Talk:Brouwer fixed-point theorem

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Accessible proof[edit]

Courant and Robbins provide an accessible proof. —Preceding unsigned comment added by (talkcontribs) 30 August 2001

First proved by Bol?[edit]

According to Lyusternik Convex Figures and Polyhedra, the theorem was first proved by a Lettish mathematician named Bol. No references are provided. Anyone know what this is about?-- 00:08, 18 Feb 2005 (UTC)

Citation style[edit]

This article mixes parenthetical referencing with footnoted references. The parenthetical ones were there first, so according to WP:CITEVAR we'd have to use that until explicit consensus. However, it would be significantly easier to turn the couple of parenthetical ones into footnotes than about 50 footnotes into parentheticals. Can we form consensus to continued using footnoted references? – Finnusertop (talkcontribs) 19:59, 24 February 2019 (UTC)

I'm sure that'd be okay here. –Deacon Vorbis (carbon • videos) 00:04, 25 February 2019 (UTC)
Great. I've turned the remaining parentheticals into footnotes. – Finnusertop (talkcontribs) 00:10, 25 February 2019 (UTC)

Function mapping in closedness section[edit]

It is stated that the function f(x) = (x+1)/2 is a continous function from the open interval (-1,1) to itself. Is it not the case that the function maps from (-1,1) to (0,1)? Salomonaber (talk) 00:13, 11 March 2020 (UTC)

It doesn't claim (nor is it required) that the function is surjective, so what's there is correct and appropriate. The example could have even arranged for a bijection, but I don't think it matters much either way. –Deacon Vorbis (carbon • videos) 00:32, 11 March 2020 (UTC)

Highly skeptical that the remarks "said to have [been] added" by Brouwer are actually due to him[edit]

Brouwer is said to have added: "I can formulate this splendid result different, I take a horizontal sheet, and another identical one which I crumple, flatten and place on the other. Then a point of the crumpled sheet is in the same place as on the other sheet."

The citation is apparently from a French-language educational TV show ( The remarks appear to be spoken by a fictional Brouwer trying to explain his result. The web page that this refers to gives no citation.

I would like to know who originally came up with the "crumpled paper theorem" explanation of the BFPT. It could have been Brouwer himself, but my guess is it was not. — Preceding unsigned comment added by Natkuhn (talkcontribs) 01:06, 8 May 2020 (UTC)

Oops, yeah, that's a good catch. This probably deserves some looking into. –Deacon Vorbis (carbon • videos) 01:19, 8 May 2020 (UTC)