Talk:Emmy Noether/Archive 2

Repetitive wording is repetitive
"abstract algebra is abstract"? Can't we do better? I know that here "abstract algebra" is a term of art while the second instance of the word abstract is used in its more colloquial meaning, but the repetition is distracting, and made worse by the recent removal of "very" from the phrase. —David Eppstein (talk) 21:07, 2 June 2008 (UTC)

Changed to : "Despite the generality of abstract algebra, some elements may be understood by analogy to the integers." However, I feel that the whole paragraph exemplifies a problem throughout: lack of homogeneity in the maths parts. The sentences "The set of integers forms a structure known as a ring, because they can be added and multiplied and the result is always another integer. However, they do not form a field, because the result of dividing one integer by another integer might not itself be an integer. The addition and multiplication of integers is commutative, meaning that their result is independent of order: for any two numbers a and b, a + b = b + a and a × b = b × a." is of the level of a hight-schooler (because explained and highly simplified). However, most of the rest of the article doesn't explain the technical terms, and a few years of university is required to grasp the meaning of the maths bits. Also, I don't think commutativity is an essential concept to be explained. However, since Noetherian rings are so well-known and important, the ascending chain condition should maybe be explained, being a more relevant technical detail. Randomblue (talk) 21:37, 2 June 2008 (UTC)


 * The ascending chain condition is easy enough to explain while remaining at the level of integers and high school math: the set of multiples of 12 has as a superset the set of multiples of 6, which has as a superset the set of multiples of 3, but any sequence of this form has to stop eventually because each set in the sequence is the set of multiples of a divisor of the first number (12), and any integer has only finitely many divisors. —David Eppstein (talk) 21:50, 2 June 2008 (UTC)


 * I have a bad feeling the "Abstract algebra is abstract" statement may have been a placeholder I inserted once upon a time with the assumption that it would improved by someone who knew something about maths. After all the hullaballoo this FAC has thrown at me, I can't even remember what's what anymore.


 * Speaking of maths, I have no doubt that there's a significant lack of coherence in the maths section, due to the fact that it's been written by 5-8 different editors. I wish I could help unify it more, but I'm completely worthless when we go beyond long division. Thanks again to everyone who's contributing to this creature. (Now, who's got a solution to the picture problem?) – Scartol  •  Tok  22:40, 2 June 2008 (UTC)


 * If it makes you feel better, the edit changing "abstract algebra is a very technical field" to "abstract algebra is very abstract" was made by another editor than you. --Lambiam 09:28, 3 June 2008 (UTC)
 * You can be more specific Lambiam, that's no problem, I'm happy taking responsibilities :). I didn't like the sentence: why is abstract algebra any more abstract than other areas of maths?Randomblue (talk)


 * I assume the "picture problem" was solved by this, but it occurred to me that this photo from the Oberwolfach collection, showing Emmy with her three brothers (assuming that Robert = Gustav Robert), should also be in the public domain. --Lambiam 09:40, 3 June 2008 (UTC)


 * Hey, good call. Thanks for these, Lambiam. – Scartol  •  Tok  11:00, 3 June 2008 (UTC)

What did Gordan and Hilbert do, exactly?
I was editing the section on Emmy's work on algebraic invariant theory, and I realized that it does not say precisely what Gordan and Hilbert proved. My question is: For which rings and which groups did they prove finite generation of invariants? My understanding is that Emmy proved finite generation for all finite groups acting by automorphisms on Noetherian rings. That part is okay. Everyone knows that Gordan proved finite generation for polynomials in two variables, but for which group actions? It can't have been all of them, because his approach was computational. The "Return to invariant theory" section indicates that Hilbert's proof needed the ring to have characteristic zero (i.e., to contain the rational numbers). What else? Did he need the ring to be a polynomial ring, or was it okay as long as it was finite type over a field of characteristic zero? And did his proof work for all finite group actions, or just some? Ozob (talk) 18:06, 3 June 2008 (UTC)


 * Hi, I'm really busy right now, so I can't answer your question as well as it deserves. A close friend of mine came down with horrible poison ivy yesterday, and we had to take her to the hospital.  Who knew that a simple oil could be that vicious?  Another drawback of living in the country... :P


 * My understanding from reading Emmy's papers and other fragmentary resources on the web is that the group for her early papers, the group of classical invariant theory, is the general linear group of transformations over the complex numbers, which if I recall correctly, is written GLm(C). In the opening sentence of her "Zur Invariantentheorie der Formen von n Variabeln", she writes, "In der projectiven Invariantentheorie der Formen von n Variabeln ist das Hauptproblem gelöst, die Endlichkeit des Formensystems bewiesen." ("In the projective invariant theory of forms of n variables, the chief problem has been solved, the proof that the system of forms is finite.")  I took "projective" to mean "affine transformations", ergo GL(C).  No rings are involved, to the best of my knowledge; that came later for her.


 * I still need to read, think and say more on this, but that's going to be difficult for a day or two. Hopefully you can make something of this in the meanwhile?  I'm secretly hoping that you all will explain it to me. ;)  Willow (talk) 19:41, 3 June 2008 (UTC)

Unimportant question about algebraic error-correcting codes?
Hey Ozob,

I was a little confused about why you took out the clause that error-correcting codes are used to store information? If I'm not mistaken, error-correcting codes — such as the Galois-field-based Reed-Solomon code — are used with compact discs, DVDs and even the hard drive on which this sentence is being stored. ;) I agree that the transmission applications, e.g., cell-phones and space probes, are important, but I'd wanted to also mention the CD/DVD/hard-disk applications.  I think it's important that we present some cool, easily visualized applications of this not-so-easily-visualized "abstract algebra".   But maybe I'm missing something?  Willow (talk) 21:06, 4 June 2008 (UTC)


 * Hi Willow,


 * I'm just showing off my failings here. I usually think of error correcting codes in terms of transmission, (after all, storage is just transmission with a long time delay,) so when I read the old description, I thought, "This should be in terms of transmission," and proceeded to attempt to fix it. Now that you mention it, CDs and DVDs are much better applications than noisy telephone lines. I repent: I've put storage devices are back in and taken noisy telephone lines out. Ozob (talk) 23:39, 4 June 2008 (UTC)

A few more comments from Randomblue
The article is looking really nice! Good job.


 * "In it, she gave the first definition of a commutative ring and used ascending chain conditions" Should 'conditions' be 'condition'?
 * I need to read that work more carefully, but I believe that more than one chain condition was used in her proof. Maybe it was one ascending (Teilerkettensatz) and one descending (Vielfachenkettensatz)?  Anyway, it is possible to use more than one ascending chain condition in a single proof; several different mathematical objects might have their own condition?  For example, some sub-objects and some combinations of (objects that satisfy a chain condition) satisfy the same condition; every sub-group and factor group of a Noetherian group is itself Noetherian.  Willow (talk) 16:02, 6 June 2008 (UTC)
 * Have you given it a closer look Willow?


 * In the book "Emmy Noether, A Tribute to Her Life and Work", one of the very first sentences is (page 5) "The mathematical atmosphere in which Emmy Noether grew up was determined by the work of her father and his friend and colleague Paul Gordan." I don't recall this being clearly mentioned in the article, but it seems rather essential.


 * The whole paragraph : "Despite the generality of abstract algebra, some elements [...] 12 residue classes associated with the ideal of 12 in the ring of integers." doesn't really fit in "historical context". I guess it is more of a "mathematical context".
 * That's a good insight. Perhaps we authors should distill that material into two separate sections?  I've been thinking of moving the explanation of ideals to the beginning of the "Second epoch" section, closer to where it's actually needed by the reader. Willow (talk) 19:42, 6 June 2008 (UTC)

algebraic invariant -> invariant theory arithmetic geometry -> Diophantine equations noncommutative algebra -> ring theory
 * Some redirects seem dubious (I don't really know :)). Maybe better can be found:


 * We already hashed out the noncommutative algebra one somewhere above; it's a better choice than the previous redirect to noncommutative geometry. I think invariant theory is the right link for algebraic invariant: it's much more specific than invariant (mathematics). As for the arithmetic geometry redirect, I just changed it to point to glossary of arithmetic and Diophantine geometry, which is I think a little more specific to this topic than the Diophantine equation article. —David Eppstein (talk) 19:39, 8 June 2008 (UTC)
 * Sorry David, I don't seem to see any edit of yours in the history.

Randomblue (talk) 15:21, 6 June 2008 (UTC)

University of Göttingen
The section on the University of Göttingen is rather too long, I think we ought to split it into smaller sections. Here is a rough suggestion. Randomblue (talk) 22:22, 13 June 2008 (UTC)


 * I don't object to subdividing it into two subsections (although I'm not convinced this is necessary), but I don't see why it's useful to split up the info about her teaching style and personality. – Scartol  •  Tok  10:47, 14 June 2008 (UTC)
 * Ok, great then. Splitting up the info about her teaching style and personality was really just a suggestion; but splitting up it shall be. Randomblue (talk) 12:36, 14 June 2008 (UTC)

Minor technical point: Definition of a ring
Hi, this is relatively minor, but I'm pretty certain that both operations of a ring must be associative. I'm basing that on the identical definitions of a ring that I've found in the sources I have available to me: Serge Lang's book Algebra (2nd edition, page 60) and the book Analysis, Manifolds and Physics by Yvonne Choquet-Bruhat and Cecile DeWitt-Morette (2nd edition, p. 8). By their definitions, the octonions do not form a ring; they form an algebra, as van der Waerden also says in his History of Algebra. Do we agree on that definition, or did I perhaps misunderstand something? Willow (talk) 22:22, 14 June 2008 (UTC)


 * R.e.b. went ahead and made the reversion that I was asking for, but I'm concerned that we're not hearing all viewpoints? Perhaps there was different definition of rings in Noether's time, or in the present itme?  It would nice if we could come to a definitive agreement. Willow (talk) 13:53, 15 June 2008 (UTC)


 * Both operations are associative indeed, and I doubt there was a different definition in Noether's day because the examples she was abstracting all had an associative multiplication. Geometry guy 16:17, 15 June 2008 (UTC)


 * In the Aufbau paper, section 1 begins (my extremely rough translations): "We consider a commutative ring...", where the word ring is footnoted "As is well known, a ring is a set ... the addition is associative, commutative, and invertible, the multiplication is associative -- commutative, when the ring is assumed commutative -- and distributes over addition." This is the common modern definition, and, as far as I can tell, is identical with that of Fraenkel and Hilbert. Gleuschk (talk) 18:19, 15 June 2008 (UTC)


 * If Noether herself considered all rings to be associative, then that's what we should adopt for this article. When you're talking about maximal generality, Lie algebras are very good examples of non-associative rings; but I don't think Noether ever worked on those.
 * As a side note, perhaps the reason for the confusion is a differing set of conventions. Where I come from, in algebraic geometry land, an algebra is a homomorphism of rings; one says things like "Let S be an R-algebra", meaning that R and S are commutative rings and that we have chosen a fixed homomorphism R &rarr; S. If one needs non-associative multiplication (like for Lie algebras) then one calls still calls the objects rings, and an algebra is a homomorphism of such objects. But outside of algebraic geometry and fields which have heavy contact with it (commutative algebra, ring theory, etc.) I don't know how common this is. Ozob (talk) 19:58, 15 June 2008 (UTC)
 * Lie algebras are great, but they are not rings! The term nonassociative ring is like the term skew field (for division ring) and herbal tea (for an infusion other than tea itself). Anyway, good to have confirmation from the sources that Noether's rings are associative. Geometry guy 20:52, 15 June 2008 (UTC)


 * Ah, but my algebraic geometry-style conventions force me to have a different definition. If an algebra is a morphism of rings, and all rings are associative, then all algebras are associative, which is obviously not what we want. We could argue endlessly about the right way to do things, but let's not. For the purposes of this article, we all agree: Rings are associative. Ozob (talk) 16:23, 16 June 2008 (UTC)

Stylistic question: how technical do we want to be?
Hi, I appreciate how my text was made more rigorous mathematically, e.g., by giving the full definition of a group. But I wonder how technical we want to be in this article, if it means sacrificing intelligibility for most readers. I deliberately left out most of those details precisely because I feel that we shouldn't be writing for mathematicians or math students, but rather for the mathematically curious lay-people. My own opinion is that we should eliminate the gory details or push them into the background, if we can bring Noether's contributions into the foreground, somehow giving an impression of what she did. Curious readers (such as mathematicians in training!) seem likely to follow the wiki-links to other articles that give the full definitions and more details.

Of course everyone likes their own prose best and their own ideas of how we should tell her story. :) I'd be very interested to hear everyone else's opinions?  I'm not attached to what I wrote earlier, and I see the advantage of splitting up the discussion of group/rings from that of modules/algebra; less for the reader to chew on at any one time! :)  But I do feel that the present discussion is too detailed and would favor a more "impressionistic" depiction of her work. I'm planning on writing another article Introduction to the algebra of Emmy Noether as an inbetween article; I have to do something with everything I've been reading! ;) Willow (talk) 22:32, 14 June 2008 (UTC)


 * If we do make any attempt at rigor, then I would like us to be correct. The problem is that correctness makes a lot of demands on the reader. The current sketch of abstract algebra is about a page of text on my screen, and for non-mathematicians I think it must be near impenetrable. (Which I feel somewhat ashamed to admit, since I was the last person to seriously copyedit it.) I suspect that most curious laypeople will be put off by it and won't even attempt to read about Noether's mathematical work, and that's bad because some of it (like her work in physics) can be appreciated even if you don't know anything about abstract algebra. (In fact, that's part of the problem with the article right now: Arranging the material this way makes it look like all she did was groups, rings, etc. and that's false.)


 * If we are going to keep this level of rigor, then I think it would be better for the purely mathematical content to be spread around: Put groups and group representations where they first turn up, in physics; put rings together with her work on commutative rings; put algebras with her work on hypercomplex numbers. That will require some rewriting so that everything flows, but it eliminates the indigestible lump of lead we have at the moment.


 * The other option is to return to a lower standard of rigor. I think that would be entirely acceptable for this article (after all, it's a biography in a hyperlinked encyclopedia); in fact I think I'd prefer the article that way. We'll still need brief sketches of the important objects. We could either put those up front like we had before or we could try to spread them out, and I'd again prefer that we spread them out (in part because that will help us all avoid the temptation to make them more rigorous).


 * On the other hand, if I understand your intention with Introduction to the algebra of Emmy Noether, you'd like that article to be a rigorous and expanded version of the "Contributions" section of the present article. The present contributions section would become a collection of non-rigorous sketches. That would solve the rigor problem that we have, assuming that we do want to go ahead and split up the information about Noether like this. I think this is my favorite option. But Willow and I aren't the only editors here; what do the rest of you think? Ozob (talk) 20:39, 15 June 2008 (UTC)

Yes, that was exactly my intention! :) Well, not too rigorous; it is supposed to be an "Introduction" article, after all, so it should be intelligible to non-mathematicians who are willing to read carefully.  My thought was that the full rigor would be put into the main mathematical articles such as module (mathematics) or algebra over a ring, to which the Introduction article could direct mathematics students.  My hope was to have somewhere to describe the details of Noether's work, together with some clarifying comments so that it's not all mathematical "shock-and-awe". ;) For example, Awadewit wished to grasp central simple algebras, and Noether's contributions; the present text is pretty arcane, don't you agree? Willow (talk) 09:43, 19 June 2008 (UTC)

"Real-world" applications of Noether's work?
Hi, I understand that algebraic coding theory does not use Noether's specific work, but I chose to mention it to illustrate for the reader that abstract algebra such as Noether's could have important real-world applications, such as CDs, cell phones and whatnot. I'm fine with all that being deleted as too tangential, but it would be nice if there were a substitute? Does anyone know of any direct applications of her work that might spark the imaginations of readers? Undoubtedly, there will be a few philistines who don't appreciate mathematics as an end in itself. ;) Willow (talk) 09:55, 19 June 2008 (UTC)


 * I'm not sure that there's a good substitute. You can always mumble something about cryptography, because elliptic curve cryptosystems use lots and lots of high-powered math (and in particular, abstract algebra). But that's as tangential to Noether's work as coding theory is. You could also mumble something about string theory for the same reason, but that's no more closely related to Noether's work and it's even less relevant to people's lives. The real problem seems to be the Noether was entirely (purely?) a pure mathematician. She didn't find any applications for her work; what applications there are were found by other people interested in other problems.
 * But I would much rather that we briefly mention coding theory and cryptography than leave the article as it is now. Modern coding theory and cryptography can't even get started without Noether's ideas; the fact that she didn't herself have anything to do with them seems to me to be no argument. Ozob (talk) 16:42, 19 June 2008 (UTC)

I removed the statement that Noether's work was related to DVDs as it sounded too much like a game of six degrees. It might be a good idea to find a reliable source stating that Noether's work is important in coding theory before adding this rather dubious claim back to the article. I don't know of any direct practical applications of her work; her theorem on conservations laws is probably as close as you can get. R.e.b. (talk) 17:10, 19 June 2008 (UTC)

Controversial converse of Noether's theorem?
Hey R.e.b.,

As discussed on its Talk page, at least one textbook says unambiguously, "the converse of Noether's theorem is not true", and cites the example of classical solitons. Also, the impression I got from my readings for the Laplace-Runge-Lenz vector article was that Noether's theorem could be shoe-horned into deriving the conservation of that vector, but it was a little like cheating, since the required symmetry transformation didn't involve only the coordinates and time, but also the conjugate momenta. Anyway, I'm willing to believe that the textbook author is mistaken, but I haven't seen any controversy in a reliable source. Can you point us to one, ideally one that addresses the soliton issue? Thanks! Willow (talk) 10:13, 19 June 2008 (UTC)


 * At one time numerical simulations for the KdV equations for classical solitions suggested the existence of an infinite number of conservations laws not corresponding to any known symmetries, (thought it was later discovered that the equations did in fact possess some non-obvious symmetries accounting for these laws), so this may have led to a mistaken belief that solitons were a counterexample to the converse of Noether's theorem. I'm not sure whether or not every conservation law corresponds to a symmetry, and would be interested to see a clear cut counter-example. In the absence of such a counter-example it seems safer just to say nothing, as there has historically been some confusion over this point, and is is not really needed in a biography. My guess would be that whether or not it is true depends on subtle questions about exactly how one defines "symmetry" and "conservation law". (Reliable sources are needed for adding controversial statements to the article, not for removing them!) R.e.b. (talk) 15:05, 19 June 2008 (UTC)

OK, I didn't know about the confused history of the KdV equations. Is that a recent discovery? Because I would just be surprised if the author of that textbook didn't know about them. His textbook seemed like a pretty reliable source.

Somewhere on the Internet, but I forget where, I read that conservation laws associated with a topological invariant cannot be derived from a continuous symmetry, since topology should change discontinuously. Does that seem reasonable? Perhaps that would be a counter-example? Willow (talk) 17:25, 19 June 2008 (UTC)


 * My attempt to find out what Goldstein says on p. 594 has been temporarily foiled by the fact that my copy stops at p. 399. I guess that explains why it was so cheap. Conservation of solitons for topological reasons does indeed sound like a plausible way of getting conservation without a symmetry, but I dont offhand know of an explicit example. R.e.b. (talk) 18:28, 19 June 2008 (UTC)


 * OK, I found a copy of the 2nd edn of Goldstein. He does not give an unambiguous statement: he only says there "appear to be" counterexamples given by the KdV equation, and adds that "the last word has probably not yet been said...". He says for the KdV equation that "No other symmetry is apparent"; in fact there are many other non-obvious symmetries. (Rather oddly, these were already known before 1980 when the 2nd edition came out.) R.e.b. (talk) 19:54, 19 June 2008 (UTC)

Article for generic algebra?
Hi all, my understanding is that a generic algebra is a generic module provided with a extra multiplication operation that must be bilinear but need not be commutative or associative or anything else. Unfortunately, I don't seem to be able to find the corresponding Wikipedia article? I don't want to start Algebra (abstract algebra) is there's a better analog elsewhere.

The closest I can find is algebra (ring theory), but that article requires that algebras have commutative module-rings (not a requirement for a generic module, I believe) and that the algebra multiplication operation be associative (unlike in the octonions). Should we perhaps generalize that article? Would it be helpful to start a new article? Willow (talk) 10:29, 19 June 2008 (UTC)


 * Algebra over a field, I think. (It also talks about algebras over rings instead of fields.) —David Eppstein (talk) 14:57, 19 June 2008 (UTC)

That seems like a good article, but maybe it's overly qualified? I'd like to be able to say something like "The algebra of integer octonions is..." and have the wikilink for "algebra" go somewhere appropriate. Willow (talk) 17:35, 19 June 2008 (UTC)


 * "Algebra" has many different meanings, depending on the author; they are sometimes assumed to be associative (or commutative), and sometimes not. If the underlying ring is not commutative you will run into problems when defining bilinearity. R.e.b. (talk) 15:11, 19 June 2008 (UTC)

That's really interesting! :) How does non-commutative multiplication in the ring result in a failure of bilinearity?  I can understand how non-commutative addition might, since the addition in the module-group must be commutative.   Thankfully, rings must have commutative addition, by definition, if I remember correctly.  I'm also glad to hear that mathematicians do disagree among themselves over these definitions, and that it's not just a vast conspiracy to confuse knitters... ;) Willow (talk) 17:35, 19 June 2008 (UTC)
 * The problem is that if ab is (left) bilinear in a and b then for x in the underlying ring you get xab = (xa)b = x(ab) =a(xb)=axb. If the algebra has an identity 1=b this forces x to commute with all elements a of the algebra, and this is pretty close to forcing the ring to be commutative. (In fact you can define algebras over noncommutative rings but they are bimodules rather than modules over the ring.) R.e.b. (talk) 18:17, 19 June 2008 (UTC)

A bunch of things
Hi all, I want to make a major edit of this page. Let me throw out a number of issues that come to mind when reading it. I have some ideas about how to address these but I wanted to open it up for feedback before I do.

Tone: I feel like the tone of this whole piece uncritically echoes the self-congratulatory accounts from her contemporaries that emphasize how much recognition and respect she got. Of course, the facts (many of which appear in this piece) show that she struggled for job security, pay, and credit for some of her ideas. Generally, the tone is a bit gushing in places (e.g., 7 distinct uses of the term "seminal," which I think was not intended ironically and which may be a record for Wikipedia pages). I just want to tone this down without changing any sourced content. A good example of this is in the description of the use of the masculine article in "der Noether." The idea that this is simply a term of respect is pretty obvious bullshit; the usage is clearly also flagging her flouting of gender norms. (It doesn't do a service to gloss over her colleagues' ambivalence about her gender, as in the famous Landau quote '...that she is a woman, I cannot swear.')

Structure of article: there are some redundancies in the writing, like the listing of her "epochs" in the introduction and then again in the "Contributions" section, or the use of some facts and quotes repeatedly (e.g., vdW's quote about her "absolute" originality). Some possible fixes include having the obituary commentary collected in "Assessment and memorials" and not repeated elsewhere, but especially: break the "Contributions to mathematics and physics" into its own article. Breaking it up makes a great deal of sense, as that section stands alone, has lots of great content, and the existing article is quite long.

"Structure" in Noether's work: I would like to add content about Noether's significance which has to do with her role in ushering in the age of axiomatic definitions. (This is, after all, part of what is so important about Noetherian rings.) Via van der Waerden and other associates, she was a major influence on Bourbaki for her ideas about axiomatic method. Here is a crucial quote from Noether: 'If one proves the equality of two numbers $a$ and $b$ by showing first that $a\le b$ and then $a\ge b$, it is unfair; one should instead show that they are really equal by disclosing the inner ground for their equality.'

Assorted details: The relevance of her political leftism is underemphasized, I think, relative to other data. There is not enough context about the expulsion from Germany-- the article makes it sound like she was singled out for an expulsion letter, when of course the purge of Jews and leftists from the civil service rolls was a major and early Hitler move, and only the ones with military service or who were especially senior (like Hausdorff) survived. The "bathhouse" story is sometimes described as apocryphal. Given the level of detail about her family, it seems relevant to mention that Fritz was executed in the USSR as a supposed Nazi spy.

Comments?

Mduchin (talk) 04:14, 9 July 2008 (UTC)


 * You have some very good ideas, and I think you know more about Noether than I do. Let me comment point by point.


 * Tone: I agree that the tone is over the top at times. I think that there are moments when it's justified (she was, after all, brilliant), and I don't think it's harmful to quote her contemporaries' opinion of her (it would be really interesting if you knew of cases where anyone was critical of her for mathematical reasons!) but you are probably right that it is emphasized too much. I agree that "seminal" seven times is about six times too much. Also, thank you for noticing the inconsistency of "der Noether"&mdash;after reading your explanation, I wonder how I was ever taken in by the present article. (As I said somewhere (on the FAC nomination page?) I once heard an elderly female mathematician recount that there were nasty jokes at Bryn Mawr about how unfeminine Noether was. "der Noether" would be entirely consistent with that.)


 * Structure of the article: You might have seen above that there was a proposal to write Introduction to the algebra of Emmy Noether; the intent was to break off the "Contributions to mathematics and physics" section that is presently so long and unwieldy. That hasn't gone anywhere, but I think that's for lack of effort, not lack of interest.


 * Structure in Noether's work: I am not sure how relevant Bourbaki is to this article. Bourbaki began working in 1935, and their Mathematical Reviews records stretches back to MR0004746 in 1939. That's late enough to have been influenced by Noether, and van der Waerden's algebra book was certainly popular; but what you hear most often is that they were reacting to the looseness of Poincaré (and if you'd had to figure out Poincaré you'd write books like theirs too). Interestingly, "Bourbaki: A Secret Society of Mathematicians" p. 46 says that "nationalist hatred prevented normal scientific relations with Germany and its allies" and then goes on to mention that many of the future members of Bourbaki visited Germany anyway, and this led the German school of algebraists to have a "strong influence on Bourbaki".


 * Other details: Yes, these sound like good changes.


 * One last comment. You said "major edit" above. Would you mind breaking it into smaller edits? Small edits are easy for the rest of us to read, comment on, copyedit, and so on. I know I have an unfortunate tendency to not save an article until I've made every change I'm going to make, but I've learned that's hard on other editors. Instead I've been trying to break up my edits, and that seems to make things go more smoothly.


 * Oh, and thank you very much for your comments. Ozob (talk) 21:04, 10 July 2008 (UTC)


 * Hi Mduchin! Your ideas for improving the article sound good, and I support most of them.  The article is incomplete in several ways, unfortunately, although we did do our best during the FAC and before; speaking for myself, I was generally too busy trying to understand her math to fret over the other parts.  I think the biggest lacuna is the lack of discussion of Richard Dedekind, e.g., her editing of his works, her admiration for his insights (Es steht alles schon bei Dedekind.) and her work extending some of his ideas, especially the ideals.  More context about the state of algebra before Noether would be nice, too, e.g., Steinitz's clarification of fields.  I tried to explain her contribution to the axiomatization of math in that blurb on begriffliche Mathematik, but it was just dashed off and could be done much better.


 * I agree with Ozob that smaller, piecemeal changes would be better than one big edit.


 * Politically, Emmy seems to have been a left-sympathizer, but not an activist. Alexandrov's obituary is the most explicit on that score.  If I recall correctly, all of her obituaries mention her strong pacifism, which seems to have been more important to her than any other political stance.  Her brother's fate might be worth noting, although I suspect it says more about the Soviet Union at that time than it does about Fritz.  A word or two about Fritz's math might be nice as well.


 * The writing could definitely be touched up as well. I'm guilty of the multiple "seminals"; I was writing in a hurry, and didn't stop to think too hard or fetch my thesaurus.  If I'm not mistaken, the adjective was used aptly, since they were works upon which many future mathematical works were built.  The repetition of the epochs was intentional, to give the reader a framework to aid their memory in such a long article.  If we break out the math sections, that repetition will be eliminated.


 * I'd like to start the "Introduction to her math" article, but I'm swamped right now with my sister's wedding, and won't be free for another nine days or so; can you wait that long? It's very hard for me to even get Internet access; my family is rather rural and a little Luddite. ;) I have a full set of notes that I've prepared for the Introduction article.


 * Thanks again for volunteering to help improve the article; the more the merrier, especially when it's informed people who really care about their subject! :) Willow (talk) 14:19, 12 July 2008 (UTC)


 * PS. By the way, it would really help us if you could also contribute to improving the List of publications by Emmy Noether. Thanks muchly! :) Willow (talk) 14:29, 12 July 2008 (UTC)

Copyedit
After quickly scanning the article, I see a bunch of opportunities for copyediting: minor consistency issues, some awkward phrasing, nonstandard name or two. I'll go over the article and implement the (hopefully) uncontroversial ones, then come back and discuss less clear-cut cases. Arcfrk (talk) 09:33, 15 July 2008 (UTC)
 * Ok, temporary break :) Arcfrk (talk) 12:09, 15 July 2008 (UTC)
 * Good god, did you return or not??? You can't drop a bombshell like the fact that you're going to copy edit the article and then not give us timely updates! This is big news, man! --136.165.112.49 (talk) 13:49, 4 September 2008 (UTC)

Seminal/germinal
It makes more sense to me to use the word germinal rather than seminal - am I just being too picky here? LadyHawk (talk) 13:18, 4 September 2008 (UTC)LadyHawk

Notability
Who cares about this silly broad? —Preceding unsigned comment added by 207.151.237.51 (talk) 20:08, 4 September 2008 (UTC)

Right. I am also wondering why there aren't more pictures of all the men who helped her. We've only got three on this page (while, if you go to their pages, there are no pictures of this Emmy girl). This makes it clear that they influenced and inspired her, she did not influence and inspire them (except for the "Noether boys" for whom she was a mother-figure, no more). I mean, it's not possible that she could have come up with this stuff herself. I think instead of a picture of her at the top there should be a cluster of photos of the men who structured the vessel of her moldable mind. LamaLoLeshLa (talk) 17:50, 5 September 2008 (UTC)

What are you talking about, Lama? Randomblue (talk) 19:07, 6 September 2008 (UTC)


 * My guess is that Lama is sarcastically responding to the sexist comment of the original poster. Scartol  •  Tok  12:44, 7 September 2008 (UTC)


 * Indeed, thanks Scartol. I suppose I was a bit incomprehensible. LamaLoLeshLa (talk) 05:09, 10 September 2008 (UTC)


 * Funny Lama. :) Sorry. Randomblue (talk) 12:55, 10 September 2008 (UTC)


 * I've gotten skilled at detecting sarcasm, even online. =) Like on The Simpsons: "Oh, a sarcasm detector! That's a real useful invention!" (the machine blows up) Scartol  •  Tok  15:09, 11 September 2008 (UTC)

Jewish family
In a normal world I agree that this would not be relevant, but to make any sense of the biography of someone living and working in Germany in the 1930s Jewish parentage is dreadfully relevant. At the time I write this, all mention of Jewish parentage has been deleted from the introduction, and we are suddenly told for no apparent reason that the Nazis fired all Jews in 1933. Whatever can be said about the relevance of "ethnicity" in general, her specifically Jewish lineage in specifically Nazi Germany is at least as relevant as being a female in a male world; though it might not be relevant for somebody whose parents were Danish working in France, for example. Being of Jewish lineage and a woman will have affected her work and professional life; even if they had not affected her work they would still be relevant to her biography, though possibly not to an article specifically on her work. A mention of her lineage is in no way boastful or POV. I will re-insert a mention. Pol098 (talk) 18:55, 6 September 2008 (UTC)

Assessment, recognition, and memorials
I don't know when (probably during the TFA moment) or why the items in the "Assessment, recognition, and memorials" section was turned into a big list, but I don't like it. I much prefer the paragraph form that was originally used when the article was taken to FAC. What do other people think? Scartol •  Tok  15:08, 3 December 2008 (UTC)


 * I agree, but am heading off for other places as we speak. Would someone else mind reverting? Ozob (talk) 02:58, 7 December 2008 (UTC)

Date of Einstein's letter
An anonymous user,, informs me that MacTutor's date for Einstein's letter to the NY Times on Noether's death is incorrect. He says that the correct date is 4 May, not 5 May, and says furthermore that a reproduction of the original can be found at the NY Times archive. It seems that this is it:. But I can't verify that this is the same as the letter MacTutor reproduces at because I don't subscribe to the Times (and I'm not going to pay $3.95). Can someone who does subscribe verify that we're talking about the same letter here and that MacTutor's transcription is accurate? Ozob (talk) 23:54, 6 July 2009 (UTC)

Reference in Fiction
Australian writer Greg Egan (who knows about Math and stuff) has a city called "Noether" (sic) in his SciFi short story Border Guards. — Preceding unsigned comment added by 83.99.45.146 (talk) 00:19, 17 October 2012 (UTC)

Speculation on "Emily"
I removed the following bit of speculation from this edit, since it veers into the realm of WP:OR:


 * There are many references in English to "Emily Noether"; possibly "Emily" is used believing that "Emmy" is a nickname, as it is in English, for the formal name "Emily"

Scartol •  Tok  19:29, 6 March 2012 (UTC)


 * I agree that's OR, and the best "source" I could come up with seemed to be a typo. I am not aware it was a commonly used nickname (unlike Emmy), and I would like a good source before mentioning in the article. Huon (talk) 19:44, 6 March 2012 (UTC)


 * Emily is not a nickname, where did you get that idea from? What seems to be happening (though there's no source for it) is that a few people who know Noether as Emmy and want to say something formal assume Emmy is a nickname and Emily the formal name, and incorrectly use "Emily", in the same way as someone who knew Dick Feynman and has to give a talk will refer to Richard Feynman. "Emily Noether -wikipedia" gets a a few thousand Google hits, s significant number but vastly less than the correct Emmy Noether. There's no way this is a typographical mistake, it's an error; she's not "called" Emily as such, but (erroneously) referred to that way. The reasons for including this in the article rather than silently correcting, as for a typo, is to let readers who have come across references to Emily Noether know that she is the same person; and to make a Wikipedia search for  find the right article without a redirect. A footnote saying something like <"There are many references in English to "Emily Noether", which is not her correct name; possibly "Emily" is used believing that "Emmy" is a nickname, as it is in English, for the formal name "Emily"> would help, but there may not be a source saying as much.  To complicate matters further, it could be said that "Emily" is unrelated to Emmy, but rather the English version of "Amalie". But the essential point is that published references to Emily Noether do mean her. Pol098 (talk) 21:50, 6 March 2012 (UTC)

Definitions
In my opinion the "definitions" of group, ring, galois theory, chain condition etc. do not belong to this article. Futhermore is the definition of chain condition wrong and also confusing. The ascending chain condition may be satisfied by a series of elements from a partially ordered set. A strictly increasing series will never satisfy a chain condition. Nijdam (talk) 22:38, 17 March 2012 (UTC)
 * I agree with Nijdam. Long passages could be dealt with with a link to the article on the group. — Preceding unsigned comment added by 92.28.8.74 (talk) 11:34, 28 February 2013 (UTC)

American citizen?
Could anybody cite the fact she was US citizen from 1933 until 1935? She immigrated in 1933, which does not mean she became US citizen.--Kiril Simeonovski (talk) 14:52, 9 December 2010 (UTC)
 * A very interesting point. There are many web sites that state that she was a US citizen from 1933-1935 (many of them otherwise credible and respectable), but without an explicit primary source they may simply be repeating a popular but unfounded assumption. From what I undersand of her personality from biographical sources, I would not expect her to have thought about adopting US nationality unless the idea was pressed upon her. She was only in the US for two years, during which time she made at least one return visit to Europe. If I had to guess, I would think it unlikely that she was ever a US citizen, but that's all it is - a guess. I would be very interested to see an authoritative primary source (or even a credible reference to one). FredV (talk) 15:53, 9 December 2010 (UTC)
 * Was it even possible to become a US citizen in under 2 years at that time? Colin McLarty (talk) 20:14, 22 September 2013 (UTC)

Inverse conservation, implications for structure
Although Noether's theorem is expressed in terms of developing conservations from observed symmetry, I've always found the converse of that statement to be equally interesting. We observe that momentum is conserved within the limit of our measurements (which means a lot today), so one can conclude that the universe is linearly symmetric. This is of no small interest: it implies that the universe is not heavier on one side than the other. When one adds angular momentum, we are left with a universe that must be both linear and rotationally symmetric, a sphere. Further, when one considers the conservation of energy, we add a symmetry in time, which is widely held to be true anyway: we believe physics in the past was the same as physics today.

I've seen developments that point this out, but they tend to be rare. If there is a reason for this I'd like to know it, because I haven't seen one yet. However, if there is no reason and the mathematics is symmetric in that respect, I think it deserves mention here.

Maury Markowitz (talk) 02:01, 23 January 2014 (UTC)


 * I believe I read once that the converse of Noether's theorem is not true: There are conserved quantities that do not come from symmetries. Though I'd have trouble thinking of the reference.  Ozob (talk) 23:40, 25 July 2014 (UTC)


 * The converse is true when the theorem is quite correctly stated, but not when symmetry is understood informally as it is here. The exact truth is in Peter Olver's book Applications of Lie Groups to Differential Equations which takes many pages to explain all the concepts involved.  I have no immediate plan to clear it up in the article. Colin McLarty (talk) 14:23, 24 October 2014 (UTC)

Heading edits etc
I made a few alteration/additions to the section headings and removed a few "Emmys" per wp:SURNAME. I didn't notice this was a featured article then. Hope I haven't upset anyone.

I feel the lead is too long, and the family/personal details there could be be left out. As Noether is 'featured' (Her 133 rd birthday) on the Google Doodle at the moment I'll leave it alone for now. 220  of  Borg 13:48, 22 March 2015 (UTC)

Brilliant Article!
Kudos to the Wikipedians who wrote this article! It is indeed one of the very best that I have seen. The part on algebra- it could be used as a 'layman's' introduction to the field like Introduction to genetics is for genetics. Pratik.mallya (talk) 10:38, 1 March 2011 (UTC)

Hear! A work of great and lasting genius! — Preceding unsigned comment added by 205.232.191.16 (talk) 18:56, 14 October 2011 (UTC)

Indeed, this article will count as one of Wikipedia's greatest contributions to humanity! Many thanks to the committed Noetherians who brought all this information to the fore. Reddyuday (talk) —Preceding undated comment added 07:05, 28 April 2013 (UTC)


 * Really? Because much of this article (as does the chimercal statements about this article in this section) sounds like over-enthusiastic, fanboy/girl cheerleading. The tone of this article almost comes under question as being unencyclopedic, but ultimately who cares really. Alialiac (talk) 06:02, 23 March 2015 (UTC)

Google Doodle Feature
The topic is featured as today's Google Doodle. Am considering request to semi-protect the page as a preventive measure against vandalism Ryan (talk) 04:16, 23 March 2015 (UTC)


 * Generally, pages are not preemptively protected. Once we get about 8 or 10 actually vandalism attempts, then it would be appropriate to put in a request. Safiel (talk) 04:47, 23 March 2015 (UTC)
 * There seems to have been enough in the last 10 hrs, to warrent this: I put pending changes on, so that we can let through the more positive stuff. Its awesome to see a featured article on a doodle though, especially for women scholars! Sadads (talk) 14:33, 23 March 2015 (UTC)

"Amalie Emmy Noether"
I was going to complain about the given names, but I see this has already been resolved back in 2006. Still, I suppose the situation should be clarified in the article, perhaps best in a footnote.

The gist seems to be this: Although sometimes misreported, Emmy is not a short form of Amalie, it is her second given name (i.e. her official name is Amalie Emmy Noether, just as given here, but the tradition of double given names in 19th-century Germany was somewhat different to the Anglo-Saxon one. As alluded to at German_name, it was frequently the case that the second given name was intended as the Rufname from childhood, and the first given name was only used in very formal contexts. This was understood to be the case when Noether supplied her CV in 1907 and gave her name as "Amalie Emmy Noether", the underlining identifying Emmy as the Rufname she would normally use. From an Anglo-Saxon perspective this offers itself to the misunderstanding that "Emmy" is to be read in quotes, as a kind of nickname (hypocoristic) derived from Amalie. --dab (𒁳) 14:21, 28 March 2013 (UTC)

The problem here is that Noether seems to be the first known person with the officially given name Emmy. The form Emmy has seen earlier use, but always as familiar forms of either Emma or Emily. E.g. Emmy Destinn, born 1878 as Emílie. These Emmies would give their name as Emma or Emily, Emilie, etc. in official contexts. Noether is the first person I can find who uses Emmy as an official given name. There is nothing wrong with this, but it explains the tendency to interpret Emmy as the familiar form of the preceding Amalie, and it would be intersting if there is any known preceding instance of Emmy having been used officially.

At this point the only people called Emmy born before WWII I can find are For the latter two, we do not have any confirmation that Emmy is their official given name. So at the very least we can state that if Emmy was indeed chosen for the official record in 1882, this was a rather unusual choice. --dab (𒁳) 15:25, 28 March 2013 (UTC)
 * Emmy Noether, b. 1882,
 * Emmy Andriesse, b. 1914
 * Emmy Werner, b. 1929


 * Just to take a small sample from the state of Missouri, U.S.A., the official death records show several women (e.g. Feldmann, Flachs, Wendrich) born in Germany before 1882 with the given name Emmy. Although death records are not as reliable as birth records, so many occurrences would seem to suggest that it was a fairly common official given name in Germany at that time. — r.e.s. (talk) 13:55, 30 March 2013 (UTC)


 * I don't know if I've ever before seen the word pairing/phrase "official name" describing a person. Given, christened, birth cert., gov't./court documented/record, marriage license, death cert., family records - I've seen. Never "official name" for a person. A city, building, ship, horse perhaps- 64.47.44.27 (talk) 17:53, 23 March 2015 (UTC)