Timeline for Most interesting mathematics mistake?
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 10, 2013 at 23:21 | comment | added | Kevin O'Bryant | That's what I had in mind, sorry for the confusion. But in my defense, can't circles on the surface of a torus have 4 intersections? And $p$-adic circles have infinitely many? | |
| Nov 7, 2013 at 22:55 | comment | added | Gerry Myerson | @Todd, yes, unless Kevin is thinking of something that has escaped both of us, then I think it is as you say. | |
| Nov 7, 2013 at 22:47 | comment | added | Todd Trimble | @GerryMyerson Yes, sure, but the way my pedantic mind works: I think it's still true that over any field, two distinct circles intersect in less than three points. So I guess what you're suggesting is that there was something buggy about the description of when each of those three cases occurs (and that Kevin's description was a shorthand). | |
| Nov 7, 2013 at 22:37 | comment | added | Gerry Myerson | @Todd, perhaps what Kevin was referring to was the assumption that, for example, the circles centered at $A$ and $B$ with radius $AB$ intersect at all. This assumes a completeness which Euclid never made explicit. | |
| Nov 7, 2013 at 22:11 | comment | added | Todd Trimble | Kevin, at the risk of asking something stupid: what's the problem with circles intersecting in 0, 1, or 2 points? | |
| Nov 7, 2013 at 13:36 | comment | added | Pietro Majer | But "Contains errors from start to finish", seems quite an exaggeration. | |
| Jun 26, 2011 at 19:38 | comment | added | Kevin O'Bryant | Some poor grammar there on my part. Hilbert tried to correct Euclid's work, and needed around 20 axioms (not 5) to do so. These are seen today as being primarily topological in nature (like that the points on a line are ordered meaningfully, or that circles have insides and outsides). en.wikipedia.org/wiki/Hilbert%27s_axioms | |
| Jun 26, 2011 at 13:25 | comment | added | Qfwfq | Wh.. what ?? | |
| Mar 14, 2010 at 19:36 | comment | added | Kevin O'Bryant | The most famous is the assumption that two circles intersect in 0, 1, or 2 points. It was already seen to be buggy in ancient times (Theon or Hypatia gap-system.org/~history/Printonly/Theon.html corrected some errors), and from what I've read Hilbert did also. | |
| Mar 13, 2010 at 7:55 | comment | added | Ilya Grigoriev | Any examples of such errors? Any interesting ones? | |
| Dec 16, 2009 at 13:58 | history | answered | Kevin O'Bryant | CC BY-SA 2.5 |