Template:Did you know nominations/Closed subgroup theorem

The following is an archived discussion of the DYK nomination of the article below. Please do not modify this page. Subsequent comments should be made on the appropriate discussion page (such as this nomination's talk page, the article's talk page or Wikipedia talk:Did you know), unless there is consensus to re-open the discussion at this page. No further edits should be made to this page.

The result was: promoted by Cwmhiraeth (talk) 06:32, 31 July 2014 (UTC)

Closed subgroup theorem

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~~... that the closed subgroup theorem was first proved in 1930 by Elie Cartan?~~

Comment: Feel free to use another hook.

Created by YohanN7 (talk). Nominated by Josve05a (talk) at 21:30, 16 July 2014 (UTC).

ALT1 ... that the closed subgroup theorem is one of several results known as Cartan's theorem?

For this hook we'll need a direct cite in the article supportin the "several known as" point. EEng (talk) 22:40, 16 July 2014 (UTC)

This version is going to be more confusing as a sound bite because there are two Cartan theorem articles, Cartan's theorem and Cartan's theorems A and B. --Mark viking (talk) 22:49, 16 July 2014 (UTC)

Confusion is a minor problem here compared to the desperate need to inject something interesting into a math hook (speaking as a degree-holder in applied math, before you say anything). EEng (talk) 23:21, 16 July 2014 (UTC)

Fair enough :) --Mark viking (talk) 00:02, 17 July 2014 (UTC)

Just in case there's some hidden romance to this theorem that can be injected, I'm paging DYK's designated math hookster David Eppstein. David, is there a love triangle we can work in here? EEng (talk) 01:32, 17 July 2014 (UTC)

Wow, this is way more technical than I usually consider appropriate for DYK in my own nominations. But anyway, how about

ALT2 ... that John von Neumann's theorem that every closed real matrix group is a Lie group inspired Élie Cartan to prove a generalization, the closed subgroup theorem?

Obviously, to use it as a hook, we would need this to be in the article (and properly sourced) first. As a source, I suggest

Bochner, S. (1958), "John von Neumann 1903–1957" (PDF), Biographical Memoirs of the National Academy of Science: 438–456. See in particular p. 441.

—David Eppstein (talk) 02:08, 17 July 2014 (UTC)

At least you've injected some inspiration. If the others want this hook, I'll augment the article per the source. EEng (talk) 02:29, 17 July 2014 (UTC)

Please augment the article anyhow. I don't know the historical order of events myself, but clearly, if von Neumann proved the theorem for closed matrix groups, it deserves to be in the article. The proof in the article is specialized to matrix groups, though the method generalizes to arbitrary groups. Come to think of it, I'm not sure Cartan proved the theorem in 1930. The cited publication is from 1930. YohanN7 (talk) 05:10, 17 July 2014 (UTC)

Happy to do it, but it might be tmw. EEng (talk) 12:08, 17 July 2014 (UTC)

I added it. —David Eppstein (talk) 18:04, 17 July 2014 (UTC)

Your alacrity is disgusting. I'll bet in school you cleaned the erasers. 19:39, 17 July 2014 (UTC)

Thank you David. But be aware of tmw. It might cause fatigue, and fatigue is not to be messed around with lightheartedly

I threw out an info-box and put a von Neumann picture in. YohanN7 (talk) 21:16, 17 July 2014 (UTC)

I think I can review this since my hook wasn't used. It's math, so NPOV, copyv/paraphr are easy passes. New enough and long enough, cites fine and hook cited as required. EEng (talk) 19:04, 30 July 2014 (UTC) P.S. I'm not applying the cite-per-paragraph thing here because that's just too ridiculous for a math proof.