Talk:Quartic reciprocity

Quartic reciprocity was a Mathematics good articles nominee, but did not meet the good article criteria at the time. There may be suggestions below for improving the article. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.

Article milestones
Date	Process	Result
July 19, 2011	Good article nominee	Not listed

A fact from this article appeared on Wikipedia's Main Page in the "Did you know?" column on November 12, 2008.

The text of the entry was: Did you know ... that quartic reciprocity was first conjectured by Swiss mathematician Euler in 1748–1750, but not proved until 1836–37 by Prussian mathematician Jacobi?

GA Review

This review is transcluded from Talk:Quartic reciprocity/GA1. The edit link for this section can be used to add comments to the review.

Reviewer: H1nkles (talk) _{citius altius fortius} 17:02, 12 July 2011 (UTC)[reply]

GA Review Philosophy

When I do an article review I like to provide a Heading-by-Heading breakdown of suggestions for how to make the article better. It is done in good faith as a means to improve the article. It does not necessarily mean that the article is not GA quality, or that the issues listed are keeping it from GA approval. I also undertake minor grammatical and prose edits. After I finish this part of the review I will look at the over arching quality of the article in light of the GA criteria. If I feel as though the article meets GA Standards I will promote it, if it does not then I will hold the article for a week pending work.

GA Checklist

GA review – see WP:WIAGA for criteria

Is it well written?
A. The prose is clear and concise, and the spelling and grammar are correct:
One-sentence paragraphs should be expanded or combined.

B. It complies with the manual of style guidelines for lead sections, layout, words to watch, fiction, and list incorporation:
Lead is minimal and needs to be expanded. Overuse of bold in writing.
Is it verifiable with no original research, as shown by a source spot-check?
A. It contains a list of all references (sources of information), presented in accordance with the layout style guideline:
Refs taken in good faith. Spotcheck not done.

B. Reliable sources are cited inline. All content that could reasonably be challenged, except for plot summaries and that which summarizes cited content elsewhere in the article, must be cited no later than the end of the paragraph (or line if the content is not in prose):

C. It contains no original research:

D. It contains no copyright violations nor plagiarism:
Is it broad in its coverage?
A. It addresses the main aspects of the topic:

B. It stays focused on the topic without going into unnecessary detail (see summary style):
Is it neutral?
It represents viewpoints fairly and without editorial bias, giving due weight to each:
Is it stable?
It does not change significantly from day to day because of an ongoing edit war or content dispute:
Is it illustrated, if possible, by images?
A. Images are tagged with their copyright status, and valid non-free use rationales are provided for non-free content:

B. Images are relevant to the topic, and have suitable captions:
Overall:
Pass or Fail:
Comments are in the review below, I will hold for a week pending work. H1nkles (talk) _{citius altius fortius} 17:32, 12 July 2011 (UTC)[reply]

Lead

See WP:LEAD for instructions on what should be in a Lead. To sum up the lead should be a skeletal outline of the article. The lead for this article is minimal and should be expanded to include all aspects of the article in a summary style.

History

Try to place refs at the end of sentences rather than in the middle.
Can some of these people be introduced? You have several names here and of course as I novice they mean nothing to me. Perhaps to a mathematician they carry credibility but perhaps a brief statement of who some of these people are would help the uninitiated. Especially the ones who are not linked.

Integers

One-sentence paragraphs are frowned upon, can the sentence about modulo prime numbers be combined with the paragraph above?
Why is bold used so frequently within the writing of the article? I'm not talking about the formuals but also the examples and even terms like quartic, biquadratic residue, etc.

References

Taken in good faith as I do not have access to the books to spotcheck for accuracy and against plagiarism.
The article appears well-referenced.
Format is good and consistent. The only thing I would suggest is that if some books are in another language (Eisenstein's perhaps?) that the language be specified.

Overall

I'm obviously not a mathematician and cannot speak to the veracity of the content. The article has been sitting at GAC since April and I think waiting 3+ months for a review is a travesty. I reviewed it against the GA Criteria.
I am taking the accuracy of the content on good faith since I'm not an expert and this is obviously a very technical article that requires some higher-than-average mathematical knowledge.
I cannot pass this article to GA at the present time as I do not feel as though the lead meets MOS criteria.
There are some other minor issues like one-sentence paragraphs, and the unnecessary use of bold, which are easily addressed. I will hold the article for a week pending work and/or discussion. H1nkles (talk) _{citius altius fortius} 17:29, 12 July 2011 (UTC)[reply]

It has been a week since this review and no work has been done. I will therefore not promote this article. Please consider my suggestions, if you have questions or comments please talk to me on my talk page. If the work is done and the article is renominated then let me know and I will happily revisit the review so that you do not have to wait such a long time. H1nkles (talk) _{citius altius fortius} 15:11, 19 July 2011 (UTC)[reply]

Question: Is this omission significant, or accidental?

In § Dirichlet, there is a definition "Let p = a² + b² ≡ 1 (mod 4) be prime, and let i ≡ b/a (mod p).". Since p is an odd prime, it is obvious that one summand must be even and one must be odd. In the previous and following sections, the same definition is used with the additional condition that b is the even one, but in § Dirichlet, this additional condition is omitted, leading to two possible reciprocal values for i.

Is this intentional, or is the additional condition supposed to be implied? 97.102.205.224 (talk) 06:30, 14 November 2023 (UTC)[reply]