Timeline for Applications of nonconstructive mathematics
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 1, 2013 at 16:52 | comment | added | Martin Ziegler | The degree of non-constructivity of Brouwer's fixed point theorem in various dimensions is explored in the following publication: link.springer.com/chapter/10.1007%2F978-3-642-30870-3_7 See in particular reference [12] to the paper by Orevkov in 1963! | |
| Jun 4, 2012 at 21:10 | comment | added | Felix Goldberg | @Andrej Bauer: Not to put too fine a point on it, but the blog post first gave a link to the paper and then explained a toy example. | |
| Jun 2, 2012 at 8:11 | comment | added | Andrej Bauer | @Michael: That's a different link. A blog post which mentions a toy example and then says "and there are other cool applications" is not a "serious application of Brouwer fixed point theorem". I never denied that there are such applications. Of course there are! | |
| May 16, 2012 at 8:12 | comment | added | Michael Greinecker | @Andrej: You consider cowles.econ.yale.edu/P/cp/p00b/p0087.pdf to be popular math?? | |
| May 15, 2012 at 8:57 | comment | added | Andrej Bauer | The jstor paper referenced above is "constructive" in the sense that it is "explicit". The paper is written in classical logic, it seems. | |
| May 15, 2012 at 5:12 | comment | added | Andrej Bauer | This worries me: jstor.org/stable/2156239. I will look at full version when I get to my office (stupid paywall), there must be an assumption that is not stated on the first page. | |
| May 15, 2012 at 5:10 | comment | added | Andrej Bauer | @Igor: arxiv.org/abs/0804.3199 | |
| May 15, 2012 at 0:16 | comment | added | Igor Rivin | I was talking about the approximate version, you are right. Can you give a reference about what you mentioned (about the effective topos)? | |
| May 14, 2012 at 21:01 | comment | added | Andrej Bauer | Thanks, but Brouwer Fixed point theorem fails in the effective topos, therefore it cannot have a constructive proof. Of course, the approximate version is constructive. The link pointed to in the answer is not a serious application, it is just popular math. | |
| May 14, 2012 at 20:45 | comment | added | Qiaochu Yuan | @Andrej: en.wikipedia.org/wiki/Sperner's_lemma | |
| May 14, 2012 at 20:40 | comment | added | Andrej Bauer | @Igor: Brouwer Fixed Point Theorem is not constructive. What are you referring to? | |
| May 14, 2012 at 18:43 | history | made wiki | Post Made Community Wiki by François G. Dorais | ||
| May 14, 2012 at 16:11 | comment | added | Felix Goldberg | Yes, you are right. I was thinking of the original proof... | |
| May 14, 2012 at 16:06 | comment | added | Igor Rivin | The standard proof (using Sperner's lemma) is quite constructive, I think. | |
| May 14, 2012 at 16:04 | history | answered | Felix Goldberg | CC BY-SA 3.0 |