Timeline for True by accident (and therefore not amenable to proof)
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Nov 4, 2023 at 20:57 | comment | added | Sidharth Ghoshal | Or to put it more succinctly, What seems “by accident” or a coincidence to us today will seem “obviously, the only way it could have ever been” tomorrow | |
| Nov 4, 2023 at 20:55 | comment | added | Sidharth Ghoshal | I made a comment on Holts comment which I deleted but now feel comfortable making again. There are no such things as accidents in math. Every coincidence supports a deeper explanation but we just might not have the machinery to explain such coincidences at the moment. The classic example that comes to mind is the Heegner numbers. Those would have seemed to be almost integers by accident until class field theory was invented. The “by accident” moniker therefore is more appropriately phrased as “by accident w.r.t our current tools” | |
| Jan 20, 2023 at 14:49 | comment | added | Timothy Chow | Regarding Gil's suggestion that a statement might admit a proof, but the proof also seems "accidental," see Derek Holt's comment on an answer to another MO question, where he expresses the feeling that Ore's conjecture might be "true by accident" even though we have a proof. | |
| Nov 27, 2022 at 2:53 | history | edited | kjetil b halvorsen | CC BY-SA 4.0 |
aome typos fixed
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| Aug 12, 2022 at 7:57 | history | edited | Martin Sleziak | CC BY-SA 4.0 |
http -> https (the question was bumped anyway)
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| Jan 21, 2020 at 3:09 | comment | added | Timothy Chow | It occurred to me today that this question is closely related to another MO question, Knuth's intuition that Goldbach might be unprovable. Knuth gives Goldbach's conjecture as an example of a statement that is "just, sort of, true because it can't be false. ... So it might very well be that the conjecture happens to be true, but there is no rigorous way to prove it." | |
| Nov 4, 2011 at 15:17 | comment | added | Gil Kalai | This is a good example. We do not expect "hidden structures" in the sequence f(n), or, more importantly in the sequence of primes, or even in the writings of Shakespeare, but we dont expect that we will be able to refute their existence either. | |
| Nov 4, 2011 at 14:19 | comment | added | Timothy Chow | I'm reminded of Problem 3c in Chapter 3 of Richard Stanley's Enumerative Combinatorics: "Let $f(n)$ be the number of non-isomorphic $n$-element posets. Let $P$ denote the statement that infinitely many values of $f(n)$ are palindromes when written in base ten. Show that $P$ cannot be proved or disproved in Zermelo-Fraenkel set theory." The bit about formal unprovability is, in my opinion, a red herring. I think Stanley is just saying that he thinks that if $P$ is false (which it surely is), then it is false by accident. | |
| Sep 1, 2011 at 2:05 | comment | added | Gordon Royle | I have accepted this as best matching the spirit of my question; additional comments are in the "Edit" above. | |
| Sep 1, 2011 at 2:05 | vote | accept | Gordon Royle | ||
| Aug 26, 2011 at 12:56 | history | answered | Gil Kalai | CC BY-SA 3.0 |