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This is an old revision of this page, as edited by JayBeeEll (talk | contribs) at 23:39, 19 November 2024 (→Emmy Noether FA review: Reply). The present address (URL) is a permanent link to this revision, which may differ significantly from the current revision.

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Emmy Noether FA review

It would be much appreciated if people could read the Emmy Noether article and check for statements that are unclear, under-cited, or otherwise unbecoming the encyclopedia project. XOR'easter (talk) 22:06, 12 October 2024 (UTC)[reply]

For those more knowledgeable with the subject matter than I am, the two sections that may need some more citations the most are the ones on ascending and descending chain conditions and algebraic invariant theory. Sgubaldo (talk) 23:29, 12 October 2024 (UTC)[reply]
My impression from working on the article previously was that everything discussed in it is addressed in the references already present (and for a math topic, having a clickly blue linky number for each sentence doesn't necessarily go further to satisfying WP:V than having one per subsection). But this would be a good opportunity to point readers at references that are particularly good. Anybody have favorite books about either of those? XOR'easter (talk) 18:30, 13 October 2024 (UTC)[reply]
The section on algebraic invariant theory doesn't make enough contact with Noether's work in the area, which was eclipsed by that of Hilbert. Both the Rowe and Dick source describe her dissertation done under Gordan, which was devoted to symbolic computation of invariants, and in fact a later source of some embarrassment. The section would benefit by emphasizing this, and summarizing the sources better (and referring to them). Tito Omburo (talk) 19:33, 13 October 2024 (UTC)[reply]
Care to tackle that? I could try, but I'm not sure when I'll have an uninterrupted block of time long enough. XOR'easter (talk) 21:00, 13 October 2024 (UTC)[reply]
@Sgubaldo, @Tito Omburo, @XOR'easter. The discussion now is into FARC: one delist and one keep. I have found some of the unsourced sections after looking up at its content. Dedhert.Jr (talk) 11:55, 29 October 2024 (UTC)[reply]
As an update to this, there's now 13 citation needed tags left to take care of. 5 are specifically in the ascending and descending chain conditions section. Sgubaldo (talk) 15:29, 3 November 2024 (UTC)[reply]
Thanks. XOR'easter (talk) 17:21, 4 November 2024 (UTC)[reply]
The first epoch of algebraic invariant theory says "an example, if a rigid yardstick is rotated, the coordinates (x1, y1, z1) and (x2, y2, z2) of its endpoints change ...". How is this related to the article but does not explicitly says about that example? Dedhert.Jr (talk) 07:25, 5 November 2024 (UTC)[reply]
I think that line was just trying to explain what "invariant" means. I trimmed the notation, since we don't use it later. 10 {{citation needed}} tags remain. XOR'easter (talk) 21:35, 10 November 2024 (UTC)[reply]
Needed: a readable introduction to algebraic invariant theory, and likewise for ascending/descending chain conditions. XOR'easter (talk) 20:17, 15 November 2024 (UTC)[reply]
I've reached out to an algebraist colleage to ask for assistance. --JBL (talk) 21:03, 16 November 2024 (UTC)[reply]
I've done the cn tag relating to Abstrakter Aufbau der Idealtheorie in algebraischen Zahl- und Funktionenkörpern, which was mentioned in the FAR. I have a question about one of the sentences in that paragraph. Full disclosure that I am not familiar with much abstract algebra. The sentence currently reads "...the Dedekind domains:[1] integral domains that are Noetherian, 0- or 1-dimensional, and integrally closed in their quotient fields.[2]" and defines Dedekind domains.
This is what Page 13 of Noether, 1983 (collected papers) says (formatted slightly for brevity):

In Abstrakter Aufbau der Idealtheorie ... Noether gave the first characterization of the class of rings now known as Dedekind rings: the commutative rings in which factorization of ideals as products of prime ideals holds. She showed that the following conditions were necessary and sufficient for the validity of the prime ideal factorization theorem:
I – The ascending chain condition for ideals.; II – The descending chain condition modulo every non-zero ideal.; III – Existence of a unit element.; IV – Non-existence of zero divisors.; V –  Integral closure in the field of fractions.

This is what Page 96 of Rowe, 2021 says:

In [Noether 1927a], Emmy Noether was able to give a general proof of Dedekind’s fundamental theorem and its converse on the basis of five axioms for a Dedekind ring. In her earlier paper [Noether 1921b], “Theory of Ideals in Ring Domains,” she introduced a general concept for rings that merely had to satisfy one axiom: the ascending chain condition. This acc now became Axiom 1 in [Noether 1927a] and its counterpart, the descending chain condition (dcc), was formulated as Axiom 2. She had not, however, explicitly stated that the ring R must possess an identity element for multiplication. Pavel Urysohn brought this oversight to her attention in 1923, and so she introduced this as Axiom 3, while pointing out that Urysohn had alerted her to it [Noether 1927a, 494]. Axiom 4 further stipulates that the ring must have no zero divisors. Finally, Axiom 5 introduces the decisive condition that the ring R must be algebraically closed in its associated quotient field (i.e. the smallest field that contains R). These are the five axioms for a Dedekind ring found in textbooks today.

I wanted to change it to something like "... Dedekind domains. Noether showed that five conditions were necessary for this to be valid: the rings have to satisfy the ascending and descending chain conditions, they must possess a unit element, but no zero divisors, and they must be integrally closed in their associated quotient fields.[3][1]" but I was worried it was either wrong or redundant. Sgubaldo (talk) 21:25, 18 November 2024 (UTC) Sgubaldo (talk) 21:25, 18 November 2024 (UTC)[reply]
The current version is heavy on modern terminology. I suggest "the ideals have unique factorization into prime ideals (now called Dedekind domains). Noether showed that these rings were characterized by five conditions: they must satisfy the ascending and descending chain conditions, they must possess a unit element but no zero divisors, and they must be integrally closed in their associated fields of fractions." + appropriate wikilinks. --JBL (talk) 23:39, 19 November 2024 (UTC)[reply]

References

  1. ^ a b Noether 1983, p. 13.
  2. ^ Atiyah & MacDonald 1994, pp. 93–95.
  3. ^ Rowe 2021, p. 96.

Dispute in Algebra

The featured article Algebra has taken onto the dispute by two users, with the reason that the article continues to expand even further or personalization things (or whatever it is). More users for giving points of view in Talk:Algebra#Recent changes to subsection "Polynomials". Dedhert.Jr (talk) 10:29, 30 October 2024 (UTC)[reply]

Area of a circle

Please see recent edit history at Area of a circle where some new editor insists that Archimedes proof needs to be labeled as "a logic proof" and that a calculation of the areas of some isosceles triangles needs to be replaced by subdividing the triangles into right triangles and summing their areas instead, in not-well-written English. —David Eppstein (talk) 06:35, 3 November 2024 (UTC)[reply]

I agree that these edits are not good. However I hope that someone can improve the readability of this section.
I think the 'not greater' argument can be described in a clear way almost entirely without symbols. It has two parts: (1) any inscribed regular polygon has smaller area than the right triangle and (2) there exist inscribed regular polygons with area arbitrarily close to the circle area. So if the circle area is greater than the triangle area, by (2) there is an inscribed regular polygon with area larger than the triangle area, but this contradicts (1).
The argument for (1) is that the polygon perimeter is less than the circle circumference (as follows from the fact that lines minimize distance between two points) and the polygon's inner radius is less than the circle radius. Since polygon area is one half the perimeter times the inner radius and triangle area is one half the circumference times the circle radius, (1) follows immediately. Fact (2) is extremely intuitive, and could even be acceptable here as self-evident. Archimedes' construction of iterated bisection is a good illustration but probably not a proper proof. Is it clear without doing some extra calculation that the 'gap area' eventually becomes arbitrarily small?
I think it's a really marvelous proof (or almost-proof) but I found its wiki-description rather hard to read. For me a description of the above kind is much easier.
(And if nothing else, symbol is presently referred to multiple times but not defined!) Gumshoe2 (talk) 09:00, 3 November 2024 (UTC)[reply]

MathJax for non-signed-in users in the future

Pinging @Salix alba:

If I understand correctly, every non-signed-in user will be forced to see math as rendered by MathML, beginning in December 2024. But since MathML has many disadvantages in comparison with MathJax, it would be illogical to shove MathML down their throat.

The users who are not signed in can change appearance of their Wikipedia. There's a panel on the right that allows them to change the size of the text, width of the text and also color. However, they should be able to change their math renderer as well. Given that they will be able to change the text, width and color, why not change the math renderer as well? I think everyone would benefit from that.

As an aside, why does the MathJax option read "[...] (for browsers with limited MathML support)"? It assumes that the only reason why one wants MathJax is that their browser has limited MathML support, which is false. Many users label MathML as inferior to MathJax, providing an overflowing supply of reasons, regardless of the level of support of MathML in the browser they use. A1E6 (talk) 17:30, 3 November 2024 (UTC)[reply]

Does there exist an exact definition of "Mathematical object"? Please join the discussion

Link to to discussion: Talk:Mathematical object#Consensus 1: Existence of an exact definition - Farkle Griffen (talk) 19:03, 13 November 2024 (UTC)[reply]

Locally Recoverable Codes

Recently, I published my first Wikipedia page about Locally Recoverable Codes, which are linear codes from a family of error correction codes, and it is still an orphan article. If someone can help improve this, I would highly appreciate it. Yaroslav-Marta (talk) 02:14, 15 November 2024 (UTC)[reply]

I suggest you expand the article slightly with a section built out of the first 5 references. It might be called "Overview" (before Definition) or "Relation to error correction codes" (just after Definition). In this section set the context. One sentence for the orients general readers on what an error correction code is and then more content how this article relates to error correction codes. Especially look for related error correction code topics which have articles. Then go into those articles and link this one in See Also or better in an appropriate sentence with a ref in the other article. Presto not an orphan. Johnjbarton (talk) 02:41, 15 November 2024 (UTC)[reply]
Ok, thank you. Yaroslav-Marta (talk) 13:55, 18 November 2024 (UTC)[reply]

I fixed the title and some capitalization per our conventions; I haven't made any substantive edits to the article. --Trovatore (talk) 02:59, 15 November 2024 (UTC)[reply]
Thank you. Yaroslav-Marta (talk) 13:56, 18 November 2024 (UTC)[reply]
@Yaroslav-Marta: I see we have an article titled locally decodable code. I can't immediately tell whether this is the same thing (in which case the articles should be merged), or a closely related topic, in which case you might be able to de-orphanize yours by linking from there. --Trovatore (talk) 03:16, 15 November 2024 (UTC)[reply]
This is a different type of codes, but I might refer my article from it I think. Yaroslav-Marta (talk) 13:56, 18 November 2024 (UTC)[reply]

Scope of List of theorems

I raised some questions at Talk:List of theorems#Scope of this list last month. There haven't been any comments there, but I suspect not many people watch that page. Thus, I'm drawing attention to those questions here in the hope that this is where more people with an interest in that list can be found. Joseph Myers (talk) 20:33, 19 November 2024 (UTC)[reply]

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