From Wikipedia, the free encyclopedia
Jump to navigation Jump to search
Former good articleMathematics was one of the Mathematics good articles, but it has been removed from the list. There are suggestions below for improving the article to meet the good article criteria. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.
Article Collaboration and Improvement Drive Article milestones
January 22, 2006Good article nomineeListed
May 19, 2006Peer reviewReviewed
April 3, 2007Featured article candidateNot promoted
September 8, 2007Good article reassessmentKept
August 3, 2009Good article reassessmentDelisted
August 26, 2009Good article reassessmentNot listed
Article Collaboration and Improvement Drive This article was on the Article Collaboration and Improvement Drive for the week of May 23, 2006.
Current status: Delisted good article

Brainstorming / what does the article need?[edit]

Before editing the article in the coming year, I just wanted to ask what everyone thinks it needs most. I've always worked on more focused topics where improvements are relatively clear, but what specifically would move this one closer to FA status? Is there anything that stands out to the veterans in particular?

I've skimmed the article and come up with my own breakdown of possible changes, but that may not line up much with what everyone else agrees is important. I can discuss my proposed changes here first too since I imagine editing needs to be incremental here. Zar2gar1 (talk) 19:19, 8 December 2018 (UTC)

Yes incremental changes, and discussing proposed changes here first, are both very good ideas. Paul August 19:49, 8 December 2018 (UTC)

If nothing jumps out at anyone, I'll start by bringing up some smaller notes to discuss...

  • I really like mentioning Aristotle where the definition section starts, but I wonder if it should convey a little more continuity with what follows. Aristotle definitely focused on quantity & magnitude more than today, but he also commented on how it relied on a sort of abstraction ("separability"): Physics II.2
  • I noticed that the article (rightly, I feel) mentions the cognitive "moves" people use in math throughout (e.g. deduction, counting, etc.). However, synthesis & analysis in the mental/philosophical sense are never really brought up. If that would be a positive change, I don't know what the best way to massage them in would be, but I did a little experiment using find in my browser just to have some data...
    • "synthesi(s/ze)", "assemble", and "combine" never appear in the article at all
    • "build" only appears in historical discussions, never as an intuitive act
    • "construct(ion)" does pop up several times, but only in this sense around the paragraph on intuitionism and maybe the discussion of Gödel's incompleteness theorem
    • "analy(ze/sis)" obviously appears several times as part of subfield names. Otherwise, except for maybe two instances (one in footnote 59 for a source on set theory and the other near the mention of Newton), the word is just used as a synonym for study
    • Other synonyms, like "divide/division", "split", "break down", and "decompose" never appear in this sense either, if it all; the one use of "reduce" near another discussion of Gödel's theorem may be the only exception.
  • Finally, without overemphasizing it and biasing the article towards an intuitionist POV, it might be worthwhile to mention the role of intuition and creativity a little more directly. The "Inspiration..." section seems especially fitting for a couple sentences, but perhaps just namedropping & linking one of the words in the lead's second paragraph wouldn't hurt either. Zar2gar1 (talk) 14:23, 15 December 2018 (UTC)
This is a digression, so I'm putting it in small type, but just so you know, you might want to be careful with the word intuitionism, which does not really mean what I think you think it means. The defining feature of intuitionists has little to do with intuition; it has to do with their rejection of excluded middle. The term "intuitionism" for this has a historical basis in Brouwer's personal intuition, but it does not have much to do with whether your foundations are based on intuition. Unfortunately the lead of our intuitionism article is misleading on this point and really ought to be corrected. --Trovatore (talk) 21:52, 15 December 2018 (UTC)
Oh, no worries. I'm aware intuitionist logic is pretty much what people usually mean by the word nowadays. My impression's always been that the different philosophical outlook is still there in the background though, even if nobody obsesses over it like Brouwer did, but I could be mistaken. Since the above changes all touch on more philosophical & mental things, I just wanted to let everyone know I was aware about it and wasn't going to use any edits to make math look like Romantic poetry or something. I really appreciate the feedback though and would be interested on what you think about the changes themselves. Zar2gar1 (talk) 00:45, 16 December 2018 (UTC)
Oh, absolutely, the import is philosophical, not just formal. But the point is that intuitionists are not the only people who place a high value on intuition. For example Gödel (Platonist) proposed that truths about underlying mathematical reality were directly accessible to intuition. --Trovatore (talk) 00:50, 16 December 2018 (UTC)
I like Zar2gar1's suggestion that there be a small section discussing how mathematicians seem to think about how they obtain results. I feel I got good at math only when I learned how to make "cognitive moves", but I never know how to explain that to someone who does not know what it means. However, the terms "synthesize", "build", "construct", "analyze", "divide", "decompose", "split" "reduce" are all far more mechanical -- that is what I do when I'm not particularly inspired or awake ... its necessary but sometimes tedious make-work to split, construct, analyze, synthesize. Without these steps, you can't quite gain the required knowledge, but they're the least-fun part of math .. the "cognitive moves" being the most fun (for me). It seems that suitable articulations are necessarily philosophical, metaphysical, or appeal to psychology, sociology or have MD's place mathematicians into MRI machines. Here is a physics paper that asks: "how can assemblages of atoms (described by equations, taking the form of humans) come up with ideas and communicate them?": "Agent Above, Atom Below: How agents causally emerge from their underlying microphysics" by Erik P Hoel (talk) 19:43, 18 April 2019 (UTC)

No mention of realism?[edit]

Prompted by my response in the previous section, I searched the article to see how the term "intuitionism" was used h:ere, to see if it needed work, and I came across this sentence:

Three leading types of definition of mathematics are called logicist, intuitionist, and formalist, each reflecting a different philosophical school of thought.[37] All have severe problems, none has widespread acceptance, and no reconciliation seems possible.[37]

Now, what jumps out at me here is that realism (Platonism) is not mentioned some people seem to think that logicism is a form of realism, but this makes no sense to me. In fact the word "realism" does not appear in the article at all, and "Platonism" shows up only in the external links.
I have to say this seems like a flaw. I'm not sure the right place to mention realism (or indeed the other schools) is in a sentence about definitions, but it's pretty weird not to mention it at all. Ideas for improvement solicited. --Trovatore (talk) 00:47, 16 December 2018 (UTC)

See the book 18 Unconventional Essays on the Nature of Mathematics and chapter one deals with platonism (and I think it makes the argument that if its accessible to intuition, it must therefore be platonic). Chapter two claims that math is an oral tradition passed from professor to student. After that things spiral out of control. Now, I'm not sure if it's just me, or if others feel this way, but whenever I read "Popper says XYZ", I always manage to think "wow, this Popper guy sure is wrong." Should I be mildly miffed, or is there a cult of Popper, or am I just a jerk? OK, the latter, but what's in the kool-aid? (talk) 04:29, 13 January 2019 (UTC)
The book is available here. Boris Tsirelson (talk) 05:50, 13 January 2019 (UTC)
I understand mathematical realism as a philosophical theory about mathematics, not a definition, i.e. not an attempt to distinguish mathematics from everything else. I do think that the realist/fictionalist controversy merits a mention. We have a section titled "Foundations and philosophy", which currently contains no philosophy. Definitions of mathematics are really part of the philosophy of mathematics—AFAICT, the main part. Perhaps, then, a good place for a quick summary of Platonism, etc. would be the "Definitions" section, perhaps summarizing the literature on how the competing definitions relate to the competing theories of what mathematical propositions correspond to? —Ben Kovitz (talk) 19:43, 9 June 2019 (UTC)

Semi-protected edit request on 4 February 2019[edit]

Could you merge the last two sentences of the introduction? "application in mind, but practical applications" (talk) 13:21, 4 February 2019 (UTC)

On an unrelated note, could you remove Encyclopedia of Mathematics from the external links? It's a link to a Wikipedia article, so it should be put into the see-also section, or it should be removed entirely. (talk) 13:25, 4 February 2019 (UTC)

I do not see any advantage in combining the two sentences, but I have fixed the link to the Springer Encyclopedia of Mathematics. Rick Norwood (talk) 15:48, 4 February 2019 (UTC)
 Done, along with a little wording tweaking to make it read a little easier still. –Deacon Vorbis (carbon • videos) 17:39, 7 February 2019 (UTC)

Nomination of Portal:Areas of mathematics for deletion[edit]

A discussion is taking place as to whether Portal:Areas of mathematics is suitable for inclusion in Wikipedia according to Wikipedia's policies and guidelines or whether it should be deleted.

The page will be discussed at Wikipedia:Miscellany for deletion/Portal:Areas of mathematics until a consensus is reached, and anyone is welcome to contribute to the discussion. The nomination will explain the policies and guidelines which are of concern. The discussion focuses on high-quality evidence and our policies and guidelines.

Users may edit the page during the discussion, including to improve the page to address concerns raised in the discussion. However, do not remove the deletion notice from the top of the page. North America1000 12:38, 26 March 2019 (UTC)

Why was the external links section removed?[edit]

On 7 February 2019, User:Deacon_Vorbis removed the external links section, justifying his edits by saying "None of this is really what external link sections are for." I have conformed with WP:NOTLINK, there was no good reason to remove the external links. I am new to editing Wikipedia, so there might be something I'm missing out, but as far as I can conclude, the external links section should be brought back. Is that right? Ambuj Shukla 15:50, 5 May 2019 (UTC)

The external link section deserves to be brought back only if there are external links that pass WP:ELNO and are useful for the article. If you think that some of the removed links belongs to this category, list them and explain why do you think that they must be added again. So we could discuss whether there is WP:consensus for that. If a consensus is reached for some of these links, then they will be added in a section "External links". Otherwise this section is not needed. D.Lazard (talk) 16:17, 5 May 2019 (UTC)

'Definitions of mathematics': section's repeated line.[edit]

In the first paragraph, the sentence "Benjamin Peirce (1809–1880) called mathematics "the science that draws necessary conclusions".[33]" is almost identical to the fourth paragraph's "An early definition of mathematics in terms of logic was Benjamin Peirce's "the science that draws necessary conclusions" (1870).[38]" I suggest keeping the second instance of the sentence because it contains a better reference and it is more vital to the paragraph. Pabsoluterince (talk) 04:41, 17 May 2019 (UTC)

@Pabsoluterince: I've gone ahead and removed the first because the context doesn't really require it to be there. the reference is [1] incase anyone would use it in the future. (Oops i forgot to sign myself) --NikkeKatski [Elite] (talk) 15:11, 17 May 2019 (UTC)


  1. ^ Peirce, p. 97.

Fuzzy beginnging of the article[edit]

I think this article should start "Mathematics is a scientific method modelling reality to understand and describing reality. This applied from children’s counting of toys to Einstein and quant physics. There are differences if the math is a part of the reality itself, due to strong correlations or an invented scientific language to describe the world. Mathematics is used in most sciences as tools in understanding and describing the reality."

--Zzalpha (talk) 17:43, 9 June 2019 (UTC)

That would count as application of mathematics, but not as creation of new mathematics by its practitioners, unfortunately. --Ancheta Wis   (talk | contribs) 17:49, 9 June 2019 (UTC)
This is a possible definition of mathematics, although very few living mathematicians would agree with it. Even among mathematicians and philosophers, there is no consensus for a definition of mathematics. Therefore, per WP:NPOV, every definition that is given in Wikipedia must be attributed to a recognized author. This is not the case for the definition the you propose.
By the way the relationship between modern mathematics and physical reality is not understood, even by the best mathematicians and philosophers. As a witness of this, I know of a well known mathematician who was strongly antimilitarist, and said that his choice of research field (modular functions) was motivated because the results that can be obtained in this area cannot be used for military purpose. Alas, a few years, applications to high energy physics were found, and the subject became useful for military purpose. Such unexpected applications of mathematics are rather common. So, the relationship between mathematics and reality cannot be described in a single sentence. Moreover, as it is an open philosophical problem, Wikipedia is not the place for trying to solve it. 18:22, 9 June 2019 (UTC) — Preceding unsigned comment added by D.Lazard (talkcontribs)
Zzalpha, please look over the literature on philosophy of mathematics, applied mathematics, and/or definitions of mathematics. You can probably find a better formulation than what we have. Please keep in mind that on Wikipedia we only summarize the literature (and provide sources); Wikipedia is not a place to publish original thought. —Ben Kovitz (talk) 20:03, 9 June 2019 (UTC)

1. The first sentence of any article should state what the subject of the article is, not what it does.

2. The idea that math has no agreed upon definition appears to be an original assertion.

Derwos (talk) 11:58, 9 August 2019 (UTC)

Your two objections correspond to the two sentences of the opening paragraph. Your second objection is handled by the references at the end of the second sentence. Then, the fact that there is no agreed-upon definition explains why the first sentence is written how it is.
If you wish to improve this part of the article, then please propose new text here, on this talk page, with Wikipedia:Reliable sources supporting your text. Mgnbar (talk) 12:14, 9 August 2019 (UTC)

Why isn't there any external links section for this article?[edit]

For an article rated B-class, with this level of accuracy, its really not good to see no external links. What's the point of this article for people looking for a serious overview. I've never created an external links section and I have no idea of the guidelines for adding external links, need help with this case. — Preceding unsigned comment added by (talk) 14:03, 5 July 2019 (UTC)

For having an external link section, one must have external links to link. See WP:External links for knowing what could appear (or what must not) in this section. Apparently, the editors of this article (myself included) do not know any relevant external link that passes the criteria given in this guideline. This is the answer that I can give to your question, as it makes no sense to have en empty section. D.Lazard (talk) 15:09, 5 July 2019 (UTC)