User talk:JackSchmidt/Archives/2008/09

Groups again
Hi Jack,

in the FAC process there are some good points raised by, some of which I'm not knowledgeable enough to answer maturely. Could you have a glance at the following remarks/concerns:

''4) In the history section the last paragraph would be better if it did not list a few selected (if important) developments, but conveyed the general importance of groups within mathematics as well as its liveliness as an autonomous subject in maths.
 * I think this is part of a valid criticism. Basically, 1882-2008 is summarized in a few sentences which over-emphasize the CFSG.  Merely indicating the general importance of group theory and its liveliness now seems to do a disservice to 1882-(whatever year the reader implicitly assumes begins "present day").  I think the last paragraph must become two paragraphs, one for 1882-1990ish, and one for the last twenty years.  However, I do not want to say this too loudly as I know the article is already too long.
 * I think the real criticism should go to the separate history article which ends too early, and forces the summarizer to awkwardly dance over 130 years. In that article we can add more detail/material for summary without worrying about the length problem.
 * "The early 20th century's group theory encompassed roughly the content of the basic concepts." is very wrong.
 * The early 20th century (say 1900-1940) saw giants such as Frobenius, Burnside, Schur, Coxeter, P. Hall, Weyl, Baer, among many others. The early 20th century already had Lie groups, representation theory of compact groups in characteristic 0 (including number fields), combinatorial group theory, Sylow-systems and normalizers (a set of permuting sylow subgroups that has had powerful effects on the study of finite soluble groups), regular p-groups, Hirsch's work on polycyclic groups.  The stuff in "basic concepts" was taught as introductory algebra in the 1910s.
 * For 1870-1960, Lie groups, Borel's essays were pretty good and referenced some other history books.
 * For 1940-1970, locally compact groups, Mackey's book on Unitary Representations has a very long appendix on the history of the representation theory of locally compact groups (which I think does 1940-1955 separately, and indicates in broad strokes the earlier history).
 * For 1880-1950, reps of finite groups, Curtis's book does a great job. It focusses on Frobenius, Burnside, Schur, and Brauer, but discusses the works of lots of others who worked in finite groups. JackSchmidt (talk) 13:35, 4 September 2008 (UTC)

5) The history section should elaborate on the emergence of the concept of group as independent of its constituent elements, a development that took place in late 19th century. The abstraction of a "group" from a transformation group is in a sense the essence of group theory and its applications.
 * This part is very easy to handle badly. I think enough is said in this direction already, and anymore would give undue weight to what is essentially a fringe idea.  Most of group theory is concerned with groups in particular representations, and virtually all of the applications are in particular representations. JackSchmidt (talk) 13:35, 4 September 2008 (UTC)

If you can, please just join in at the FAC discussion or at the article directly. Thank you! Jakob.scholbach (talk) 20:55, 3 September 2008 (UTC)


 * Sorry that my comments are not as useful here as there, and even less so than fixing things. Lately I have been very busy, so my contributions here are pretty sporadic.  I am trying to be creative this month, so perhaps a project for one day will be to flesh out the history article.  Once that is done, it should be easy to summarize it into a final paragraph for the history section of Groups (mathematics). JackSchmidt (talk) 13:35, 4 September 2008 (UTC)
 * Oh, that's fine. You are not supposed to patch the holes I and others produce! I'll try and see what I get out of the refs above. (This is enough material for another FAC, it seems!) Have a good day, Jakob.scholbach (talk) 16:29, 4 September 2008 (UTC)

History of group theory
Hi Jack, I'm glad that you liked Chandler and Magnus. I, too, am very fond of that book. Both your top–down approach and your outline of the topics seem very viable, that's half the task. Keep up the good work! Now you just need to carry out the plan (easier said than done, I know, so good luck!) I may be a bit too busy to split the labour even, but will try to help out some once you get the foundations in place, sketch the topics, and feel like taking a break. Best, Arcfrk (talk) 23:49, 11 September 2008 (UTC)


 * Thanks for the support. I spent a few hours drafting today, but haven't had time to commit it.  I finished "Part I" of C-M today (indeed, one might say I got so distracted with it; I hardly even considered post 1920 today).  I'll have to finish work on it tomorrow as it too late tonight.  I think I will try to merely get one of the time periods done as a model, and then concentrate on the instructions Magnus passed on, "Write down what you know, then check the literature, and expand."
 * The basic outline will be 20yr-ish periods for sections, and each of finite, discrete, and continuous getting a paragraph or two. The greats of each period should be mentioned and linked, as well as good topic articles.  I am hoping that in each period, at least one historically important topic will have its own article to highlight the period, and ideally one topic in each of the three main disciplines.
 * Chandler and Magnus has also helped clear up my muddled ideas about infinite groups, especially regarding the distinction between discrete and continuous. For me, there were basically finite groups, infinite groups with Sylow theorems, and completely ignorable stuff.  Since both discrete and continuous have some nice groups with Sylow theorems, they were fairly mixed in my head.  C-M mentions a simple result of Hurwitz, that a discrete, linear group is countable and acts discontinuously on some (finite dimensional, I think) manifold.  So now we have the finite groups, like PSL(n,q), the discrete groups, like PSL(n,Z), and the continuous groups, like PSL(n,C).  Algebraic groups and profinite groups still seem to straddle genres, but if I place them poorly, they can easily be fixed. JackSchmidt (talk) 03:57, 12 September 2008 (UTC)

Easy as pi?: Making mathematics articles more accessible to a general readership
The discussion, to which you contributed, has been archived, with very much additional commentary, at Village pump (proposals)/Archive 35 (subsectioned and sub-subsectioned). A related discussion is at (Temporary link) Talk:Mathematics and (Permanent link) Talk:Mathematics (Section "Making mathematics articles more accessible to a general readership"). Another related discussion is at (Temporary link) Wikipedia talk:WikiProject Mathematics and (Permanent link) Wikipedia talk:WikiProject Mathematics (Section "Making mathematics articles more accessible to a general readership"). -- Wavelength (talk) 01:28, 29 September 2008 (UTC)