Timeline for Most interesting mathematics mistake?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Mar 28, 2018 at 17:48 | comment | added | roy smith | Thank you Danny! I have now read more in detail from talks by Bott and see that he mentions a controversy over the correct value of the 10th! homotopy group of U, as inspiring his interest. ac.els-cdn.com/0001870870900307/… | |
| Mar 26, 2018 at 17:02 | comment | added | Danny Ruberman | @roysmith: I think you're mixing a couple of stories. The computation of $\pi_2$ was sorted out by 1950, probably much earlier, but certainly before Bott had really started down the path to periodicity. See Pontrjagin's 1950 paper, Homotopy classification of the mappings of an (n+2)-dimensional sphere on an n-dimensional one, or G. Whitehead (Ann. of Math. 52 (1950)). Eckmann's review of the former clearly indicates the role of the Arf invariant. There were early homotopy theory calculations that seemed to contradict Bott periodicity; Bott tells the story in various autobiographical pieces. | |
| Feb 7, 2016 at 0:13 | comment | added | roy smith | I am glad this mistake had some good consequence. i had only heard that it delayed Bott's proof of his periodicity theorem, since it seemed to contradict that result. | |
| Oct 1, 2015 at 23:09 | comment | added | Ilya Grigoriev | @JimConant: Yes, of course. | |
| Sep 29, 2015 at 13:30 | comment | added | Jim Conant | @IlyaGrigoriev: Do you mean "before Milnor, everybody thought it obvious that two topological n-spheres could NOT have different structures as differentiable manifolds"? | |
| Mar 13, 2010 at 8:02 | comment | added | Ilya Grigoriev | A mistake in a close field (I can't do another answer): before Milnor, everybody thought it obvious that two topological n-spheres could have different structures as differentiable manifolds. I'm pretty sure Milnor himself thought he made a mistake when some invariant turned out to be different for two topological spheres. For details, see the third volume of his collected papers. | |
| Oct 17, 2009 at 17:58 | history | made wiki | Post Made Community Wiki by David Zureick-Brown | ||
| Oct 17, 2009 at 16:09 | history | answered | Reid Barton | CC BY-SA 2.5 |