Talk:Erdős conjecture on arithmetic progressions

Turán

Was Turán a coconjecturer? I don't see any reference that mentions his name specifically in connection with this problem. For example, Bollobás attributes the conjecture to Erdős and only him in Paul Erdős—Life and work, in: The Mathematics of Paul Erdős, I, Springer, p. 40. Erdős himself writes "In this connection I conjecture that if $\sum _{r=1}^{\infty }{\frac {1}{a_{r}}}=\infty$ then for every k there are k $a_{r}$ 's in an arithmetic progression." P. Erdős: On the combinatorial problems which I would most like to see solved, Combinatorica, '1(1981), 28.Kope 06:57, 16 July 2007 (UTC)[reply]

I don't see the revelance of the two references. No 1 (the 1936 Erdős-Turán paper) does not, repeat does not mention this statement. I can only get the first page of the No. 2 reference which specifically mentions only Erdős' name ("these results have led Erdős to conjectue...") in connection witHe h this conjecture. So, why don't we agree that it is a conjecture of Erdős? Kope 14:25, 16 July 2007 (UTC)[reply]

For what it's worth, Green and Tao in their famous proof of the special case of the primes credit this to both Erdős and Turán.

CRGreathouse (t | c) 14:43, 16 July 2007 (UTC)[reply]

Well and they refer to the 1936 Erdos-Turan paper.... Let me quote one more paper of Erdos: Problems in number theory and combinatorics, Prooc. Sixth Manitoba Conf. on Num. Math., Congress Numer XVIII, 35-58. "Here I state the following old conjecture of mine: let $a_{1}<a_{2}<\cdots$ be an infinite sequence of integers satisfying $\sum {\frac {1}{a_{i}}}=\infty$ ....". Kope 15:16, 16 July 2007 (UTC)[reply]

Yes, it was an old conjecture of his -- but it may have been one of Turan's as well, and that doesn't convince me otherwise. Richard Guy attributes it to both, and he's essentially the authority about these things. (I couldn't find anything in my biography, sadly -- maybe you have a batter one of Erdos? Or even better, one of Turan?)

CRGreathouse (t | c) 02:48, 17 July 2007 (UTC)[reply]

With regards to whether Turan should be cited, the answer is not entirely clear. See the answer to this MathOverflow post:

https://mathoverflow.net/questions/132648/the-erd%C5%91s-tur%C3%A1n-conjecture-or-the-erd%C5%91s-conjecture

From the top answer there: "As far as I can tell, the question is sometimes called the Erdős-Turán conjecture for two reasons: First, it extends their older conjecture (now Szemerédi's theorem). Second, it was first popularized in connection to Turán, see below."

It seems that Erdos may have stated the conjecture, or the prize, in memory of Turan.

Given the complexity of the history, I think it is best to leave both names for the Wikipedia article, and to cite both the MathOverflow page and Soifer's book with regards to why both names are reasonable/applicable, even if the conjecture seems primarily due to Erdos. Enaslund (talk) 15:28, 8 August 2023 (UTC)[reply]

Thank you for the Green-Tao reference. I sent an email to Tao yesterday. He was easier to convince than you, as he already changed their Scholarpedia article on Szemerédi's theorem. Where does Guy attribute the conjecture to Turán? Kope 04:27, 17 July 2007 (UTC)[reply]

Excellent, that's someone who really is in the field. I haven't had luck in the past getting responses from Guy; he's a very busy man. You're welcome to email him if you think you'll have better luck. CRGreathouse (t | c) 12:33, 18 July 2007 (UTC)[reply]

Any clue where we would go to get the $5000 if we HAD found the answer? —Preceding unsigned comment added by 207.118.82.216 (talk) 02:33, 22 June 2009 (UTC)[reply]

Answered in Paul Erdős#Erdős problems, although I can't vouch for it still being open. Although I've met Ron Graham recently, I cannot confirm the offer is still in effect. — Arthur Rubin (talk) 14:01, 22 June 2009 (UTC)[reply]

Semi-protected edit request on 8 August 2023

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Can the edit protection be removed from this article? It impedes community members ability to make the article better. I wanted to make clearer some details concerning the recent progress that was made, but I cannot edit the article. Enaslund (talk) 15:31, 8 August 2023 (UTC)[reply]

Not done: To make such a request, please consult this page for requesting page protection reduction. Pinchme123 (talk) 15:54, 8 August 2023 (UTC)[reply]

Examining the edit history, it appears that this article has been the target of persistent crank-research results, spanning a decade, from 2013 to Jan 2023, coming from many different sock-puppet accounts, all trying to add variants of the same info. Examining some of the sock puppets, it appears to be an individual with at least a decades worth of intellectual investments in a broad range of recreational number theory topics (all cranky-ish). Interesting psychological profile. Made me wonder about how I spend my time. ☺ 67.198.37.16 (talk) 20:09, 14 April 2024 (UTC)[reply]