Timeline for Is this function concave?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| Aug 24, 2021 at 23:44 | comment | added | mathworker21 | @fedja Awarded bounty. Still reading your 'ordering preference' answer. I wanted to thank you now, though, for taking the time to write it. It is beyond helpful. | |
| Aug 24, 2021 at 23:43 | history | bounty ended | mathworker21 | ||
| Aug 18, 2021 at 15:27 | comment | added | fedja | @mathworker21 "I have absolutely no idea how you came up with this" I'll try to elaborate on what I think is the general idea behind doing such manipulations on some trivial example next time I post a proof of some elementary inequality (I have one almost ready by now). The problem with the current versions of AI is that their idea to check some inequality like $\frac{2345678}{12345678}<\frac{2345679}{12345679}$ is to bring the fractions to the common denominator, which makes the computation unverifiable to a human without pen and paper. They should start with teaching it basic arithmetic. | |
| Aug 18, 2021 at 15:15 | comment | added | fedja | @mathworker21 "there shouldn't be a 2 in the integration by parts" Why? I believe that $(T^2)'=2T$, isn't it? As to the AI, the tables of Laplace transforms and elementary explicitly integrable functions are known even to Matematica, which can compute some quite tricky definite integrals, and the rest is just pure algebraic manipulation with the single goal: to reduce the double integral to a single integral with as few occurrences of the parameter in the formula as possible. I managed to get $u$ just at one single place in the formula and that was the key. AI can definitely do that too. | |
| Aug 18, 2021 at 6:46 | comment | added | mathworker21 | @fedja I have absolutely no idea how you came up with this. I don't see why a (minimally intelligent) AI would think to write $\frac{1}{(s+1)^3} = c \int_0^\infty t^2 e^{-(s+1)t}dt$ and, more generally, just end up deciding to use the "convenient representation" you use. Enjoy a bounty for how everything comes together so nicely in your solution (and because I couldn't figure out this question, so I'm happy to see a solution). Finally, super minor point but can't edit your solution: there shouldn't be a $2$ in the integration by parts. | |
| Aug 11, 2021 at 14:38 | comment | added | fedja | @IosifPinelis You are most cordially welcome! | |
| Aug 11, 2021 at 13:09 | comment | added | Iosif Pinelis | Thank you very much! Your "Moral" and its use at the end is really funny, and the entire proof is very nice. | |
| Aug 11, 2021 at 13:06 | vote | accept | Iosif Pinelis | ||
| Aug 11, 2021 at 12:39 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
deleted 3 characters in body
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| Aug 11, 2021 at 9:51 | comment | added | fedja | @MattF. In a sense you always have it: just emulate it in your brain. Solving such problems is similar to the chess game: you just consider finitely many available moves at each step and evaluate the resulting positions by some simple score function, which in this case reflects the simplicity of the resulting expression and applicability of well-known general principles. Computers nowadays beat grand masters in chess, so I see no reason why they couldn't beat an average mathematician in the game of finding short proofs of elementary inequalities. | |
| Aug 11, 2021 at 1:13 | comment | added | user44143 | If a minimally intelligent AI might solve this, then I would love to have access to it. | |
| Aug 11, 2021 at 0:00 | history | answered | fedja | CC BY-SA 4.0 |