Timeline for Analogues of P vs. NP in the history of mathematics
Current License: CC BY-SA 3.0
24 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 6, 2020 at 23:23 | answer | added | Timothy Chow | timeline score: 7 | |
| May 14, 2019 at 16:21 | comment | added | ANone | It seems to me the question is of when things that have a lot of circumstantial evidence turn out to be "true". Almost any theorem can be rephrased as whether or not two classes are equal. | |
| Mar 17, 2014 at 14:08 | comment | added | Benjamin Dickman | I think many were aware of (potential) equivalence (in ZF) between e.g. Zorn's Lemma and the Axiom of Choice, but there might be an example here if you do some digging: if not in terms of equivalence, then perhaps in terms of implied results. (Even today one formulation is frequently preferable over another depending on what one wishes to prove.) | |
| Mar 17, 2014 at 13:27 | history | edited | svick | CC BY-SA 3.0 |
list formatting
|
| Mar 16, 2014 at 16:13 | comment | added | John Sidles | Four now-deleted comments were merged into one answer (below) Lessons from crystallographic classification. | |
| Mar 16, 2014 at 15:39 | answer | added | John Sidles | timeline score: 11 | |
| Mar 16, 2014 at 1:22 | answer | added | vzn | timeline score: 14 | |
| Mar 14, 2014 at 22:00 | history | made wiki | Post Made Community Wiki by Todd Trimble | ||
| Mar 14, 2014 at 17:34 | comment | added | Suvrit | Do $\epsilon$ fences count? Example, the Riemannian Hypothesis is equivalent to: for each $\epsilon > 0$, there is a constant $C_\epsilon$ such that $|\pi(x)-\text{Li}(x)| \le C_\epsilon x^{1/2+\epsilon}$ for all $x \ge 2$. | |
| Mar 14, 2014 at 16:09 | answer | added | Terry Tao | timeline score: 62 | |
| Mar 14, 2014 at 15:06 | answer | added | John Sidles | timeline score: 0 | |
| Mar 14, 2014 at 9:02 | answer | added | Mikhail Katz | timeline score: 2 | |
| Mar 14, 2014 at 1:09 | answer | added | John Baldwin | timeline score: 9 | |
| Mar 13, 2014 at 23:41 | comment | added | Sam Hopkins | Perhaps similar to the manifold example I gave earlier, we have the question of whether all smooth manifolds homeomorphic to the standard sphere are diffeomorphic to the standard sphere, answered in the negative by Milnor in 1956 (see en.wikipedia.org/wiki/Exotic_sphere). | |
| Mar 13, 2014 at 23:27 | answer | added | Joel David Hamkins | timeline score: 27 | |
| Mar 13, 2014 at 22:05 | comment | added | Andrés E. Caicedo | (The point is that Cohen's technique gives us a method to prove independence results, but we already knew that independent statements exist. What was perhaps surprising was the huge variety of such statements that are not of metamathematical character -- unlike Gödel sentences.) | |
| Mar 13, 2014 at 22:02 | comment | added | Andrés E. Caicedo | I think in the last example it would be better to talk of being provable vs. being true (in arithmetic, rather than set theory). Gödel's incompleteness shows that the two are not the same. | |
| Mar 13, 2014 at 21:16 | comment | added | Scott Aaronson | Well, the fences represent current knowledge. So let's put it this way: if it turns out that either fence is indeed impassable, then not only is the other one too, but there are then infinitely many other impassable fences divvying up the DMZ. Conversely, if it's possible to pass from one country to the other, then there are no impassable fences anywhere. | |
| Mar 13, 2014 at 21:10 | comment | added | Gerhard Paseman | Actually, Ladner shows that there has to be more than any finite number of such zones, if there is at least one. Gerhard "Let's Start 'Mathematicians With Borders'" Paseman, 2014.03.13 | |
| Mar 13, 2014 at 20:57 | comment | added | Scott Aaronson | Tell you what: it's a thin demilitarized zone, with invisible fences on either side. Factoring and graph isomorphism live in that DMZ, unable to reach either country but in no immediate danger of electrocution. | |
| Mar 13, 2014 at 20:49 | answer | added | user46855 | timeline score: 42 | |
| Mar 13, 2014 at 20:43 | answer | added | Gerhard Paseman | timeline score: 3 | |
| Mar 13, 2014 at 20:38 | comment | added | Emil Jeřábek | Can I respectfully ask for the electricity to be switched off? Now I’m left with the mental image of poor guys like graph isomorphism and factoring stuck to the fence, electrocuted. | |
| Mar 13, 2014 at 20:12 | history | asked | Scott Aaronson | CC BY-SA 3.0 |