6063 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6063#Comment_6063 Sun, 13 Jun 2010 10:16:02 -0700 Harry Gindi @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.

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Noah Snyder comments on "Who is the last mathematician that understood all of mathematics" (6062) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6062#Comment_6062 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6062#Comment_6062 Sun, 13 Jun 2010 10:06:52 -0700 Noah Snyder danseetea comments on "Who is the last mathematician that understood all of mathematics" (6061) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6061#Comment_6061 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6061#Comment_6061 Sun, 13 Jun 2010 10:04:39 -0700 danseetea [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.

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Emerton comments on "Who is the last mathematician that understood all of mathematics" (6058) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6058#Comment_6058 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6058#Comment_6058 Sun, 13 Jun 2010 07:06:42 -0700 Emerton 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).

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Harry Gindi comments on "Who is the last mathematician that understood all of mathematics" (6050) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6050#Comment_6050 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6050#Comment_6050 Sun, 13 Jun 2010 02:30:55 -0700 Harry Gindi 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).

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Qiaochu Yuan comments on "Who is the last mathematician that understood all of mathematics" (6048) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6048#Comment_6048 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6048#Comment_6048 Sun, 13 Jun 2010 02:13:28 -0700 Qiaochu Yuan @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.

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Harry Gindi comments on "Who is the last mathematician that understood all of mathematics" (6045) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6045#Comment_6045 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6045#Comment_6045 Sat, 12 Jun 2010 23:15:13 -0700 Harry Gindi

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

Same here.

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Jeremy comments on "Who is the last mathematician that understood all of mathematics" (6044) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6044#Comment_6044 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6044#Comment_6044 Sat, 12 Jun 2010 21:04:18 -0700 Jeremy
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. ]]>
Scott Carnahan comments on "Who is the last mathematician that understood all of mathematics" (6043) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6043#Comment_6043 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6043#Comment_6043 Sat, 12 Jun 2010 20:54:35 -0700 Scott Carnahan 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.

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Noah Snyder comments on "Who is the last mathematician that understood all of mathematics" (6039) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6039#Comment_6039 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6039#Comment_6039 Sat, 12 Jun 2010 18:31:24 -0700 Noah Snyder François G. Dorais comments on "Who is the last mathematician that understood all of mathematics" (6034) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6034#Comment_6034 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6034#Comment_6034 Sat, 12 Jun 2010 14:12:50 -0700 François G. Dorais 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.

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Steve Huntsman comments on "Who is the last mathematician that understood all of mathematics" (6033) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6033#Comment_6033 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6033#Comment_6033 Sat, 12 Jun 2010 14:05:56 -0700 Steve Huntsman François G. Dorais comments on "Who is the last mathematician that understood all of mathematics" (6031) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6031#Comment_6031 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6031#Comment_6031 Sat, 12 Jun 2010 12:53:10 -0700 François G. Dorais 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.

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Emerton comments on "Who is the last mathematician that understood all of mathematics" (6029) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6029#Comment_6029 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6029#Comment_6029 Sat, 12 Jun 2010 11:51:13 -0700 Emerton 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).

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François G. Dorais comments on "Who is the last mathematician that understood all of mathematics" (6026) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6026#Comment_6026 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6026#Comment_6026 Sat, 12 Jun 2010 06:05:43 -0700 François G. Dorais I haven't been convinced by the arguments so far, so I'm voting to reopen.

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Harry Gindi comments on "Who is the last mathematician that understood all of mathematics" (6025) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6025#Comment_6025 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6025#Comment_6025 Sat, 12 Jun 2010 02:29:36 -0700 Harry Gindi @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?)!

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VP comments on "Who is the last mathematician that understood all of mathematics" (6024) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6024#Comment_6024 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6024#Comment_6024 Sat, 12 Jun 2010 01:58:10 -0700 VP Qiaochu Yuan comments on "Who is the last mathematician that understood all of mathematics" (6023) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6023#Comment_6023 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6023#Comment_6023 Fri, 11 Jun 2010 21:34:09 -0700 Qiaochu Yuan 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.

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Harald Hanche-Olsen comments on "Who is the last mathematician that understood all of mathematics" (6021) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6021#Comment_6021 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6021#Comment_6021 Fri, 11 Jun 2010 18:54:27 -0700 Harald Hanche-Olsen @Scott: +1. The first names that occured to me was first Euler, then Gauss.

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Scott Carnahan comments on "Who is the last mathematician that understood all of mathematics" (6020) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6020#Comment_6020 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6020#Comment_6020 Fri, 11 Jun 2010 18:16:59 -0700 Scott Carnahan
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. ]]>
danseetea comments on "Who is the last mathematician that understood all of mathematics" (6019) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6019#Comment_6019 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6019#Comment_6019 Fri, 11 Jun 2010 17:34:02 -0700 danseetea @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?

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Harry Gindi comments on "Who is the last mathematician that understood all of mathematics" (6018) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6018#Comment_6018 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6018#Comment_6018 Fri, 11 Jun 2010 17:17:34 -0700 Harry Gindi

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.

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danseetea comments on "Who is the last mathematician that understood all of mathematics" (6017) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6017#Comment_6017 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6017#Comment_6017 Fri, 11 Jun 2010 17:10:54 -0700 danseetea 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"). ]]>
Harry Gindi comments on "Who is the last mathematician that understood all of mathematics" (6016) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6016#Comment_6016 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6016#Comment_6016 Fri, 11 Jun 2010 17:04:10 -0700 Harry Gindi I've voted to close as subjective and argumentative.

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Jon Awbrey comments on "Who is the last mathematician that understood all of mathematics" (6015) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6015#Comment_6015 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6015#Comment_6015 Fri, 11 Jun 2010 17:00:48 -0700 Jon Awbrey No, clearly it should be, "Who is the last mathematician who understood all of mathematics?"

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danseetea comments on "Who is the last mathematician that understood all of mathematics" (6014) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6014#Comment_6014 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6014#Comment_6014 Fri, 11 Jun 2010 16:55:32 -0700 danseetea 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. ]]>
François G. Dorais comments on "Who is the last mathematician that understood all of mathematics" (6013) http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6013#Comment_6013 http://mathoverflow.tqft.net/discussion/439/who-is-the-last-mathematician-that-understood-all-of-mathematics/?Focus=6013#Comment_6013 Fri, 11 Jun 2010 16:42:38 -0700 François G. Dorais 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.

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