Talk:List of important publications in mathematics

From Wikipedia, the free encyclopedia

Why the name change? Listing 'all and any' publications isn't so reasonable.

Charles Matthews 09:35, 8 Jun 2004 (UTC)

Contents

[edit] Merging lists

I have taken the existing list that was a sub-section in List of mathematics history topics and attached it to this article (removing Elements to avoid duplication). I have left this as a pure list - others can add summaries in the style of the Elements section if they wish - my own opinion is that this duplicates the contents of the articles themselves, and so List of ... pages should just be pure lists. Gandalf61 15:25, Jun 18, 2004 (UTC)

What about works that are very important but do not qualify as publications? For example, Thurston's Princeton lecture notes. It created new areas and introduced many breakthroughs, some of which are not clearly understood still. C S

[edit] Formatting

Can we use just one system of formatting entries on this page? Having half the entries in one format and half in another makes it hard to read. I've marked this article as needing cleanup. -- Fropuff 04:32, 2005 Feb 4 (UTC)

Made format of all entries consistent with format of majority, and removed cleanup notice. Gandalf61 10:21, Feb 4, 2005 (UTC)

[edit] Goal of this list?

A rather bold question: what is this list good for (other than honoring great authors and works)? Isn't it more reasonable to have literature (of which there is usually a lot, even if one only considers the great contributions!) within the respective (main) articles? Or is there an effort to create an external bibliography to avoid repetition? I greatly agree to having good lists of commented references for all math topics, but is it helpful to have all in one list? Won't it just explode?

To substantiate this, consider the list of category books given at topos theory. Quite some of them are to be considered "great" and they are very different in purpose and targeted audience, but all of them would be classified as "introduction" here. And of course, there are varying opinions on the quality of a book. Mac Lane is wonderfully to the point and quite condensed (compare Johnstone), but I would consider Lawvere/Rosebrugh as an easier introduction and Borceux as a better comprehensive reference work. Shall this list contain all these books only as introductions? When adding works for the other types of publications, the category theory literature alone would make quite a long list. Can the completion of the present article thus really be a goal to pursue?

Maybe a list of "famous historical math publications" would yield an interesting subset of the present list? --Markus Krötzsch 20:43, 19 Feb 2005 (UTC)

That the publications are 'notable' is always implicit. Well, this list was created by analogy with some other lists, for other academic areas. I think it is supposed to list the 'breakthrough' papers; that means it might help someone who wanted a list of the 50 most important theorems of all time ... Anyway if someone wants to build up such a list, it will do little harm. Charles Matthews 23:06, 19 Feb 2005 (UTC)

As the intro. says, this list was originally intended to be "a list of important publications in mathematics, organized by field". It is part of a series of "List of publications in ..." articles (see the "Lists of publications in science" category). It was supposed to be an index to other articles rather than just a list of titles i.e. each of the publications in the list should have its own main article (although this rule was never explicitly stated, and has not always been followed by subsequent editors). What qualifies as an "important publication" could be debated endlessly. There was a separate list of historical publications articles at one point, but it was merged into this list, as there seemed little point in having two potentially overlapping lists. If the number of articles on publications in any one topic area became large enough, then it could be factored out into its own separate ""List of publications in ..." article. Gandalf61 10:52, Feb 21, 2005 (UTC)

[edit] Suggestions for additions

How about the following publications? EGA and SGA by Grothendieck et al for algebraic geometry; "Topology from the Differentiable Viewpoint" by Milnor for differential topology; "Topology" by Munkres for general topology; "A Course in Arithmetic" by Serre and/or "Basic Number Theory" by Weil for number theory; "Finite Dimensional Vector Spaces" by Halmos for linear algebra; "Modern Algebra" by van der Waerden for abstract algebra; "Elements of Set Theory" by Enderton or "Set Theory" by Jech for set theory. Some of the books are important as standard and popular introductions to the subject and some for historical significance (e.g. Grothendieck's works). Thoughts? nparikh 18:58, Apr 19, 2005 (UTC)

Yes to: EGA, SGA, the Milnor book, the Weil book, the Halmos book, the German version of Modern Algebra. The rest, I think, don't have enough innovation (the Serre book is very good, but not very original). Well, I guess that's true in the case of the set theory, but there I'm not an expert. Charles Matthews 19:19, 19 Apr 2005 (UTC)

Should there be a "List of textbooks in mathematics" page to avoid clutter on this one? No matter how good they are, textbooks usually aren't groundbreaking (perhaps something like MacLane's categories book would belong here). I think there ought to be a page that lists, for example (and aside from those already mentioned): MacLane/Birkhoff, Hungerford, Lang, Weibel, Rudin, Ahlfors, Milnor, Hartshorne, Griffiths/Harris. I don't know if this is the page for them. Thorne 16:13, 9 October 2005 (UTC)

I see the list as a temporary stage before moving to article on each publication and the categories system (See Wikipedia:WikiProject Science pearls) . The structure of lists is used since it is more suitable for information gathering. Therefore, please add the textbooks you mentioned. At later stage, they will be categorized with the proper importance. APH

I think Diophantus' Arithmetica is very important, because Fermat studied it a lot. Timothy Clemans 00:07, 11 March 2006 (UTC)

[edit] More suggestions: Differential geometry and Lie groups

I notice that there differential geometry and Lie groups are rather under-represented here (particularly in relation to algebraic geometry). Arguably Gaston Darboux's massive treatise on surfaces should be included, as this is perhaps the most comprehensive culmination of 19th century investigations of the classical differential geometry initiated by Euler and Gauss:

As for differential geometry from a modern perspective, the most influential book I can name are the two volumes of Kobayashi and Nomizu (originally published in 1963):

  • Kobayashi, Shoshichi and Nomizu, Katsumi (1996 (New edition)). Foundations of Differential Geometry, Vol. 1. Wiley-Interscience. ISBN 0471157333. 
  • Kobayashi, Shoshichi and Nomizu, Katsumi (1996 (New edition)). Foundations of Differential Geometry, Vol. 2. Wiley-Interscience. ISBN 0471157325. 

This might serve as the differential equivalent of Hartshorne's Algebraic Geometry (which, I am happy to say, is on the list already).

Lie groups are trickier, but I nominate Lie and Engel's treatise:

  • Lie, S. and Engel, F. "Theorie der Transformationsgruppen", 3 volumes, B.G. Teubner, Verlagsgesellschaft, mbH, Leipzig, 1888-1893.

Elie Cartan may also deserve a place, if anyone cares to single out a book or paper in his "Groupes finis et continus..." series. Chevalley has arguably set the modern standard with his two-volume work on Lie groups, and may also be considered for inclusion here.

Any thoughts? Silly rabbit 15:02, 8 June 2007 (UTC)

Agree re Darboux and Lie, less sure about Kobayashi as I've not encountered these books. --Salix alba (talk) 17:02, 8 June 2007 (UTC)
As far as I am aware, it is the first sizeable publication dealing with differential geometry from the principal bundle point of view. Kobayashi, who had worked closely with Charles Ehresmann on the theory of connections, seems to have been the first to bring this body of work to the forefront of modern differential geometry. Then again, if you're not familiar with the books, I suppose they aren't as significant as I thought. So, nevermind. A related note: In that case, is there no "Hartshorne" for differential geometry? (Obviously not Spivak ;-) Silly rabbit 19:54, 8 June 2007 (UTC)

[edit] Suggestions for removals and reorganizations

GEB is a very interesting book (it had a marked influence on my own thinking when I was younger), but it does not belong here. It could be considered an important publication in computer science, but not in mathematics. BTW, the computer science list is much more readable and better organized than this one.

The game theory field has lumped combinatorial game theory together with economic game theory without making distinguishing them at all. It should be noted somewhere that these two are in fact two completely different fields with little relation to each other.

Feel free to uapdate the list. Please keep commenting about the changes in the talk page. APH 05:55, 28 August 2005 (UTC)
Strongly disagree with the proposal to remove the GEB entry from this list. GEB is an exposition of the work of Kurt Gödel in mathematics and logic. The computer science stuff is included to illustrate Gödel's arguments and conclusions, to make them more understandable. GEB is not primarily about computer science, any more than it is primarily about art, music or typography - they are secondary topics used to illuminate its main theme, which is mathematical. By all means feel free to re-organise or add to the list, but please do not remove GEB. Gandalf61 11:44, August 28, 2005 (UTC)
I agree with Gandalf61's comments: while the book can be perceived in many ways, the exposition of the Incompleteness Theorem - meaning, proof and relevance - is primary. Hv 13:01, 28 August 2005 (UTC)
Strongly disagree with both Gandalf61 and Hv. GEB is first and foremost a book about AI. That is its central theme. Gödel's work is woven into this because Hofstadter feels it has profound implications for AI (more correctly, he believes that "strange loops" are essential to cognition, and that Gödel's Incompleteness Proofs are prime examples of such). It is my belief that anyone who thinks that AI is used to "illustrate Gödel's arguments and conclusions" has fundamentally misunderstood what GEB is about. Sorry if that sounds harsh, but I'm not the only one is of that view. Hofstadter himself tends to get upset when people suggest that GEB is merely an original exposition of Gödel's proofs (he has written on this several times, even in the preface to the 20th anniversery edition of GEB, if I remember correctly). However, regardless of what the book is about, it is an indisputable fact that the impact GEB has had is on computer science and computer scientists, not mathematics and mathematicians. GEB suggests no new mathematics, and has not inspired new generations of mathematicians in any particular way (other than making clear how interesting mathematics can be, but that can be said of any number of books, many which have little to do with mathematics per se -- Stephen Hawkins' books could be said to be important publications in mathematics by that standard) but it really _does_ suggest new approaches in AI, cognitive science, etc. and this is where it has earned the title as a classic. Remember that this is a list of "important publications". GEB simply cannot be considered as such in the field of mathematics, no matter how central mathematics is to the exposition of its ideas.

[edit] Standards in all the Wikipedia:WikiProject Science pearls articles

List of publications in biology was put up for deletion at AfD but survived the process as there was no consensus. However, as someone who has been concerned with this Wikipedia:WikiProject Science pearls project for some months now, I am concerned. There is indeed a case that the material here is not free of a POV. How do we determine importance? Earlier this year the participants on List of publications in chemistry debated this and decided on two matters. First, they tightened up the criteria for inclusion, in particular insisted that publications that were important as an introduction had to have had a wider importance such as altering the way all future text books were written or altered the way the subject was taught. Second, they decided that all new entries should be raised for debate over a 10 day period on the talk page to determine whether they should be kept or deleted. Most existing entries were debated and several were deleted. This has worked reasonably well although it would be better if more people had participated. It is clear enough that it is not, for these articles, sufficient to allow anyone to add entries, as only very obvious nonsense is likely to be deleted. Each entry needs the consideration of several editors. I urge all interested in this project to look at what the chemists here have done and consider whether something similar or even better can be used on all pages in the project. I am putting this paragraph on all the other talk pages of this project. --Bduke 08:36, 22 April 2006 (UTC)

[edit] Related AFD

Wikipedia:Articles for deletion/List of publications in biology (2nd nomination) Kappa 08:14, 10 September 2006 (UTC)

[edit] Entries with no description or importance sections

I have deleted all entries that do not give a description or details of importance and moved them here.

Universal algebra

  • Wolfgang Wechler.
  • Springer-Verlag.

Description:

Importance:

Order theory

Lattice Theory, Garret Birkhoff, 1935.

Note I have removed the heading tags to format this section here better. Feel free to move them back if you can give a proper description and importance section. There are many entries with a description section but no importance section. Perhaps these should be moved here too, but then most of the importance sections are, in my opinion, quite useless. It is not sufficient to just state "introduction" without saying why it is a better introduction than others and whether it has had a wider influence, or to state "influence" without explaining what the influence is or was. It is precisely this that makes this list break the NPOV criteria. --Bduke 21:54, 13 November 2006 (UTC)

[edit] The criteria for entries

Please take a look at a discussion at Wikipedia talk:WikiProject Science pearls#Header template to all project list pages on rewording the template that generates the header to this list of publications to make the criteria for entries to the list rather tighter and better reflecting the notability criteria of WP. The motivation is to better take into account comments that have been made when some of these lists have been proposed for deletion. --Bduke 00:34, 17 December 2006 (UTC)

[edit] Categories of important publications

Please note Wikipedia:WikiProject Science pearls##Categories of important publications. Thanks, APH 10:23, 15 January 2007 (UTC)

[edit] Broken Link

The link to an online version of Gödel's paper is broken at the moment. That page is available through the Internet Archive, there is also a modernized, incomplete (pun intended) translation available (that is linked from Gödel's incompleteness theorems), and other sources. Although the modernized notation is easier for me to read, that version isn't finished and is certainly less "official". I think having an online link here to some translation of this paper is invaluable. Does anyone have preferences on a translation to choose? skip (t / c) 02:15, 6 February 2007 (UTC)

[edit] Additions to Number Theory

I had a few suggestions to be added to the number theory section and thought I'd post them here first (though I'm pretty sure they should be on the list). 1) Tate's Thesis for influence. 2) Jacquet-Langlands for influence. and 3) Wiles' Fermat paper for breakthrough and influence. Cheers. RobHar 01:12, 18 May 2007 (UTC)

By all means add them. This list could definitely use some expansion, especially for significant publications from 1950 and later. Myasuda 23:01, 19 May 2007 (UTC)
Just added them. Sorry to take so long. RobHar 18:02, 28 August 2007 (UTC)

[edit] Titles in italics or not?

There doesn't appear to be a consensus on whether or not publication titles on this page should appear in italics or not. Any opinions? I guess I'd suggest no italics. RobHar 18:04, 28 August 2007 (UTC)

[edit] Various proposals

  1. Remove the Importance row of the publication entries. While most of the Wikipedia lists of publications in science have them, I don't feel they add much value. The few Importance rows in this article that have content beyond the subjective pigeon-holing into the Topic creator, Breakthrough, etc categories could just be subsumed into the Description area. A well-written description should make the Importance row irrelevant.
  2. Remove the publications by Edmonds (Paths, trees, and flowers), Cook (The complexity of theorem proving procedures), and Karp (Reducibility among combinatorial problems). These are already present in List of important publications in computer science, and while the various science lists don't need to be non-overlapping, these papers belong more to the domain of theoretical computer science than mathematics. If the consensus is to keep these entries, then the Edmonds paper needs a description.
  3. Find more appropriate section titles than Elementary algebra and Abstract algebra. Perhaps the category for Grothendieck's Tohoku paper could be Homological algebra . . . though this might be too restrictive for a section title.
  4. More entries are needed, especially in Analysis and Topology. This can certainly be done without diminishing the overall quality of the current list.
— Myasuda (talk) 03:27, 22 May 2008 (UTC)
I agree with points 1, 2, and 4. For 3, I would suggest putting the Grothendieck paper under Category theory. Is that completely offbase? siℓℓy rabbit (talk) 04:08, 22 May 2008 (UTC)
No, it's not off-base. But since I just noticed that the Abstract algebra article has a link to the Abstract algebra section in this article, I think I'll hold off on changing the section titles until there's more feedback. For now, I'll just proceed with items 1 and 2. Thanks. — Myasuda (talk) 15:46, 23 May 2008 (UTC)
I've gone ahead and introduced some sub-sectioning. Entries formerly under Elementary algebra now falls under the Theory of equations. If anyone doesn't like it, feel free to revert. I've made a concession to the link from Abstract algebra by leaving this as a subsection title. — Myasuda (talk) 15:42, 8 June 2008 (UTC)