Timeline for Not especially famous, long-open problems which anyone can understand
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Nov 9, 2022 at 11:26 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Jun 25, 2020 at 14:56 | comment | added | Ryan | I would make the same bet for mathematicians to be honest, especially since you’ve already pitched it as “drawing” a curve.... I don’t think that addresses YCor’s point. | |
| Oct 24, 2019 at 19:02 | comment | added | Noah Snyder | I'm very happy to bet if you ask 100 non-mathematicians to draw a curve in the plane that at least 99 of them will draw something piecewise smooth! | |
| Oct 24, 2019 at 16:12 | comment | added | YCor | @NoahSnyder I know people who have an intuition of what is a "curve in the plane" and do not know what a derivative is. What is their intuition of what it is, and whether it involves smoothness, I wouldn't decide for them. | |
| Oct 24, 2019 at 15:40 | comment | added | Noah Snyder | @YCor: I think there's a huge difference between how easy it is to imagine the line being infinitely thin, and how easy it is to imagine continuous functions that are not piecewise smooth. I think the average calculus student thinks the word function means piecewise smooth function (possibly with isolated non-continuous points). | |
| Oct 24, 2019 at 14:36 | comment | added | YCor | @NoahSnyder also if you draw with the pencil the thickness of the line is not zero. Actually I think that people beyond mathematicians are able to conceive by themselves that the mathematical definition is an extrapolation of the intuitive definition, rather than a literal interpretation. | |
| Oct 24, 2019 at 14:32 | comment | added | YCor | For reference, this was asked by Toeplitz in 1911. Here is a text by Étienne Ghys (in French) with various historical facts about it. | |
| Sep 14, 2018 at 21:56 | comment | added | Zemyla | 3Blue1Brown did a video on this problem and a weakening of it (the inscribed rectangle problem) which was recently solved, that I feel is rather understandable to a layman. | |
| Oct 30, 2016 at 19:56 | history | edited | Timothy Chow | CC BY-SA 3.0 |
added reference
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| Jul 19, 2013 at 5:33 | history | edited | Igor Pak | CC BY-SA 3.0 |
simpler version
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| Aug 24, 2012 at 22:48 | comment | added | Feldmann Denis | Well, not if you shake your hand fast enough (or with enough brownian motion) | |
| Jun 24, 2012 at 3:40 | comment | added | Noah Snyder | The issue here is that intuitive "definitions" of continuous tend to be wrong. "You can draw it without lifting your pencil" really means at least piecewise smooth. | |
| Jun 22, 2012 at 13:14 | comment | added | Henry Cohn | Actually, I disagree that anyone can (quickly, easily) understand what such a map is for the purposes of this problem, since the maps for which it's not known are of a sort even mathematicians didn't realize existed until well into the 19th century. One can still state the problem, but it's likely to lead to conversations of the following sort. "Wow, so you mean nobody knows in advance if this curve [draws a curve] has a square in it?" "Well, actually we know that case, or really any curve you can draw, but mathematicians have discovered exotic curves for which we don't know the answer." | |
| Jun 22, 2012 at 6:44 | comment | added | Fernando Muro | I do think that anyone can understand whats an injective, continuous map from the circle to the plane. | |
| Jun 22, 2012 at 2:05 | comment | added | Timothy Chow | This is a nice problem but it's only open in the case where the curve is pathologically ugly, in a way that perhaps not "anyone can understand." | |
| Jun 21, 2012 at 23:46 | history | answered | Malik Younsi | CC BY-SA 3.0 |