Timeline for What is the most "informative" Yes/No math question you know?
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| May 5, 2022 at 15:08 | comment | added | Stefan Kohl♦ | Aren't the practical consequences it would have if P=NP highly over-rated? -- I mean, if P=NP, this would by far not guarantee that one can get any practical algorithm from it (my gut feeling is that it would be just a result of theoretical interest). On the other hand, even if P!=NP, there may still be algorithmic breakthroughs of ENORMOUS practical importance -- even if the asymptotic complexity of the new algorithms is quite boring. | |
| May 4, 2022 at 22:28 | comment | added | Timothy Chow | @CarloBeenakker If we were handed a proof of a contradiction from the assumption that there does not exist a positive integer $d$ such that SAT is solvable in time $O(n^d)$, but with no effective upper bound on the value of $d$, then that might not be so informative. | |
| May 4, 2022 at 14:31 | history | made wiki | Post Made Community Wiki by Stefan Kohl♦ | ||
| May 4, 2022 at 11:23 | comment | added | Carlo Beenakker | my fear with RH would be to receive as an answer a single number --- like "42" --- en.wikipedia.org/wiki/… | |
| May 4, 2022 at 11:21 | comment | added | user44143 | I don’t think the proof would be so informative — eg if we asked about the prime number theorem, we might only get Zagier’s proof. | |
| May 4, 2022 at 11:07 | comment | added | mathworker21 | Huh? If we thought a proof of RH would be $1000$x more informative than a proof or a disproof of P = NP, and we thought RH was true with probability $\ge 0.99$, then we should ask the aliens about RH. | |
| May 4, 2022 at 10:50 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
deleted 41 characters in body
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| May 4, 2022 at 10:22 | comment | added | Carlo Beenakker | @mathworker21 --- not if the answer would be informative either way: if P != NP the proof is likely profound and will teach us much new mathematics; if P = NP then the proof may well be simple, but the consequences will be far reaching (there would be a way to solve NP-complete problems in polynomial time). | |
| May 4, 2022 at 9:10 | comment | added | mathworker21 | Really? You don't want to weight by the likelihood the answer is "yes" (or "no")? | |
| May 4, 2022 at 9:02 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |