Wikipedia:Featured list candidates/Hilbert's problems
Hilbert's problems[edit]
Noone has taken the hint on the talk page: I think this is good enough. -- ALoan (Talk) 14:12, 26 July 2005 (UTC)
- It's an appealing idea to have this page as a featured list. I'm not sure, though, that it's ever really going to meet the criterion of non-controversiality, especially if people start looking at it closely again. My position on Problem 1 is stark: The continuum problem is still open. Many disagree; I recently changed the entry to "No consensus". --Trovatore 15:13, 26 July 2005 (UTC)
- Complicating matters is the fact that Hilbert spoke for some time about some of the problems; boiling each of them down to a phrase is sure to lose some information. In particular, the discussion of Problem 2 would have to include a close reading trying to figure out just what he meant. --Trovatore 15:13, 26 July 2005 (UTC)
- Still, I like the idea--provided the finished product does not claim agreement among mathematicians that does not in fact exist. --Trovatore 15:13, 26 July 2005 (UTC)
- Object Can't understand it, and that's with a first-class degree in mathematics from 10 years ago. Needs to be simplified so a layman can understand what it's all about, jguk 18:02, 26 July 2005 (UTC)
- Sorry - please could you explain in more detail which parts of the list do you not understand. I am not a mathematician at all, but I can see that this is a list of 23 (or 24) "important" maths problems selected in 1900 by a leading mathemetician, with an indication of the status of the problem ("solved" or not), a brief description of the problem, and the link to the relevant "main" article, such as Hilbert's first problem. This page page is not meant to give more than a brief description of the problem: each problem is discussed in further detail in its own page (although 8 out of 23 are still unfortunately red). Would it help to add more wikilinks to the brief descriptions? (I have tweaked a bit)-- ALoan (Talk) 18:48, 26 July 2005 (UTC)
- It's the brief descriptions I don't understand - they need to be expanded at least to give an idea to the layman as to what the problem is, jguk 19:28, 26 July 2005 (UTC)
- In the light of the comments below, can I invite you to reconsider, or at least explain what you would like the description column to say. For example, what should Problem 6 ("Axiomatize all of physics.") say? -- ALoan (Talk) 18:46, 2 August 2005 (UTC)
- Well let's take Problem 12, for example: Extend Kronecker's theorem on abelian extensions of the rational numbers to any base number field. What does this mean? Or problem 21: Proof of the existence of linear differential equations having a prescribed monodromic group. I can't even begin to form a view as to what the problem really is. Surely there must be some way of explaining the concepts briefly to a layman? jguk 19:10, 2 August 2005 (UTC)
- Well, you are the mathematician, but:
- 12th - can I assume you have read Hilbert's twelfth problem, Kronecker's theorem, abelian extension, rational number and number field?
- 21st - ditto Hilbert's twenty-first problemlinear differential equation and monodromic group?
- However, I have just found this excellent site which may help massively on an attempt to describe many of the other problems, since I am already well out of my depth, but is not much use on the 12th and 21st problems. -- ALoan (Talk)
- Well, you are the mathematician, but:
- Well let's take Problem 12, for example: Extend Kronecker's theorem on abelian extensions of the rational numbers to any base number field. What does this mean? Or problem 21: Proof of the existence of linear differential equations having a prescribed monodromic group. I can't even begin to form a view as to what the problem really is. Surely there must be some way of explaining the concepts briefly to a layman? jguk 19:10, 2 August 2005 (UTC)
- In the light of the comments below, can I invite you to reconsider, or at least explain what you would like the description column to say. For example, what should Problem 6 ("Axiomatize all of physics.") say? -- ALoan (Talk) 18:46, 2 August 2005 (UTC)
- It's the brief descriptions I don't understand - they need to be expanded at least to give an idea to the layman as to what the problem is, jguk 19:28, 26 July 2005 (UTC)
- Sorry - please could you explain in more detail which parts of the list do you not understand. I am not a mathematician at all, but I can see that this is a list of 23 (or 24) "important" maths problems selected in 1900 by a leading mathemetician, with an indication of the status of the problem ("solved" or not), a brief description of the problem, and the link to the relevant "main" article, such as Hilbert's first problem. This page page is not meant to give more than a brief description of the problem: each problem is discussed in further detail in its own page (although 8 out of 23 are still unfortunately red). Would it help to add more wikilinks to the brief descriptions? (I have tweaked a bit)-- ALoan (Talk) 18:48, 26 July 2005 (UTC)
- Comment I have to admit that I have no idea what some of the terms used in the list mean, but I expect that's what the list is for - a bunch of links to more comprehensive articles that (hopefully, if I cared about math at all) would explain them. As such, I'd like to support, but first I want to see a few less redlinks for the problems. Eight out of 23 isn't a lot, but even a few less would be much better. If this changes, I will support. --Sophitus 21:01, July 26, 2005 (UTC)
- Right, I've added some stubs to deal with the redlink issue. I've also tweaked the descriptions in a few cases, but I'm not entirely sure how to turn the Riemann hypothesis (and others) into layman's language. -- ALoan (Talk) 19:46, 30 July 2005 (UTC)
- Support. Grue 11:52, 1 August 2005 (UTC)
- Support now that I have added percentage widths to each column of the table. --Spangineer (háblame) 17:59, August 2, 2005 (UTC)
- Thanks, but I'm not sure that explicitly setting widths is really needed where there is only one table (where there is more than one table, it helps to make them consistent). I've tweaked to make "Problem" and the number appear on the same line on narrower displays. -- ALoan (Talk) 18:46, 2 August 2005 (UTC)
- That was my concern. I'm using 1024x768 and before I made the change I saw them on two lines. I guess I didn't make the column big enough for 800x600. If it's possible to define the first column to be a set number of pixels and let the others do what they please, that would be great, but I'm not sure it's possible. --Spangineer (háblame) 19:27, August 2, 2005 (UTC)
- Ah - when the columns get small enough to be shorter than the longest word, the % width is ignored anyway. Perhaps the best way to achieve this would be to add a between them? -- ALoan (Talk) 11:29, 3 August 2005 (UTC)
- I thought about that last night; I guess great minds think alike =). Looks great now. --Spangineer (háblame) 14:16, August 3, 2005 (UTC)
- Ah - when the columns get small enough to be shorter than the longest word, the % width is ignored anyway. Perhaps the best way to achieve this would be to add a between them? -- ALoan (Talk) 11:29, 3 August 2005 (UTC)
- That was my concern. I'm using 1024x768 and before I made the change I saw them on two lines. I guess I didn't make the column big enough for 800x600. If it's possible to define the first column to be a set number of pixels and let the others do what they please, that would be great, but I'm not sure it's possible. --Spangineer (háblame) 19:27, August 2, 2005 (UTC)
- Thanks, but I'm not sure that explicitly setting widths is really needed where there is only one table (where there is more than one table, it helps to make them consistent). I've tweaked to make "Problem" and the number appear on the same line on narrower displays. -- ALoan (Talk) 18:46, 2 August 2005 (UTC)
- NOTE: Another borderline one. ALoan doesn't appear to have used his "find" to alter the article (though if I'm wrong I'm sure I'll be corrected). Leave listed to 14:12 on 9 August to allow for more comments/improvements, jguk 08:57, 6 August 2005 (UTC)
- Sorry, just not had time in the last few days. I also need to tweak United Nations member states, as it happens. -- ALoan (Talk) 21:33, 7 August 2005 (UTC)
- (I'm afraid I don't have time to do these myself; I've just moved and don't have a permanent place to stay yet, so apartment hunting comes first.) Two big problems with 1 and 2: Prob 1 is still a redirect to Continuum hypothesis, which is not quite accurate; the first problem also involved finding a wellordering of the reals. Just what "finding" means here is not entirely clear. It could be argued that this part of the first problem was solved by Zermelo in the proof of the Well-ordering theorem from the axiom of choice, but it depends upon the reading. There are several interesting things that could be said about finding a particular wellordering, depending again on what "particular" means. --Trovatore 23:20, 7 August 2005 (UTC)
- I don't disagree with the "resolved" label for prob 2, because we now know rather precisely under just what assumptions the consistency of PA may be proved, but this should be explained explicitly somewhere. --Trovatore 23:24, 7 August 2005 (UTC)