Talk:Glossary of areas of mathematics

We wanted to learn all these terms in a flashcard format so we built one and made it freely available. Thought it would be helpful for anyone who wanted to learn the content of this glossary in a flashcard format like Anki to also be able to discover that they exist and have access to it from the source.

Was going to suggest it to be added in an external links section like the following but as it is linking to our own site, following the instructions of the Wikipedia guidelines, thought it would be best to leave this in the talk page for other contributors to see if it would be relevant or see if there was a better place/format to put it

• Flashcard version of the Wikipedia Glossary of areas of mathematics in an Anki-readable format

Darigov Research (talk) 20:18, 6 March 2021 (UTC)Reply

Presently, this glossary list a number of items supposed to be areas of mathematics. In fact, many items are not areas of mathematics.

For example, the first item, Absolute differential calculus, links to Ricci calculus, and this article says that Ricci calculus is a notation in tensor calculus. Most source of this article are titled Tensor calculus or Tensor analysis, showing that the relevant area is Tensor calculus.

Similarly, if one follows the link of the second item, Absolute geometry, one sees that this is a geometry, that is, a sort of mathematical structure, that has nothing to do in a list of areas of mathematics.

Also, many items are labelled "something theory", and editors who entered them did not care that "theory" is often used in mathematics for refering to a specific method, and many mathematical theories are not areas of mathematics.

So, presently, this article is an indiscriminate (see WP:INDISCRIMINATE) list of things which may be areas of mathematics or may be not. Inclusions criteria must be defined. I propose the followings one.

For being included an area must satisfy at least one of the following conditions:

1. Being commonly the name of a course in college and university
2. Being the title of a textbook (research monographies being excluded per WP:OR)
3. Being explicitly in the scope of a mathematical journal or of a recurrent international mathematical conference (an isolated conference does not warrant the notoriety of the subject).

Clearly, the second criterion is the easiest to verify. It allows an easy sourcing by citing one of the textbooks titled after the area. D.Lazard (talk) 11:32, 5 July 2022 (UTC)Reply

• A glossary can includes rarer terms, such as Ricci calculus, that's one of the reasons they are helpful. A flexible ontological basis for areas of mathematics is another reason the glossary is helpful, to clarify the meaning of terms. Notational systems of course are going to overlap with areas of mathematics, because mathematics involves a lot of notation, and as long as the notational system is notable, and an a indicator of mathematical concerns or methods that people learn, then it makes sense to have them included in the ontology of area of mathematics; because that's how the terminology is used in discourse. The same can be said about geometries that are titles of books, where it's clear the term is polysemic. The same can be said about theories too; if there is a persistent trend of applying a theory to new concerns, development of the theory, and the theory is technical enough to require effort in learning, then it's fair to say that it's an area of mathematics. It would be ridiculous to base an inclusion criteria on ontology, as other terminology can be relevant in the discussions of areas of mathematics. The inclusion criteria should be language related to encapsulations of concerns, methods, and theories within mathematics. Brad7777 (talk) 14:30, 5 July 2022 (UTC)Reply

  ... includes rarer terms, such as Ricci calculus: this is maybe a rare term in your domain of competence, but certainly not in mathematical physics. In any case, this is not helpful to readers to say them that it is an area of mathematics without reliable source asserting this, and when the linked article says the contrary.

  helpful to clarify the meaning of terms: WP:Wikipedia is not a dictionary, and this is the role of a dictionary.

  mathematical concerns: this is not a mathematical term. So, using it is confusing, because of the work needed for the reader to understand that it is your personal term for mathematical problem.

  Please read WP:INDISCRIMINATE and WP:DICTIONARY. You will see that your views on this article go against the foundational principles of Wikipedia (WP:Five Pillars). D.Lazard (talk) 17:00, 5 July 2022 (UTC)Reply

  The frequency of the use of a term is only relevant to this article in proving it's actually in use. And we don't need to rigorously define an area of mathematics to recognise them as distinct from other areas of discourse. The glossary doesn't even need to include only terms that *are* areas of mathematics in the strictest sense, as it's a glossary, meaning related jargon is ok. The entry of ricci calculus doesn't say "this is an area of mathematics" to back that up. But ricci calculus is certainly related seeing as the term is used to organise content of mathematics in a decent amount of textbooks, so at least is polysemic to some. The organisational approach of those authors may not be your cup of tea, but WP:NPOV applies here. If you want to explain how ricci calculus is definitely not polysemic, feel free adjust the entry with sources, because I've provided one where it's used as an area of mathematics in the entry already. According to WP:GLOSSARIES, entries are for the broad audience. Clarification of the meaning of terms can be approached through descriptions too, which is perfectly acceptable according to WP:GLOSSARIES. It's a common pattern that words are confusing you, yet words like "concern" are extremely common in English speaking countries, so I suspect this is due to English being your second language. If anybody else feels the word "concern" is too technical can you back D.Lazard up here? These sorts of points clearly indicate you are not interested in glossaries. (Should I even ask which of the five pillars my views seem to go against?) Brad7777 (talk) 17:51, 5 July 2022 (UTC)Reply

  Strange that some people who do not know mathematics feel competent for talking about mathematics, and think that they make mathematics easier to understand by changing mathematical words with a precise meaning to common words that have many meanings. D.Lazard (talk) 20:00, 5 July 2022 (UTC)Reply

  You realise that wikipedia is a community effort? If i make a mistake you can tag / edit it. So far your complaints of my entries have been: "I dont like the source, its better if there is no source." "I dont like your POV, it's better if its my POV", "I don't like your sourced entry, you made that up". Which entries have you actually contributed content to? Your recent edit to abstract algebra / modern algebra has been a restyling, the deletion of a reference, with the edition of an unsourced clause. Do you not remember tagging the page as unreliable, asking for inline citations? Why is it only you not using them? Brad7777 (talk) 05:12, 6 July 2022 (UTC)Reply

In the preceding section, I pointed that this article (Glossary of areas of mathematics) is a WP:INDISCRIMINATE list of things that are sometimes areas of mathematics, and sometimes not in which some entries are areas of mathematics and some are not. So clear inclusion criteria are required. I suggested the following criteria:

For being included an area must satisfy at least one of the following conditions:

1. Being commonly the name of a course in colleges or universities
2. Being the title of a textbook (research monographies being excluded per WP:OR)
3. Being explicitly in the scope of a mathematical journal or of a recurrent international mathematical conference (an isolated conference does not warrant the notoriety of the subject).

My question: Should this, or a modified version, be accepted as inclusion criteria for the glossary of areas of mathematics? D.Lazard (talk) 14:13, 5 July 2022 (UTC)Reply

D.Lazard, The suggested criteria do not seem to me to be good ways to identify an area of mathematics, but I am not a mathematician and would not presume to specify how an area of mathematics should be defined. A term in a glossary does not have to meet notability requirements. · · · Peter Southwood ^(talk): 15:55, 5 July 2022 (UTC)Reply

The context of the page is the glossary it is, and the areas of mathematics is themed on, which exist according to the article on mathematics, as well numerous other sources, including references on the article itself. This pattern of attack by D.Lazard, despite the article failing two nomination of deletion, is little more than WP:VANDALISM. Repeated bad faith edits make this clear. Inclusion criteria for glossaries is outlined on WP:GLOSSARIES. If you are unfamiliar with what could be constituted areas of mathematics, find some sources or listen to what other people are telling you. Your repeated unsourced adjustments go against the tag you've placed on the page, and it looks like you are more interested in time wasting. Brad7777 (talk) 15:56, 5 July 2022 (UTC)Reply

If anyone doubts that one of the terms refers to an area of mathematics they can tag it with {{Citation needed}}, like any other statement in Wikipedia where reasonable doubt exists.· · · Peter Southwood ^(talk):

Brad7777. It may qualify as contentious editing (I have no personal opinion at this stage), but it is not vandalism by the criteria used on Wikipeduia, which are quite specific. Cheers, · · · Peter Southwood ^(talk): 17:09, 5 July 2022 (UTC)Reply

This section is about a request for comments, not for personal attacks against the creator of the request. Moreover, if you had spent a few minutes to look at the history of my edits, (maybe) you would have avoided ridiculous assertions such as "If you are unfamiliar with what could be constituted areas of mathematics ...".

Also, you refer to the article Mathematics. Apparently, you have not read it recently. D.Lazard (talk) 17:20, 5 July 2022 (UTC)Reply

D.Lazard, Would you clarify your intended meaning in Apparently, you have not read it recently, {in what way is it "apparent") it comes over as unnecessary snarkiness. Please try to keep personal differences off the talk page so we can concentrate on the topic of the RfC. · · · Peter Southwood ^(talk): 06:20, 6 July 2022 (UTC)Reply

"things that are sometimes areas of mathematics, and sometimes not" are still within the scope of the glossary. These are very interdisciplinary times.  — SMcCandlish ☏ ¢ 😼  19:40, 5 July 2022 (UTC)Reply

Sorry for my confusing formulation. I have fixed it. D.Lazard (talk) 20:13, 5 July 2022 (UTC)Reply

I am not a mathematician so commenting on a glossary may be inappropriate but my first reaction is that this is not a glossary as much as it is a list of articles on mathematics in Wikipeidia so maybe the only criteria should be the linked article so states and no redlinks are permitted. A few examples of links currently in the article that are inappropriate would help me better formulate a comment. Tom94022 (talk) 00:53, 6 July 2022 (UTC)Reply

If it is a glossary, it should define and explain terms. Many of the terms are not well defined or explained. In a glossary it should not be necessary to refer to the linked article for the definition, that link should be to get a more detailed exposition. If it is just an annotated alphabetical list of Wikipedia articles it should be titled Index, not Glossary. Redlinked terms are acceptable in a glossary provided they are properly referenced. They would be out of place in an index. Also agree with what SMcCandlish said about scope of glossaries. · · · Peter Southwood ^(talk): 06:09, 6 July 2022 (UTC)Reply

Agreed, but that's a writing problem, not a scope problem. The entries – if this it remain "Glossary of ..." – need to be more definitional, whether they link to articles or not (and I expect they all would; this is not like Glossary of cue sports terms which contains mostly entries not notable on their own).  — SMcCandlish ☏ ¢ 😼  07:13, 6 July 2022 (UTC)Reply

Tom94022 This page is not meant to be a "Glossary of mathematical terms" as you suggest. It's meant as a "Glossary of areas of mathematics", which is something of much smaller scope. PatrickR2 (talk) 02:14, 8 July 2022 (UTC)Reply

What is an "Area of mathematics"? Is there any authoritative definition? · · · Peter Southwood ^(talk): 06:33, 6 July 2022 (UTC)Reply

There's not an authoritative definition, 'area' here is used colloquially; there's 11.7million hits for "area of mathematics" on google. The relevant google definition of area would be: "3. a subject or range of activity or interest." The prepositional phrase "of mathematics" is sort of self-explanatory as a qualifier, but there could be some disputes there. There are classification schemes that people can interpret as describing areas of mathematics. The other indicator of areas are the usage of terms as titles of discourse, sometimes outside of those classification schemes. I'm not sure that there is any reason to not be inclusive of areas beyond the classification schemes if they are notable, common, or historical because glossaries are intended to suit the broad audience according to wP:GLOSSARIES, and there is jargon outside of those classification schemes too. Brad7777 (talk) 07:22, 6 July 2022 (UTC)Reply

• Oppose as OR and inconsistent with the many "Glossary of ..." articles in Wikipedia. A brief but unscientific survey suggest no such article has a definition but all seem to rely upon links to a Wikipedia article for inclusion. So if there are elements of this glossary that are not supported in the linked article they should be deleted per se and not require an definition. Tom94022 (talk) 20:46, 6 July 2022 (UTC)Reply

  To editor Tom94022: The problem is that in most linked articles, it is unclear whether the item is an are of mathematics or not, and some linked articles say implicitly that they are not. Maybe, you can support the proposition if preceded by something like: The criteria apply to entries that are not explicitly qualified as area, branch or part of mathematics by the linked article. D.Lazard (talk) 09:42, 7 July 2022 (UTC)Reply

The solution is to delete the link from this article or fix the linked article so that only qualified articles are linked. Tom94022 (talk) 00:12, 10 July 2022 (UTC)Reply

• Comment. This is a list article per WP:SAL#Specialized list articles, and the corresponding guideline must apply. In WP:LSC, one reads :Selection criteria (also known as inclusion criteria or membership criteria) should be unambiguous, objective, and supported by reliable sources.. The selection criterias that are proposed are exactly aimed to define what is unambiguous and objective in this case and what are reliable sources for supporting inclusion. To editor Tom94022: If this is OR, then all guidelines of WP are also OR. D.Lazard (talk) 09:08, 7 July 2022 (UTC)Reply

True for Wikipedia guidelines, but that doesn't allow OR within articles such as this one. AFAIK there is no RS for the proposed guidelines. Tom94022 (talk) 00:12, 10 July 2022 (UTC)Reply

• Comment. The entries of typical glossaries are not usually the same part of speech. There is a focus here on guaranteeing all entries have the same hypernym; that all entries *are* areas of mathematics. But I disagree that this is necessary. This glossary could be akin to Glossary of Mathematical Subject Classification, including for example both 'fluid mechanics' and 'transonic flows' because these terms are used in MSC2020 as classificatory areas of research mathematics. It's irrelevant whether 'fluid mechanics' and 'transonic flows' *are* areas of mathematics. If this was the decided solution, then I would suggest a rename or merge to remove any confusion. Otherwise most of the terms should be deleted as WP:OR, despite organising areas of mathematics implicitly. — Preceding unsigned comment added by Brad7777 (talk • contribs)
• Comment The most recent deletion discussion suggested the Mathematics Subject Classification as a way of telling what counts as an "area". Inclusion at some level of such a hierarchy seems like a good criterion to adopt here. I think the textbook/monograph distinction is fuzzier than the proposal implies, and in any case the No Original Research policy does not prevent our citing monographs. XOR'easter (talk) 17:31, 7 July 2022 (UTC)Reply
• Support: As Peter Southwood mentioned, the problem seems to be the definition of area of mathematics. Is the representation theory of Lie algebras an area of mathematics?, while Lie algebra certainly is, not sure which subarea is an area of mathematics. One can argue any subarea or subsubarea (e.g., representation theory of semisimple Lie algebras) is but that’s surely problematic. I can’t think of better criteria than what is proposed here. (So support absence of a better alternative). —- Taku (talk) 06:35, 10 July 2022 (UTC)Reply

• Oppose: Going off what is said in WP:INDISCRIMINATE, I think it is pretty clear the glossary is not indiscriminate by the relevant definition there a "summary-only description of works"; this is an issue for each individual article that should be treated on an individual basis. It seems to me the main issue here is not necessarily that the topics aren't related to maths at all (at a cursory glance they all seem to be). Instead, as described by TakuyaMurata, the issue seems that different levels of subfields are all listed on the same glossary with no organisation.

I think inclusion criteria would be good, and I also think the proposed ones wouldn't work. I think it would be best to model on prior consensus for other list articles that have had issues about ambiguous inclusion criteria, and I know of one with a similarly huge list of entries that has been at pretty stable consensus for a while: Talk:List of common misconceptions. If I just take the first three from there and modify the wording slightly to match the different context, I end up with something like this:

1. The area's main topic has an article of its own.

2. The area is reliably sourced, both with respect to the factual contents of the item and the fact that it is a subfield.

3. The area is mentioned in its umbrella topic article with sources.

Since virtually all the entries on this list have articles of their own, (1) is no problem here. (3) should be no issue to add in using WP:SS, although it may take some time to review that everything is covered with due weight in the umbrella topic articles. About (2) I can see some disagreement about what really constitutes reliable sourcing for maths, which I would defer to WP:GNG which I would interpret as requiring at least two independent sources published in a mathematics journal (maths journals tend to be pretty broad with subfield coverage in my experience). We can draw on a comparison to the reliable sources guidelines for WikiProject Psychology:

[...] articles should be based predominantly on scholarly sources, including:

• Academic textbooks
• Review papers
• Peer-reviewed research, including papers and monographs
• Popularisations by a scientist

Based on this I think it is arbitrary/unrealistic to expect each field and subfield to specifically be in a textbook publication or university coursework, since that's not aligned with the notability criteria required for each individual subfield article to exist.

According to WP:CSC, Short, complete lists of every item that is verifiably a member of the group are acceptable, and I interpret this as suggesting: once they are too long it's no longer as useful/interesting as an index for readers. The current size of this glossary is 71 kB wikitext, well past the recommended WP:CSC limit of 32kB. So I suggest instead that this glossary instead list the entries at Category:Glossaries of mathematics, ideally with each one having a short summary when it is listed. Current glossary items that easily fit under one of those glossaries can be moved there if they are not already there, and if there are enough that don't neatly fit into one or more sub-glossaries then I think it's likely they can be created/discussed as needed. One aspect of this approach is the glossaries in that category seem to contain a mix of both definitions and subfields. I think it is fine to have both of them in the glossary when the topic is narrow in terms of a subfield.

Darcyisverycute (talk) 11:25, 10 July 2022 (UTC)Reply

Short, complete lists of every item that is verifiably a member of the group are acceptable: This RfC is just aimed to clarify what is "verifiably a member" of the the group called "areas of mathematics".

So I suggest instead that this glossary instead list the entries at Category:Glossaries of mathematics, ideally with each one having a short summary when it is listed. If I understand well, you suggest to have this glossary as an item of itself, since it is listed at Category:Glossaries of mathematics. Also, since Category:Glossaries of mathematics includes Glossary of mathematical symbols, your suggestion implies that you consider that "mathematical symbols" is an area of mathematics

The area is reliably sourced ... with respect to ... the fact that it is a subfield. This is the subject of this RfC to define what "reliably sourced" means for the assertion that something is a subfield. It must be taken into account that it is not common for mathematicians to say "this is a subfield". They prefer to say "this applies there and there". In other terms, most mathematicians think mathematics as a continuum, and consider that if does not help to categorize mathematics into narrow subfields. This may be problematic to find reliable sources for the fact that something is a subfield. D.Lazard (talk) 14:02, 10 July 2022 (UTC)Reply

I raise the point the list is possibly too long/unstructured to be useful as a glossary, that's all. I think it is well within the scope of RfC to consider the length of the glossary, how inclusion criteria may impact that, and how the article can be made more beneficial for readers by being easier to navigate.

I'm not suggesting to include those two glossaries since I agree that would not make sense. I don't know all the Wikipedia mathematics categories and that one just seems the most relevant for organising subfields. If you can find more relevant ones I think it would be useful to mention them here for consideration too.

I can't speak for other mathematicians, but the term subfield and the phrase "x is a subfield" is widely used in my maths research. And on Wikipedia too, here are a few examples: 1 2 3. I think there is a lot of merit to organising maths content on an encyclopedia which has happened in those examples in the form of summary style and using categories. And there is also substantial overlap between fields due to interdisciplinary applications which summary style and categories work pretty well for describing.

Could you point me to a few examples of where it "may be problematic to find reliable sources for the fact that something is a subfield", which you also believe meets WP:GNG? I think that would be useful to work out better wording for establishing notability. Darcyisverycute (talk) 15:30, 10 July 2022 (UTC)Reply

Oppose: these inclusion criteria are actually too lax in my view. Presumably we'd exercise common sense in textbook titles, so "Introduction to information theory" is not an area, but information theory is. But I think that if we allow anything in a textbook, grad course or journal scope then we'll have 300 different "areas" of Lie algebra, and end up defining every mathematical object. For instance, at undergrad I took a course titled "Rings and Modules", but that's not really an "area": it was a course in (introductory) algebra, or ring theory if you really want to be specific. A glossary on areas of maths shouldn't go into the definition of a ring or a module.

I find it strange that the page is ordered alphabetically, rather than by field. I suppose that's the nature of a glossary. But I wonder if a list of areas of mathematics would be better, and we would divide it into subsections like "Number theory", "Logic" and "Algebra". The disadvantage is that many areas of maths are at the intersection of multiple fields: take the proof of Fermat's Last Theorem as something that's hard to categorise. So you might have some things listed in multiple sections. But then you might hope that a non-maths PhD reader could make some sense of the page (hell, I doubt anyone in the world understands all these definitions, like Multilinear algebra: an extension of linear algebra building upon concepts of p-vectors and multivectors with Grassmann algebra).

In any case, the glossary at present has too much bloat. — Bilorv (talk) 20:58, 28 July 2022 (UTC)Reply

Note. We had an areas of mathematics page, organized as you described, but it was speedy deleted recently by this RFC creator. Brad7777 (talk) 17:58, 30 July 2022 (UTC)Reply

This glossary is ungrammatical by capitalizing every term including ones that aren't proper nouns. Look at dictionaries and most higher academic glossaries on Wikipedia and you'll see they only capitalize names/titles such as people and named places. While it's true in academic usage an entire term (like a department or field/subject) may be capitalized, in casual usage, they're not. The entries also aren't sentences (just are like dictionary entries) so it's incorrect to capitalize only the first word. Pick one usage: casual (probably) or academic (if you really want, but isn't all usage) and stick to it. This whole thing needs reformatting for grammar.--dchmelik☀️🦉🐝🐍(talk|contrib) 01:38, 24 July 2024 (UTC)Reply

Capitalization is only a minor issue of this article. The main issues are WP:INDISCRIMINATE and that this is a poor linearization of the structure of category:Fields of mathematics. So, I'll boldy redirect this glossary to Mathematics#Areas of mathematics, and also create category:Areas of mathematics as a redirect to category:Fields of mathematics. D.Lazard (talk) 10:02, 24 July 2024 (UTC)Reply

That redirect is effectively vandalism as you are clearly aware of the two attempts to delete the page. Please see Wikipedia:Articles for deletion/Glossary of areas of mathematics (2nd nomination) for example, that you instigated. Brad7777 (talk) 21:46, 25 July 2024 (UTC)Reply

To clarify, the consensus both times was to *keep* the page. Brad7777 (talk) 21:47, 25 July 2024 (UTC)Reply