Timeline for What is the oldest open problem in mathematics?
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 16 at 7:07 | comment | added | Jeppe Stig Nielsen | The reason why you consider this still open (despite the Gauss–Wantzel theorem from 1837) is because it is not known what Fermat primes exist other than $F_0$ through $F_4$? | |
| Dec 31, 2022 at 23:54 | comment | added | Oscar Lanzi | Just because they found a neusis construction for the regular heptagon (which I don't think is undisputed), it does not follow that they thought it was not constructible by Euclidean methods. They may have meant the neusis solution to be a "stopgap" pending a Euclidean one. | |
| Jun 5, 2010 at 8:05 | comment | added | John Stillwell | @coudy: I think it very plausible that the Greeks asked whether there are $n$-gons that can't be constructed with ruler and compass, and that they thought $n=7$ is an example (because they were willing to use neusis to construct it).However, under your reference/date conditions I'm afraid no question from ancient Greek times is going to qualify. There is no exact date for the works of Euclid or Archimedes, and we don't have the original manuscripts. | |
| Jun 5, 2010 at 7:38 | comment | added | coudy | @Gerald. Not really. I insist on providing a reference and a date, so that anybody can make its own opinion. Also the question about the seven-gon is solved, isn't it ? @John. Is it plausible that the greek actually asked "which regular n-gons are constructible by ruler and compass" ? It is more likely that they asked "Whether there are n-gons that can't be constructed with ruler and compass" (which is solved). The former question does not really make sense before you have the answer for the later. Any reference welcome. | |
| Jun 5, 2010 at 3:37 | comment | added | Gerald Edgar | "the question probably crossed their minds" ... the OP will have to tell us if that qualifies. | |
| Jun 5, 2010 at 1:33 | comment | added | John Stillwell | I can't say that the Greeks explicitly asked the question about $n$-gons, but they considered enough special cases that the question probably crossed their minds. Euclid has $n=3,4,5,6,15$ and there were attempts for $n=7$. Archimedes gave a construction of the 7-gon using "neusis" (a sliding ruler device that also allows trisection of angles) so the 7-gon problem was certainly of interest to the Greeks. | |
| Jun 5, 2010 at 1:30 | history | edited | John Stillwell | CC BY-SA 2.5 |
constructible
|
| Jun 4, 2010 at 23:00 | comment | added | Noah Snyder | Why wasn't constructing the 7-gon a famous question like squaring the circle, doubling the cube, and trisecting the angle? If the Greeks did consider this an open problem, why was it considered less important than the others? (Or is the emphasis of those three problems something that happened later?) | |
| Jun 4, 2010 at 22:53 | comment | added | Victor Protsak | Do you know whether the question was explicitly asked, outside of the context of trisecting the angle? I thought that a revolutionary aspect of Gauss's discovery was that it had been assumed no cases beyond classically known were possible, but I don't know whether there was a specific claim made to that effect. | |
| Jun 4, 2010 at 22:44 | comment | added | Gerald Edgar | Is there evidence that the Greeks asked this question? | |
| Jun 4, 2010 at 22:09 | history | answered | John Stillwell | CC BY-SA 2.5 |