Timeline for Was there a time in mathematics when a counterexample was wrong? [closed]
Current License: CC BY-SA 4.0
21 events
| when toggle format | what | by | license | comment | |
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| Oct 10, 2021 at 19:49 | comment | added | Pietro Majer | Zeno’s paradoxes against motion may be considered as wrong mathematical counter-examples, although they address to the physic side | |
| Jun 3, 2021 at 3:06 | review | Reopen votes | |||
| Jun 4, 2021 at 3:07 | |||||
| May 27, 2021 at 21:49 | comment | added | Yaakov Baruch | @KConrad Besides Timothy's good point, a (wrong) counterexample (temporarily) proves the claim to be false, unlike finding a mistake in the proof, which only reverts the claim to unproven status. | |
| May 27, 2021 at 20:39 | comment | added | Timothy Chow | @KConrad I interpret Mage Magic to be asking essentially the same question as the other MO question (Widely accepted mathematical results that were later shown to be wrong?) except that Mage Magic is specifically asking for a widely accepted counterexample, because counterexamples have a reputation for being "easy to check." It's harder to imagine an incorrect counterexample being erroneously accepted as correct than it is to imagine an arbitrary wrong proof being erroneously accepted as correct. | |
| May 27, 2021 at 20:29 | comment | added | Timothy Chow | The top answer to Widely accepted mathematical results that were later shown to be wrong? mentions a 1994 Annals paper by Gaoyong Zhang, whose main result can be interpreted as stating that the unit cube in $\mathbb{R}^4$ is a counterexample to the claim that every origin-symmetric convex body in $\mathbb{R}^4$ is something called an "intersection body." This was regarded at the time as demonstrating that the Busemann-Petty problem has a negative answer in dimension 4. But Zhang's paper turned out to be wrong. | |
| May 27, 2021 at 15:10 | review | Reopen votes | |||
| May 27, 2021 at 23:51 | |||||
| May 27, 2021 at 14:45 | comment | added | Yaakov Baruch | @ZhenLin. I took a look. What really happens there is that the definition of polyhedron is stretched in such a way that yes the conjecture fails for it, but it's not an instance where a good faith wrong counterexample is given. | |
| May 27, 2021 at 13:01 | history | closed |
Steven Landsburg Sam Hopkins YCor Alex M. Alexandre Eremenko |
Not suitable for this site | |
| S May 27, 2021 at 10:22 | history | edited | Alec Rhea | CC BY-SA 4.0 |
fixed punctuation
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| S May 27, 2021 at 10:22 | history | suggested | Buzz | CC BY-SA 4.0 |
fixed punctuation
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| May 27, 2021 at 10:19 | history | became hot network question | |||
| May 27, 2021 at 10:19 | history | became hot network question | |||
| May 27, 2021 at 10:19 | history | became hot network question | |||
| May 27, 2021 at 5:37 | comment | added | Zhen Lin | Perhaps the theorem that the Euler characteristic of a polyhedron is 2 is an example of what you are looking for. The telling in Proofs and Refutations is a very good read. | |
| May 27, 2021 at 3:59 | answer | added | Buzz | timeline score: 23 | |
| May 27, 2021 at 3:27 | review | Suggested edits | |||
| S May 27, 2021 at 10:22 | |||||
| May 27, 2021 at 3:20 | comment | added | KConrad | For the issue of "how we know what we know to be true" I think something in the spirit of what you are asking is a proof of a theorem that is accepted for a reasonable period of time, the proof turns out to be wrong, and later the theorem is proved correctly by another method. After all, why is it important for a supposed theorem to be disproved by a counterexample that winds up being wrong instead of the original proposed proof of the theorem being wrong instead? Something along those lines is the saga of the four-color theorem. It was conjectured in 1852 and "proved" by Kempe in 1879 and T | |
| May 27, 2021 at 2:55 | review | Close votes | |||
| May 27, 2021 at 13:06 | |||||
| May 27, 2021 at 2:35 | comment | added | Steven Landsburg | This happens to me approximately once per week. | |
| May 27, 2021 at 2:21 | review | First posts | |||
| May 27, 2021 at 7:10 | |||||
| May 27, 2021 at 2:18 | history | asked | Mage Magic | CC BY-SA 4.0 |