Timeline for Am I allowed to do non-rigorous numerical analysis?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Oct 20, 2011 at 0:15 | answer | added | Nilima Nigam | timeline score: 19 | |
| Oct 19, 2011 at 16:54 | comment | added | Henry Cohn | I think there's an important meta-question implicit here, about the role of rigor in pure mathematics (it's implicit in Emil's answer and in the comments). The defining characteristic of pure mathematics isn't that you prove everything rigorously, but rather that you maintain a clear distinction between what you have or haven't proved. Of course it's valuable to prove whatever you reasonably can, but you are always free to include heuristic or approximate remarks as well, as long as you make their status clear. | |
| Oct 19, 2011 at 14:28 | comment | added | Timothy Chow | @David Harris: It might help if you explain why you're bothering to compute $a$ numerically at all. What are you using $a$ for, or what will your readers use $a$ for? If the value is not going to be used for anything except to satisfy idle curiosity, then it should be fine to report a non-rigorously computed value and label it as such. On the other hand, if you think someone else may want to use your reported value of a for subsequent rigorous computations, or might record it in some standards table, then that's a different story. | |
| Oct 19, 2011 at 14:00 | comment | added | Gil Kalai | The short answer is, yes it is OK not to prove a sufficiently accurate numerical estimation. After you proved that a exists and presented a formula, rigorously computing or giving very good estimations of the actual value of a will not be important, especially if this is difficult, tedious and uninteresting. It can be useful to remark about the outcomes of the numeric programs and mention the fact that they dont compute a rigorously. If you can give some estimation rigorously and painlessly this may good to add. | |
| Oct 19, 2011 at 13:42 | answer | added | Emil Jeřábek | timeline score: 14 | |
| Oct 19, 2011 at 13:32 | comment | added | David E Speyer | Agreed that standards are going to be very different between fields, including within pure math. | |
| Oct 19, 2011 at 13:32 | comment | added | David E Speyer | Meta thread started. tea.mathoverflow.net/discussion/1178/… Personally, I like this question. | |
| Oct 19, 2011 at 13:29 | comment | added | Mark Meckes | It definitely matters what the subject of the paper is, and more especially, who the audience is and where you intend to publish it. The standards of such things are very different in different fields, and if your intended audience does not consist of pure mathematicians then this site is probably not a useful place to get an answer to your question. | |
| Oct 19, 2011 at 13:17 | history | edited | David Harris | CC BY-SA 3.0 |
added 162 characters in body
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| Oct 19, 2011 at 13:05 | history | asked | David Harris | CC BY-SA 3.0 |