Timeline for Does anyone know a polynomial whose lack of roots can't be proved?
Current License: CC BY-SA 2.5
18 events
| when toggle format | what | by | license | comment | |
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| Aug 26 at 17:28 | comment | added | Daniel Genin | This may be a naive question but can't the integer root of a polynomial equation be found by iterating over all possible inputs? So, if a root is found this way there would be no problem showing that the equation is solvable? Is the point that there is no computational procedure to decide whether a root exists relying only on the axioms of ZFC? | |
| Nov 27, 2011 at 5:47 | answer | added | Vladimir Reshetnikov | timeline score: 39 | |
| Jul 23, 2010 at 1:29 | comment | added | Akhil Mathew | @Anweshi: I think so, at least if you can prove ZFC consistent in some other system. But my knowledge here is very lacking. | |
| Jul 22, 2010 at 18:19 | comment | added | Anweshi | Oh, so you mean there is a proof in some other system, but you cannot prove in ZFC? | |
| Jul 22, 2010 at 16:51 | comment | added | BlueRaja | For those unaware: The site is math.stackexchange.com, and is meant for the kind of questions that would get closed on MO. It is in closed beta, but will be open to the public in 5 or 6 days. | |
| Jul 22, 2010 at 16:37 | comment | added | Akhil Mathew | @Anweshi: That there isn't a proof using ZFC that the polynomial has no roots. | |
| Jul 22, 2010 at 12:15 | comment | added | Anweshi | What is the meaning of "lack of roots can't be proved"? That the existence of roots, and the nonexistence, are both consistent with ZFC? Or that it actually does not have roots, but you cannot prove it? | |
| Jul 22, 2010 at 12:10 | vote | accept | Akhil Mathew | ||
| Jul 22, 2010 at 7:57 | answer | added | Stefan Geschke | timeline score: 44 | |
| Jul 22, 2010 at 5:54 | comment | added | Wadim Zudilin | Akhil and Harry, there is no relation between the question I mention and this one. "Sounds" means that the existence is known (for periods) but nobody can give an explicit (explicitly computed, if you wish) example. | |
| Jul 22, 2010 at 5:33 | answer | added | T.. | timeline score: 13 | |
| Jul 22, 2010 at 5:06 | answer | added | John Stillwell | timeline score: 34 | |
| Jul 22, 2010 at 4:24 | history | edited | Akhil Mathew | CC BY-SA 2.5 |
deleted 8 characters in body
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| Jul 22, 2010 at 4:23 | answer | added | Joel David Hamkins | timeline score: 20 | |
| Jul 22, 2010 at 4:15 | comment | added | Harry Gindi | @Wadim: The question is whether or not such a polynomial has ever been explicitly computed, not whether or not one exists. | |
| Jul 22, 2010 at 4:12 | comment | added | Akhil Mathew | @Wadim: Could you clarify how the answer to that question answers this one? I don't follow. | |
| Jul 22, 2010 at 4:09 | comment | added | Wadim Zudilin | The question is equivalent to constructing a polynomial diophantine equation in the Hilbert's 10th. It sounds to me as mathoverflow.net/questions/20430... | |
| Jul 22, 2010 at 3:59 | history | asked | Akhil Mathew | CC BY-SA 2.5 |