Talk:Brouwer fixed-point theorem

Accessible proof

Courant and Robbins provide an accessible proof. —Preceding unsigned comment added by 198.144.199.xxx (talk • contribs) 30 August 2001

First proved by Bohl or Brouwer?

According to Lyusternik Convex Figures and Polyhedra, the theorem was first proved by a Lettish mathematician named Bohl. No references are provided. Anyone know what this is about?--192.35.35.36 00:08, 18 Feb 2005 (UTC)

- In the book History of Topology by James, on pages 273-274, it says: "Bohl's theorem is also equivalent to the Brouwer theorem. Bohl's theorem was published in 1904, with a proof that required that f be differentiable. Brouwer published his fixed point theorem, for continuous functions on the 3-ball, in 1909. When the first proof for the n-ball, with f differentiable, appeared in print a year later, in an appendix by J. Hadamard to a text by Tannery, the theorem was called the 'Brouwer Fixed Point Theorem', which suggests that the result was already famous by that time. It is not known in what year Brouwer made his discovery and, apparently, communicated it to other mathematicians in an informal manner. The first published proof of the general case, that is, for continuous functions on the n-ball, was by Brouwer himself in 1912."

Citation style

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 (talk ⋅ contribs) 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 (talk ⋅ contribs) 00:10, 25 February 2019 (UTC)

Function mapping in closedness section

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

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 (https://archive.is/20130113210953/http://archives.arte.tv/hebdo/archimed/19990921/ftext/sujet5.html). 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 (talk • contribs) 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)