Timeline for Uninteresting questions with interesting answers
Current License: CC BY-SA 3.0
13 events
| when toggle format | what | by | license | comment | |
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| Mar 25, 2015 at 22:52 | history | edited | Michael Hardy | CC BY-SA 3.0 |
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| Mar 25, 2015 at 19:52 | history | edited | Michael Hardy | CC BY-SA 3.0 |
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| Mar 25, 2015 at 1:16 | comment | added | Michael Hardy | Probably. @BenjaminSteinberg ${}\qquad{}$ | |
| Mar 24, 2015 at 23:20 | comment | added | Todd Trimble | @MichaelHardy Did you mean to address Benjamin Steinberg? My comment was about what the theorem should be called. | |
| Mar 24, 2015 at 22:41 | comment | added | Michael Hardy | @ToddTrimble : My posting says, in the first sentence in the second paragraph "Doubtless it's an interesting problem, to those who are interested in that sort of thing; otherwise Hilbert would not have included it in his list." That says it. But I was saying that even those who take no particular interest in that sort of thing can find Matiyasevich's theorem interesting because of the surprising nature of the result: that there are no semi-decidable sets except diophantine sets. | |
| Mar 24, 2015 at 22:39 | comment | added | Michael Hardy | @Ryan : I don't think it's a precise definition with "may". And I state explictly in my posting that a set is decidable if and only if both it and its complement are semi-decidable, so that makes it clear if it weren't already that every decidable set is semi-decidable. That all decidable sets are semi-decidable is an easy exercise. ${}\qquad{}$ | |
| Mar 24, 2015 at 20:35 | comment | added | Benjamin Steinberg | My point is to disagree with the question being uninteresting. I think the question of which diophantine problems have solutions goes back to the earliest days of mathematics and is as natural as any mathematical problem I can imagine and I am not a number theorist. So I really don't think the problem was uninteresting until the answer was known. | |
| Mar 24, 2015 at 18:49 | comment | added | Todd Trimble | I think it should not be referred to as just Matiyasevich's theorem, since (as you say) Davis, Robinson, and Putnam spent years and years on preliminary groundwork. Technically what Matiyasevich did in 1970 was prove the Fibonacci sequence is Diophantine; this by itself might not seem terribly exciting, but due to the work of the other three, all four knew that this technical result would imply the J.R. (Julia Robinson) hypothesis which in turn settled Hilbert's 10th. The theorem is often referred to as "the MRDP theorem". | |
| Mar 24, 2015 at 18:18 | comment | added | Ryan Dougherty | For semi-decidable, you may want to change it to say "may run forever if the input is not a member" because all decidable sets are semi-decidable (the current wording does not make it seem so). | |
| Mar 24, 2015 at 17:55 | comment | added | Michael Hardy | @BenjaminSteinberg : OK, so your point is simply to agree with my second paragraph? | |
| Mar 24, 2015 at 17:04 | comment | added | Benjamin Steinberg | I would say that the problem is interesting and natural. Hilbert almost surely thought there would be an algorithm and was undoubtedly aware that many natural algorithmic problems are naturally (as opposed to the Halting problem) diophantine problems. | |
| S Mar 24, 2015 at 16:30 | history | answered | Michael Hardy | CC BY-SA 3.0 | |
| S Mar 24, 2015 at 16:30 | history | made wiki | Post Made Community Wiki by Michael Hardy |