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
11 events
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| Feb 11, 2019 at 0:35 | comment | added | Mark S | In the comments in the Quanta article Thomas Bloom states: "Actually it was Shkredov and Konyagin who were the first to improve the 4/3 exponent of Solymosi, and it was their approach that was subsequently improved by Rudnev, Shkredov, and Stevens." | |
| Feb 10, 2019 at 19:58 | comment | added | Fedor Petrov | @MarkS probably it does (I did not check the Shakan's proof myself). The Quanta article somehow misses the Konyagin-Shkredov result in the brief historical survey, I hope that it was not intentional. | |
| Feb 8, 2019 at 13:34 | comment | added | Mark S | Does this Quanta article on the problem and of Shakan's recent paper claiming $4/3+5/5277$ further the story? | |
| Jan 17, 2019 at 21:46 | history | edited | Fedor Petrov | CC BY-SA 4.0 |
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| Sep 8, 2018 at 12:33 | comment | added | Wojowu | @VesselinDimitrov I would say this deserves a separate answer. Regardless of how one judges this result, I think it fits well with the spirit of the question. | |
| Sep 7, 2018 at 22:13 | comment | added | Vesselin Dimitrov | One other notable example from the same area, already mentioned in the very first section 1.1.1 of Tao and Vu's book. Erdos showed that any finite set $A \subset \mathbb{Z}$ of integers contains a subset $B \subset A$ with $|B| > (|A| + 1)/3$ and free of solutions to $x+y = z$. In Estimates related to sumfree subsets of sets of integers (Israel J. Math., 1997), Bourgain applies an ingenious harmonic analysis to strengthen this bound to... $(|A| + 2)/3$. Then again, this establishes the non-sharpness of a classical result, so who judges whether the improvement is "only by a short amount?" | |
| Sep 6, 2018 at 15:59 | history | made wiki | Post Made Community Wiki by S. Carnahan♦ | ||
| Sep 6, 2018 at 12:56 | history | edited | Fedor Petrov | CC BY-SA 4.0 |
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| S Sep 6, 2018 at 12:20 | history | suggested | user21820 | CC BY-SA 4.0 |
grammar ≥ 10 char
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| Sep 6, 2018 at 10:52 | review | Suggested edits | |||
| S Sep 6, 2018 at 12:20 | |||||
| Sep 6, 2018 at 9:25 | history | answered | Fedor Petrov | CC BY-SA 4.0 |