Talk:Dirichlet problem

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Oleg Alexandrov made a minor change while I was adding text and the equation, which was inadvertantly wiped out when I saved. I've removed the "homeschooler" as Oleg did, as I concur with his edit -- D'n 02:46, 6 December 2005 (UTC)


The "formal mathematical definition" appears to be an attempt to state a theorem, NOT a definition. Michael Hardy 02:59, 6 December 2005 (UTC)

In Line[edit]

Oleg writes (in D'n's Talk): I did minor style fix-ups. The most important one in my view is that per the math style manual one should attempt to avoid having inline formulas show up as PNG images, as then they may show up of different size than text.

Since the \partial and \bar occur in-line and can only be PNG, wouldn't the other math expressions look more consistent that way also? D'n 03:09, 6 December 2005 (UTC)
I don't know what to say. As long as you are aware of the policy (of which you may have not), you can do anything you please. :) You have a good point. Oleg Alexandrov (talk) 03:13, 6 December 2005 (UTC)
I wasn't aware of the policy, thank you, Oleg, and I forgot completely that there's a ∂ HTML construction for ∂! D'n

Article Introduction[edit]

To Brian Tvedt (talk), I like what you did for the opening sentence. I was trying to get to that, but you've done it better than I could! D'n 00:20, 8 December 2005 (UTC)

Thanks. One way the intro could be improved is to make it more clear that the term is ambigous. Historically it referred specifically to Laplace's equation, and that is what the article mostly talks about, but nowadays it usally refers to the analogous problem for other classes of PDE. Brian Tvedt 12:17, 8 December 2005 (UTC)

Viscardi's prize[edit]

I do, however, feel that Viscardi's work, albeit too recent to judge if it is notable in the mathematical or application sense, is definitely notable in that it brought this highly refined mathematical topic to the headlines of many major news sources and blogs. For that reason I've reinstated a paragraph about this event, but linked it to the Forbes publishing of the AP lead on this article rather than to the Yahoo site. D'n 02:10, 8 December 2005 (UTC)

So far, it doesn't seem to have made "headlines" anywhere. An AP wire story is not a headline. I did a search on Google News, and the story has only appeared in the local Southern California press and the business press, who carry these sorts of corporate-PR stories in the back pages routinely. I have to say that many of the news stories that have appeared seem to be poorly informed on the mathematics, leaving the impression the Dirichlet Problem is a famous unsolved question, when in fact it was pretty well understood by the early twentieth century. Let's be real here: the current Wikipedia article doesn't even mention the important contributions that great mathematicians including Green, Gauss, Poincaré, Lebesgue and Hadamard have made to this problem. I have no doubt that Viscardi is a "super-duper mathematics student" (as one of the judges said about him), but there is absolutely nothing to indicate that he's done anything comparable to those historical figures. High school students win science competitions every year. Brian Tvedt 12:12, 8 December 2005 (UTC)
Thank you for taking the time to respond. I don't agree, and I don't want to get into an edit war, so let's see if I can convince you of my POV ;)
You say (please correct me if I err) that 1) the news story isn't as big as I think it is, just locally important or corporate, and 2) The current article is incomplete in that it doesn't mention various major mathemetiticians' work on the Dirichlet problem.
As far as being not being major or being merely local, I'm nowhere near Southern California -- yet I picked up the story enough to realize that the stub in Wiki was so sparse and complex, as to cry out for revision. Now, I routinely don't use Google, but other search engines. This is what I discovered, outside of California & Corporate press, and it's just the first 4 pages of listings:
  • TECH Press
Regarding the lack of mention of major mathemeticians, I agree -- this is a lack. But I don't think that merely because we (the Wiki community) haven't gotten around to doing this, is a reason to drop the Viscardi's mention. Perhaps new section at the end, ==History==, and detail the input of the mathemeticians, as well as Viscardi.
You also say, "I have to say that many of the news stories that have appeared seem to be poorly informed on the mathematics..." I fully concur! I think, however, that making the Dirichlet problem clearer to the non-mathematical reader should be the goal here. I've always understood that Wiki is not a series of specialized texts, but aimed at bringing information and knowledge to the general non-specialist public. Here we have rather unique opportunity to do this, where this rather obscure area in mathematics suddenly was whisked into the public, non-mathematical limelight, and people of all backgrounds and ages will be turning to this article to understand just what it was that the 16-yr-old did. D'n 22:46, 8 December 2005 (UTC)
We really need a statement of what was proved, whether this was numerical analysis or a piece of pure mathematics (I expect the former) and so on. The emphasis on areas of application is something that makes anyone familiar with science journalism very suspicious. Charles Matthews 23:07, 8 December 2005 (UTC)
Even more than that, we need some independent verification that this is an important contribution - original, correct, and a significant advance over the prior state of knowledge. If the young man gets his work published in a peer-reviewed journal, that would mean something. The judges of the Siemens Westinghouse competition are simply not qualifed to make this determination. Brian Tvedt 01:34, 10 December 2005 (UTC)
D'n: I still think you are vastly overestimating the newsworthiness of this. Most of the links you found are just verbatim copies of the AP wire story, which many news outlets carry routinely on their web sites. There is no evidence that the story was broadcast on CBS or ABC, or that it made the print edition of the Washington Post (much less as a headline). And those stories give about the same amount of space to the other winners of the competition, a team that developed "computer technology that could help locate the genetic roots of some inherited diseases..." (and won the same amount of money as Viscardi). Do we need to insert that story into the article on inherited disease? Every time a high school student wins a science competition on topic X, are we going to insert that into the Wikipedia article on X? I think you are very unlikely to prevail if you try to persuade editors that this belongs in the article. There are fairly widely agreed upon notabillity standards for inclusion in Wikipedia, and it seems to me this clearly does not meet them. Brian Tvedt 01:34, 10 December 2005 (UTC)

Probabilistic Solution[edit]

Do you think it would be appropriate to mention the probabilistic solution to the Dirichlet problem? I.e., u(z) = E[f(B(\tau_D))|B(0) = z], where B is Brownian motion and \tau_D is the exit time from the domain. If so, I'll create an account and suggest some text. (talk) 22:57, 30 July 2008 (UTC)

WikiProject class rating[edit]

This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 09:48, 10 November 2007 (UTC)