Template talk:Areas of mathematics

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Although much of the theoretical foundations of statistics are built on probability theory and other mathematical fields, I believe many statisticians feel that statistics is no longer simply a part of mathematics. I changed the Statistics link to Mathematical statistics to reflect this, and gave some justification in the edit summary. User:Fropuff effectively reverted my edit, giving no reason.

My version is similar in spirit to some of the other links here. For example, we link to Probability theory, not Probability; Optimization (mathematics), not Operations research; and Mathematical logic, not Logic. Abbreviated forms are used for the last two. I will do something similar and change the Statistics link to Mathematical statistics, abbreviated as Statistics. If you think it should be changed back, please discuss your reasons here first.

-- Avenue 13:19, 16 December 2005 (UTC)[reply]

Don't be ridiculous. When someone clicks on Statistics in this box they expect to see an article on statistics (which is still a branch of mathematics the last time I checked). The article on mathematical statistics needs to be listed for an AfD (IMHO). -- Fropuff 18:38, 16 December 2005 (UTC)[reply]
I agree that the article on mathematical statistics isn't in a good state. However I believe mathematical statistics was one of the major intellectual triumphs of the 20th century, so I'd prefer to see the article improved rather than deleted.
Comments like "Don't be ridiculous" don't help the debate much, in my opinion. Your position that Statistics shouldn't link to mathematical statistics seems inconsistent with your apparent acceptance of other links in the template. For example, when someone clicks on Logic here they get to see an article on Mathematical logic, not Logic. Do you feel this should be changed as well? Part of my reason for linking Statistics to mathematical statistics was that I wasn't sure if you were objecting to me not using this style of aggressive abbreviation, because your edit summary was silent on the issue. On this broader point, I note that User:Lethe has since reverted my last edit without comment (as part of a wider edit). This doesn't help us understand his reasons for doing so. Everyone, please make your summaries of edits on this topic more specific while it's being debated here.
On statistics being a branch of mathematics, did you check with someone who knows a lot about statistics (and not just mathematical statistics)? I'll quote the first sentence from Moore and Cobb (2000), Statistics and Mathematics: Tension and Cooperation, American Mathematical Monthly, pp. 615-630 pdf. (Moore is a past president of the American Statistical Association.)

It has become a truism, at least among statisticians, that while statistics is a mathematical science, it is not a subfield of mathematics.

The rest of this paper's lead paragraph gives further support to my argument that we should link to mathematical statistics, not simply statistics, as do the reasons listed here. -- Avenue 11:56, 18 December 2005 (UTC)[reply]
Since no disagreement with my last post has been expressed over the last few days, I will change the template to link to Mathematical statistics again. -- Avenue 02:39, 22 December 2005 (UTC)[reply]

too many[edit]

This list is inconsistent. Why do we separate geometry from differential geometry but not topology from differential topology? We could write in the 3 or 4 branches of topology, but I'd prefer to merge the two branches of geometry. Of course, before that happens, we have to make sure that the article geometry actually mentions differential geometry. At the moment, it does not. I would also like to see numerical analysis, functional analysis, calculus, and differential equations all fall under analysis. And linear algebra and abstract algebra (and maybe category theory as well, but maybe not) all go under algebra. Hmm... this all sounds like a lot of work. Maybe for the moment, it would be better to just split topology. -lethe talk 20:50, 16 December 2005 (UTC)

I did it, but now I'm afraid of escalation. I feel bad about leaving out algebraic geometry, for example. -lethe talk 20:59, 16 December 2005 (UTC)
Oops, apparently differential topology and differential geometry both redirect to differential geometry and topology. That's a bunch of crap though, if you ask me. -lethe talk 21:02, 16 December 2005 (UTC)

identity crisis[edit]

This template seems to have any identity crisis. It seems to me that there are three (different but related) questions it could be trying to answer:

  1. What are the major brances of elementary mathematics?
  2. What are the major areas of (contemporary) mathematical inquiry?
  3. What are the major theories of mathematics?

In some cases, there is no problem (probability is a good answer to all three!). But overall, it seems to answer some combination of the three of these. I think it might be more useful if it were more focused. For example, it has appears to include algebra, set theory, logic, calculus, differential equations and linear algebra because every undergraduate in a mathematical field learns something about this. They are answers to the first question, but they would be subsumed in abstract algebra, analysis, functional analysis and foundations of mathematics. I mean, it seems weird to see algebraic geometry and algebraic topology in there, doesn't it, when it is something that many people in serious math programs don't learn about until grad school? –Joke 14:26, 24 July 2006 (UTC)[reply]

A relevant discussion...[edit]

... with regards to this navigational box is currently taking place at Wikipedia_talk:WikiProject_Mathematics#Navigational_templates Tompw 21:40, 10 October 2006 (UTC)[reply]

Category theory[edit]

I added category theory, if set theory is there, category theory should be there too. Set theory and Category theory are certainly the two fundamental revolutions of the XXth century in Mathematics. Cenarium (talk) 17:20, 8 March 2008 (UTC)[reply]

As a professional mathematician, I have to protest the inclusion of category theory as a major field. There are only a handful of serious category theorists working in major research departments, whereas there are scores of set theorists. What are the major theorems in category theory? I can't think of any, although I can think of a great many major theorems in branches of mathematics other than my own. (talk) 01:43, 12 January 2010 (UTC)[reply]

Where does this fit in? Also, I think calculus should be split off from its parenthetical position "within" Analytics Analysis. It goes beyond that. —Anonymous DissidentTalk 08:06, 28 May 2009 (UTC)[reply]

It's not analytics. It's called analysis which is mathematical jargon for the study of concepts involving limits. Calculus does not go beyond analysis. Calculus is analysis. I've changed it to Analysis/Calculus. Charvest (talk) 07:54, 29 May 2009 (UTC)[reply]
Sorry, slip of the mind. —Anonymous DissidentTalk 08:01, 29 May 2009 (UTC)[reply]
Also the template at present is about the most major fields. If we are going to include things like knot theory then the template should really be expanded to include all the subdisciplines of each area. Charvest (talk) 07:58, 29 May 2009 (UTC)[reply]
Why should algebra have three subfields mentioned, then? —Anonymous DissidentTalk 08:00, 29 May 2009 (UTC)[reply]
Well no categorization is perfect, but I think the point of that is mainly to distinguish elementary algebra amd abstract algebra. Mathematicians often refer to abstract algebra simply as algebra and elementary algebra as arithmetic. Charvest (talk) 08:06, 29 May 2009 (UTC)[reply]

Proposed changes[edit]

Arithmetic and trigonometry should be removed - these are by no means "major fields" in mathematics (I've removed them).

Also, I think that a section should be made for differential equations (ordinary and partial), separate from "analysis/calculus" (this one seems to containt to may distinct fields). —Preceding unsigned comment added by Neworder1 (talkcontribs) 20:40, 30 June 2009 (UTC)[reply]

Comparison with Applied Mathematics template[edit]

Could this template be improved by adopting the hierarchical organization of the Applied Mathematics template?

I would suggest (roughly) following the MSC classification system.

  • Foundations & (Mathematical) Logic
  • Algebra
  • Analysis
  • Topology & Geometry:
  • Applied Mathematics: Main topics (left-hand side categories) from the AM template.

This division, using the MSC, seems to be the best available (one-dimensional) hierarchy, and does reflect the organization of the mathematical sciences' review journals. Thanks, Kiefer.Wolfowitz (talk) 16:40, 16 March 2010 (UTC)[reply]

Pure Mathematics template[edit]


This is a rough suggestion. Kiefer.Wolfowitz (talk) 17:22, 16 March 2010 (UTC)[reply]

Basic mathematics[edit]

It would be good to create another template for "Basic Mathematics" with

  • topics Basic algebra, Euclidean geometry, trigonometry, Calculus, linear algebra, ordinary differential equations, partial differential equations, Fourier analysis, probability, statistics, discrete mathematics, logic, combinatorics, operations research
  • Modeling and simulation: Mathematical models, Scientific computing,
  • Statistics: experiment, surveys, analyzing data, etc.

Thanks. Kiefer.Wolfowitz (talk) 17:22, 16 March 2010 (UTC)[reply]


Hello D.Lazard. Well, the Mathematics article and link belong on this template somewhere, as it is the main template at the Mathematics page and seems to be the main mathematics template. In a 'Related' section? You decide, but it does belong on this one. Thanks. Randy Kryn (talk) 13:59, 9 January 2020 (UTC)[reply]

I agree that it is better to have a link to mathematics, but certainly not at the end with transversal areas. There are several possibilities:
  • Changing the title into Areas of Mathematics (I do not like this very much, but I would not revert it)
  • Changing the title into Areas of mathematics (Mathematics)
  • The same with parentheses replaced by a mdash or "see also"
  • Making a subtite (that is, a centered multicolumn) Mathematics (probably the best, but more difficult to implement).
D.Lazard (talk) 14:48, 9 January 2020 (UTC)[reply]
Another way would be to change the visible title, but the other way around. Mathematics (areas) or even the full Mathematics (Areas of mathematics), although one word in parenthesis describes the link without the duplication. Looking at it the latter full name probably fits better. Randy Kryn (talk) 15:11, 9 January 2020 (UTC)[reply]
I agree with the latter full name. D.Lazard (talk) 15:57, 9 January 2020 (UTC)[reply]
It does seem appropriate for the template, let's give it a go and see if anyone objects or has other ideas. Randy Kryn (talk) 22:49, 9 January 2020 (UTC)[reply]