Timeline for Deep theorems and long proofs
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:57 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Nov 18, 2013 at 14:20 | vote | accept | Joseph O'Rourke | ||
| Nov 17, 2013 at 20:39 | comment | added | Igor Rivin | Many deep facts (poster child is the ergodic theorem) have one page proofs In the case of the ergodic theorem the easy proof took half a century to discover, but some deep facts were always known to be trivial... | |
| Nov 17, 2013 at 14:32 | comment | added | Joseph O'Rourke | @IgorRivin: In some sense Shanks argues (in the book I cited) that the quadratic reciprocity theorem is deep because the proof is broad, in that it draws on many areas of mathematics not evidently close to the statement of the theorem. | |
| Nov 17, 2013 at 11:44 | comment | added | Derek Holt | @Igor I would expect a positive correlation between "long" and "deep" but I agree that they are not the same thing. | |
| Nov 17, 2013 at 3:53 | comment | added | Igor Rivin | Why does "long" have anything to do with "deep"? | |
| Nov 17, 2013 at 3:52 | answer | added | Henry Cohn | timeline score: 20 | |
| Nov 17, 2013 at 3:45 | answer | added | Joel David Hamkins | timeline score: 18 | |
| Nov 17, 2013 at 2:28 | comment | added | Richard | Nice question, indeed! As readers, however, guess we shouldn't be fooled by that: we're still under the "1-page bound", I mean there are probably plenty of new & interesting things to be discovered, fitting on 1 page of less, let's try first to have that done! | |
| Nov 17, 2013 at 2:08 | comment | added | Qiaochu Yuan | In fact the function $f(n)$ describing the length of the longest proof (in some reasonably powerful formal system) of a sentence on $n$ letters grows faster than any computable function. Sketch: if it didn't, then exhaustive search would give an algorithm to determine provability, and for a formal system powerful enough to discuss the solvability of the halting problem this is a contradiction. | |
| Nov 17, 2013 at 1:58 | history | asked | Joseph O'Rourke | CC BY-SA 3.0 |