Timeline for Examples of notably long or difficult proofs that only improve upon existing results by a small amount
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Sep 11, 2018 at 21:01 | comment | added | tparker | @Stopple Good point - I got it from Tao's blog post, where he does not credit it to Newman as he should have. | |
| Sep 11, 2018 at 18:44 | comment | added | Stopple | @mbrig Many RH equivalences are deep, but this one is built into the definition of $\Lambda$. | |
| Sep 11, 2018 at 18:43 | comment | added | Stopple | @tparker The quote "This new conjecture is a quantitative version of the dictum that the Riemann hypothesis, if true, is only barely so" is due to Newman himself. | |
| Sep 11, 2018 at 15:21 | comment | added | mbrig | As a (mostly) non-mathematician, can I say I'm constantly shocked by how many things are apparently equivalent to the Riemann hypothesis? | |
| Sep 8, 2018 at 23:11 | comment | added | Matemáticos Chibchas | From $\Lambda\leq1/2$ to $\Lambda<1/2$ I would not say that is a 0% improvement but instead a "0$^{+}$"% improvement. | |
| Sep 7, 2018 at 21:41 | history | edited | Fedor Petrov | CC BY-SA 4.0 |
[Edit removed during grace period]
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| Sep 7, 2018 at 20:06 | comment | added | tparker | As Tao put it, "If the Riemann hypothesis is true, then it's 'just barely' true." | |
| Sep 7, 2018 at 19:55 | comment | added | Andrés E. Caicedo | I added a link to the relevant Polymath page. | |
| Sep 7, 2018 at 19:53 | history | edited | Andrés E. Caicedo | CC BY-SA 4.0 |
added 95 characters in body
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| Sep 7, 2018 at 19:53 | comment | added | tparker | Apparently if one thinks about the De Bruijn-Newman constant in isolation, without its connection to the Riemann hypothesis, then it's arguably more natural to conjecture that $\Lambda > 0$ than $\Lambda = 0$. This is considered one of the strongest heuristic arguments against the Riemann hypothesis (although of course not nearly as strong as the many heuristic arguments for it). | |
| Sep 7, 2018 at 19:51 | comment | added | tparker | @M.Khan Indeed. The Riemann hypothesis was already known to be equivalent to the statement $\Lambda \leq 0$, so their proof tightened the equivalence to the statement $\Lambda = 0$. | |
| Sep 7, 2018 at 19:19 | comment | added | M. Khan | Rogers and Tao have proved that constant is non-negative. See arxiv.org/abs/1801.05914. | |
| Sep 7, 2018 at 17:12 | comment | added | Wojowu | I think this is a winner when it comes to both relative and absolute smallest improvement! | |
| S Sep 7, 2018 at 16:57 | history | answered | tparker | CC BY-SA 4.0 | |
| S Sep 7, 2018 at 16:57 | history | made wiki | Post Made Community Wiki by tparker |