Talk:Erdős–Straus conjecture/GA1

GA Review
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Reviewer: HenryCrun15 (talk · contribs) 04:27, 8 January 2022 (UTC)

Volunteering
Hi, I will review this article. HenryCrun15 (talk) 04:27, 8 January 2022 (UTC)

Review against the GA criteria
Thank you for the opportunity to review this article. I found the subject fascinating. A couple of points before I continue with my review:


 * My apologies for rushing in and incorrectly editing the article when I first started working on this review. I had clearly skimmed the article and jumped to certain conclusions. Thank you for your corrections
 * I have a Bachelor's degree in mathematics, but no further, so my ability to comment on highly specialised concepts in number theory will be limited.
 * I got a Good Article mentor to look over my draft review. Thanks to for the advice, and I have incorporated their suggested changes.

My comments on the article are below:

The article has now been significantly rearranged in reponse to these comments. Some more detailed remarks:
 * Lead:
 * All comments under 1b done. I also added a sentence at the end summarizing the generalizations section.


 * Formulation:
 * Fine, both moved. I'm not convinced that moving the polynomial version up is an improvement, but it also doesn't really hurt.


 * Background:
 * Explanation for why indistinct fractions can be made distinct moved to a new section.
 * Worst-case length for each numerator and behavior of the greedy algorithm separated into two paragraphs.


 * Modular identities:
 * Split into two sections and combined with the theoretical part of the "number of solutions" section. The computational part of the "number of solutions" section has instead been merged into the other computation section.
 * Attempted to explain Hasse principle more clearly
 * The section on computational verification does not belong in this section, but I did repeat in more detail the explanation for why the search can be limited to primes.
 * The " one of six values modulo 840" is not a computational result, it is a mathematical result. It is incorrect that this statement appeared only in the lead. It is a summary of a statement later in the article, "except possibly those that are 1, 121, 169, 289, 361, or 529 mod 840".


 * Negative-number solutions and Generalizations
 * The negative-number part is not really a generalization. Or if it is it's a trivial generalization that nobody cares about because it's trivial. Really it's an explanation for why the formulation of the main problem uses positive numbers. I moved it into the formulation section. Same goes for the distinct vs not distinct part.
 * "The proof that the conjecture is true when negative unit fractions are allowed seems incomplete. It shows (two ways) that odd values of n have solutions, but doesn't show how even values have solutions. If so, add this in. ": This was omitted because it's so totally trivial that no source even mentions it. It's just a special case of the expansion for $$n=2$$ and the fact that a solution for any $$n$$ gives a solution for any multiple of $$n$$. No negative numbers needed. (Allowing them doesn't mean they are required to be used.)
 * Have shown => showed: Done.
 * Remove "trivially": done.
 * Add a colon at the end of the sentence.: not done.: We don't end sentences that way.: We also don't put: colons before: nouns in: sentences. The equation in this sentence is, grammatically, a noun. It doesn't need a colon.


 * External links
 * Re: "There doesn't seem a need for a link to the Tao blog post in the External links section given it is already linked in the notes.": It is false that it is already linked in the notes. The references link to a technical paper by Tao. The external link goes to a blog post of Tao, describing his work in that paper in a more accessible way (or at least trying to; I don't always find Tao's blog posts to be easy to read). They have the same title but are different links. The notes link to a different blog post by Tao with a different title.


 * Broadness of coverage
 * Re "It isn't stated in the article why the Erdős–Straus conjecture is important.": it isn't important, in the sense that (as far as I know) it has no real-world applications. Why would you think that it would? This is not the sort of topic that is studied for its importance. In any case, without sources that make editorial judgements about its importance, we cannot add those judgements to the article.
 * Re "Why do some researchers investigate this alternative of the conjecture?": It isn't because they want to study a different variation. It's merely that there are two different ways you can define the problem, so when you write down what problem you are defining, you are going to pick one of those two ways. It's an arbitrary choice, but it's not possible to avoid choosing.
 * Re "If Erdős didn't publish the conjecture until 1950, how was he able to work on the conjecture in 1948? Was he working with Erdős or Straus, or did he hear about it another way?": We can only write what our sources say. Our sources say that it was formulated in 1948 and published in 1950. You know that researchers talk to each other, both formally (in conference talks and seminars) and informally, right? Also that the journal publication process for mathematics papers can take years, with long delays sometimes occurring between coming up with an idea and polishing it to the point that it is suitable for publication, between submitting the paper and getting back a referee report, between that report and the paper's final revision and acceptance, and between acceptance and its actual appearance in the journal? So it is not surprising that Erdős and Straus talked to each other, and maybe to other people like Obláth or maybe to people who talked to other people who talked to Obláth, long before the paper made its way through the long process of getting published. A discussion of the sociology of mathematics publication in the late 1940s is probably well beyond the scope of this article.
 * Re when did Sierpinski and Schinzel conjecture it: They are both in Sierpinski's 1956 paper. The first part, for 5/n, is stated as "J'oserai aussi poser l'hypothèse que pour les entiers n > 1 tout nombre 5/n est un B3". Here B3 means expressible as a sum of three unit fractions. The phrasing suggests that Sierpinski is making the 5/n conjecture at that point in the paper rather than repeating a conjecture from earlier work. A few lines down he credits the generalization to his student Schinzel: "D'après une hypothèse de A. Schinzel, quel que soit le nombre naturel m donné, il n'y a qu'un nombre fini de nombres naturels n pour lesquels le nombre m/n n'est pas un B3". I added the 1956 date to the article text.

I think now I've addressed all of the comments you made, so could you take another look, please? —David Eppstein (talk) 22:17, 16 January 2022 (UTC)

Updated review of 17 Jan 2021
Hi. I see that you've edited the article following my first review and have requested another look. My updated review is below.

Congratulations on bringing this article to Good Article status!

HenryCrun15 (talk) 05:13, 17 January 2022 (UTC)