Talk:Branches of mathematics

about cryptology
Nothing on the page about either computational number theory or cryptology, as far as I can see. This makes me sceptical about the claim that all areas are covered. Charles Matthews 23:00, 19 Feb 2005 (UTC)

Cryptology belongs under 'Information and communication' (#94) and computational number theory belongs under 'Number theory' (#11).

What I would like to see is the raw sub-headings expanded in the same way as those under Geometry and some of the Physical sciences. Tompw 14:44, 28 Apr 2005 (UTC)

Other lists
Charles Matthews had some other lists/categorizations, but I can't find these now. I've been staring at bits of AMS for a while, and, while the top-level categories make sense, some of the subcategories seem insane to me. 11B in particular seemed bizarre. For example, where can we classify stuff published in "Journal of Integer Sequences"? Thus, I am lead to look for Charles other lists ... linas 18:22, 24 July 2005 (UTC)
 * I don't know if this is helpful, but see Wikipedia:Classifications_of_mathematics_topics which I made redirect to Areas of mathematics. Oleg Alexandrov 20:45, 24 July 2005 (UTC)
 * There was some non-AMS list that he'd scavenged from somewhere. I didn't much care for such questions when I first saw it. Maybe I should ask directly. linas 03:27, 25 July 2005 (UTC)
 * Actually, Intereger sequences come under 11Y55. I agree that the AMS has severe limitations when used in a context like Wikipedia. However, as the article states, the AMS classifcation "has been used as a starting point to ensure all areas are covered, and related areas are close together". I fully expect the headings to be tweaked and moved around within the article. Tompw 15:11, 25 July 2005 (UTC)

Deletion of MSC numbers?
I note User:Tompw recently deleted, without explaination, some MSC numbers I'd just added. Why? Maybe I misunderstand the purpose of this list, but it seems that it was trying to be a cross-list to the MSC numberigng system, so I'm wondering why these are now being deleted. linas 21:39, 25 July 2005 (UTC)
 * I thought I had replied to this, but it seems not. I didn't delete it because it had the extra AMSC numbers, I deleted it because I felt it went into too much detail for the page, although I should've stated this under the edit summary. On reflection, it would be nice to re-include them as easily comprehended areas of Number Theory. I also feel that putting in AMSC numbers below the top level makes the article less readable. (There is something to be said for removing all AMSC numbers - they are a hang over of a copy and paste of the AMSC top levels. - see first few edits). Anyway, hope tha tclears that one up. Tompw 00:21, 9 December 2005 (UTC)


 * OK, not too big a deal, otherwise I would ave argued. I think it might be useful to have, somewhere, a cross-reference between MSC numbers and WP categories. However, this is not so urgent that I'll push on this. BTW, you may want to (re-) announce this page on Wikipedia talk:WikiProject Mathematics, as this may get you help filling out some missing sections. linas 23:21, 9 December 2005 (UTC)


 * I think I wrote about it a while ago. I have a map between MSC and WP categories, at User:Mathbot/msc. Oleg Alexandrov (talk) 01:02, 10 December 2005 (UTC)

about differential geometry
Wouldn´t it be more appropiate to include differential geometry in applied mathematics and appart of the algebraic structures? --anon

Most differential geometers I know would place themselves in the study of analysis, geometry, or topology rather than applied mathematics, despite its breadth of applications. FunctorialNonsense (talk) 06:55, 29 October 2021 (UTC)

Intro line to analysis
I think it is misleading to say that analysis is primarily related to rates of change. Many aspects to the theory do not arise in this way. I think it would be better to say that analysis is the study of inequalities, because this is the theme that runs through every branch, at least it seems to me. To quote Krantz (from a book review of 'A Companion to Analysis: A Second First and First Second Course in Analysis') "Analysis is dirty, rotten, hard work. It is estimates and more estimates. And what are those estimates good for? Additional estimates, of course. We do hard estimates of integrals in order to obtain estimates for operators. We obtain estimates for operators in order to say something about estimates for solutions of partial differential equations. And so it goes." Any comments? I tried to change it initially myself, but instantly got reverted. :) I should have started here I suppose. Thenub314 02:51, 28 September 2006 (UTC)
 * Inequalities play an important role in analysis, but this is not what the analysis is about however. I would argue that derivatives and integrals are much more important. Either way, I would suggest you copy your post to Wikipedia talk:WikiProject Mathematics where more people will see it. Oleg Alexandrov (talk) 03:15, 28 September 2006 (UTC)

Will do thanks. Thenub314 03:26, 28 September 2006 (UTC)


 * I just rewrote the introduction to analysis, incorporating most of what was already there. My goal is to add paragraphs for most of the subdivisions of analysis that are already present in skeletal form. I do have a question about content, and style, though.


 * Since the math portal points directly to this page, I think this ought to be a survey article describing things at a fairly high level. And since the non-mathematical reader is likely to look at it, I also think it ought to be lively and entertaining, to the extent that is possible. So I tried to make the lead-in to "analysis" informative, but also fun to read.


 * I'm interested in other people's opinions. Brickbats? Laurels? Whatever you think I deserve, please send it my way! Thank you. ;^>  DavidCBryant 18:59, 13 December 2006 (UTC)


 * Well, I'm starting to understand why Thenub314 gave up and wandered away without contributing anything to this article. My new intro to analysis lasted exactly 45 minutes. And it took almost an hour to write it! That's pretty discouraging.


 * Just so it will still be easy to find, I'm going to quote it here. If I don't get some feedback in a couple of days, I'll probably drag this whole discussion over to the general math forum and see what kind of response I can elicit over there. Oh -- here's the intro to analysis as I rewrote it.


 * "More than 2,500 years ago, Heraclitus of Ephesus taught the ancient Greeks that the world itself is change."


 * "Within the world of mathematics, analysis is the branch that focuses on change: rates of change, accumulated change, and multiple things changing relative to (or independently of) one another. From Archimedes to Zeno, the ancient Greek mathematicians and logicians embraced Heraclitus's idea, thus planting the seeds that would finally spring into full flower with the advent of Newton's and Leibniz's calculus during the seventeenth century."


 * "Modern analysis is a vast and rapidly expanding branch of mathematics that touches almost every other subdivision of the discipline, finding direct and indirect applications in topics as diverse as number theory, cryptography, and abstract algebra. It is also the lingua franca of science itself. In chemistry, biology, and physics, from astrophysics to X-ray crystallography, the language of analysis is spoken."


 * I'm still hoping to get some feedback! DavidCBryant 19:45, 13 December 2006 (UTC)
 * theres nothing about the subdivisions of analysis! Brad7777 (talk) 18:24, 10 November 2011 (UTC)

Added a blurb about subdivisions, feel free to build on it. FunctorialNonsense (talk) 06:45, 29 October 2021 (UTC) FunctorialNonsense

Combinatorics
I don't see the reason for classifying combinatorics under algebra. It is not algebra. Some combinatorics is algebraic, much is not. Any replies? (Is this the wrong place for this comment?) Zaslav 06:15, 1 December 2006 (UTC)


 * seems ok to me. go ahead and split it. Mct mht 06:34, 1 December 2006 (UTC)

mere stub, with an "appendix" of citing the American Mathematical Society's Mathematics Subject Classification
This "article" is a mere reproduction of American Mathematical Society's Mathematics Subject Classification. It does not even establish basic facts that Analysis is commonly divided in two major branches. It does not meet C criteria but is a mere stub. Mootros (talk) 23:31, 27 September 2010 (UTC)
 * I'm making an effort to clean up the article. It looks like the material can be divided naturally with encyclopedic information with external sources given here and a page for navigating withing WP at List of mathematics lists. I've already moved some the purely MSC listings to the MSC article.--RDBury (talk) 10:49, 5 October 2010 (UTC)
 * While I support removing the AMSC numbers (see my comments a few sections up), please ensure that the areas they refer to are still covered. It looks like the numebrs have been removed without adding any real content in their place... for example, there is now nothing on group theory, differential equations, sequences/series or game theory. Tom pw (talk) (review) 01:33, 6 October 2010 (UTC)

Suggested reading
Suggested reading for editors of this page:

. --Siddhant (talk) 06:13, 1 February 2014 (UTC)
 * I'd like to add Timothy Gowers, June Barrow-Green, Imre Leader (editors): The Princeton Companion to Princeton University Press, Jul 18, 2010, Part IV: Branches of Mathematics.--Vujkovica brdo (talk) 12:41, 6 March 2016 (UTC)

External links modified
Hello fellow Wikipedians,

I have just modified 1 one external link on Areas of mathematics. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:
 * Added archive https://web.archive.org/web/20100815034900/http://www.math.niu.edu:80/~rusin/known-math/index/tour_div.html to http://www.math.niu.edu/~rusin/known-math/index/tour_div.html

When you have finished reviewing my changes, please set the checked parameter below to true or failed to let others know (documentation at ).

Cheers.— InternetArchiveBot  (Report bug) 13:05, 17 October 2016 (UTC)

Innovation is one thing, but...
Since when is it good form to craft our own punctuation to effect language functions already fulfilled by long-established norms? Or should I say long:established ones. At first, I thought it was just a typo, but as I stopped to consider a helpful edit, I noticed that it's actually the usage decided on for the article. Personally, I don't believe the use of terms such as point:like or real:world has any merit that would lead us to replace the established versions. Wanting to do so seems a bit silly. Aboctok (talk) 14:56, 8 December 2020 (UTC)
 * I agree, and I made the edit. Hopefully I did not miss any of them. Ebony Jackson (talk) 04:40, 7 February 2021 (UTC)

An Ambigous Sentence
This sentence is ambigous and/or wrong and should be changed:

"In addition, as mathematics difficult by some subjects, often the most active, which straddle the boundary between different areas."

I will remove it temporarily. You can replace it with something better if you want.

Mojtabakd (talk) 12:26, 30 January 2021 (UTC)

Differential Equations
Differential equations should have its own sub-category under applied mathematics, preferably written by someone who knows more about the subject than I. I would imagine most folks who study differential equations would consider themselves applied mathematicians, but would raise their eyebrows if referred to as an analyst, so I would argue the template at the bottom should be modified accordingly, but I leave it up to an actual researcher of differential equations (as opposed to myself) to make said call. FunctorialNonsense (talk) 06:50, 29 October 2021 (UTC) FunctorialNonsense

"language of science" remark
In the introductory section of the Analysis subsection it is written "It is also the language of science itself and is used across chemistry, biology, and physics, from astrophysics to X-ray crystallography" when describing analysis as a whole. While analysis and particularly differential equations are widely used for modelling various phenomena in science I don't see any particular reason for why analysis should be called "the language of analysis" which would probably be better used to describe mathematics as a whole. — Preceding unsigned comment added by STEMster42 (talk • contribs) 21:52, 1 March 2022 (UTC)