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Former good article Mathematics 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.

Godel's Incompleteness Theorem[edit]

In the part of the article fields of mathematics logic is mentioned. There Godel's incompleteness theorem is mentioned and it is said that it shows that for any valid axiomatic system there exists "a true mathematical fact" that can't be proved. This is incorrect and misleading since if a theorem is unprovable it is not in any way a "true mathematical fact. Godel's incompleteness theorem simply shows the for any axiomatic system that the peano arithmetic axioms are derived from it there exists a property that is unprovable to be true nor false.

Remomer (talk) 21:14, 18 November 2016 (UTC)

Yes, in some reasonable (but rather formal) sense you are right. On the other hand, in another, even more reasonable (and somewhat informal) sense, the statement "Peano arithmetics is consistent" IS true but not provable in the Peano arithmetics. And of course, it IS provable in the Zermelo-Frenkel set theory. Boris Tsirelson (talk) 21:32, 18 November 2016 (UTC)

Semi-protected edit request on 1 April 2017[edit]

Defining Mathematics--- Mathematics in both practical and theoretical forms mean studying the consistency and change in the nature i.e. quantity, structure and value of both intangible and tangible sources which occupy space. It's the only thing which helps in solving queries related to time perfectly. Existence of time is fully dependent on pre-existence of "Mathematics" which sets the rules for all actions going around. It's the tool given to brain of animals only. When correctly applied by human to different forms of physical, biological and even psychological sciences mathematics can discover the facts and figures related to them which further helps in understanding the design and pattern of existing life and death circle. AnkurKatyal (talk) 07:45, 1 April 2017 (UTC)

If this is not an April-1 joke, then this should be a point-of-view, unless a number of sources will be added. Boris Tsirelson (talk) 08:28, 1 April 2017 (UTC)

Missing some critical disciplines[edit]

Any math discipline that is the root of a branch of science really belongs on this page. The one that jumped out at me was combinatorics, which is the root of statistical mechanics and thermodynamics. Others include spherical geometry, which was driven almost entirely by navigation. — Preceding unsigned comment added by (talk) 06:44, 8 May 2017 (UTC)

Combinatorics is already mentioned in the article. Spherical geometry is a particular kind of non-Euclidean geometry, which is already mentioned in the article. I don't think either topic needs heavier treatment here. Mgnbar (talk) 12:34, 8 May 2017 (UTC)

Opening Sentence/Paragraph[edit]

Currently: "Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers),[2] structure,[3] space,[2] and change.[4][5][6] There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics.[7][8]"

Here are my thoughts.

  • "There is a range of views" is weasel words; I'd recommend deleting the entire sentence.
  • I'd mention addition, subtraction, multiplication, and division (or at least arithmetic), for the benefit of an elementary-aged audience.
  • I'm not sure "structure, space, and change" is more understandable than "Algebra, Geometry, and Analysis".
  • Should "logic" be listed as a sub-division of mathematics, or of philosophy?

Power~enwiki (talk) 06:18, 16 May 2017 (UTC)

Please understand that this intro is highly contentious, precisely because there is a range of views. We get a lot of editors saying "this is the right way to define mathematics", often neglecting sources and ignoring other definitions. Similarly, we can argue forever about whether logic is math or philosophy. I do think that "structure, space, and change" is vague, but they are actually supported by sources, and probably more meaningful to non-mathematicians than "algebra, geometry, and analysis". In short, I do not agree with your proposal. Mgnbar (talk) 12:15, 16 May 2017 (UTC)
This sentence has been discussed many many times, by many editors. You should search through the "Archives" of this talk page (listed above). Paul August 16:58, 16 May 2017 (UTC)
Yes, I understand the first sentence has been debated extensively, I'm not terribly interested in arguing about it if the consensus still holds. The second sentence is egregiously bad and I am deliberately attempting to re-open discussion. There are many things far more important about mathematics than the fact that its exact definition is vague. Power~enwiki (talk) 19:37, 16 May 2017 (UTC)
Why "bad"? We honestly inform the reader that the first phrase is somewhat controversial. Boris Tsirelson (talk) 19:44, 16 May 2017 (UTC)
Everyone knows that arithmetic is part of mathematics, that's not controversial. "The lead should stand on its own as a concise overview of the article's topic." (from WP:LEAD). I fail to see why "teaching the controversy" should be in the lead; there's a full section on it later in the article. Power~enwiki (talk) 19:51, 16 May 2017 (UTC)
The controversial claim is not that "arithmetic is part of mathematics", but that the four listed aspects cover most of mathematics. Boris Tsirelson (talk) 20:09, 16 May 2017 (UTC)
This ("egregiously bad") sentence links to "Definitions of mathematics"; there, the lead (three sentences) end with "All are controversial". Is it even more "egregiously bad"? Boris Tsirelson (talk) 20:17, 16 May 2017 (UTC)
There is a difference between an article on "Mathematics" and an article on "Definitions of mathematics". Power~enwiki (talk) 20:23, 16 May 2017 (UTC)
Sure. For that reason the former just contains a hint and the link to the latter. Boris Tsirelson (talk) 20:36, 16 May 2017 (UTC)
I would not oppose moving the second sentence to the section "Definitions of mathematics". Paul August 20:41, 16 May 2017 (UTC)
I usually agree with Paul, but in this case I don't. The move leaves a one-sentence lead paragraph, and (much worse) makes the proffered definition appear, well, definitive. --Trovatore (talk) 20:37, 19 May 2017 (UTC)
I find it absurd that Wikipedia is incapable of saying anything definitive on the subject of "What is mathematics". Power~enwiki (talk) 20:40, 19 May 2017 (UTC)
You're allowed to find it absurd, but them's the facts. There is no agreement in the mathematical community, so we can't invent one here. --Trovatore (talk) 20:45, 19 May 2017 (UTC)
That's right. As for the one sentence lead, that could of course be fixed by combining that sentence with the following paragraph. But I understand Trovatore's concern. Paul August 23:58, 19 May 2017 (UTC)

Lots of sources do say that the definition of mathematics is complicated. The first sentence of Chapter 1 of Boyer's "A History of Mathematics" is "Mathematicians of the twentieth century carry on a highly sophisticated intellectual activity which is not easily defined". The book then goes on to discuss the history of arithmetic, algebra, geometry, and analysis. I see no dispute that those four topics are mathematics, and other topics (such as music and astronomy) are not. While "the set of all mathematical facts" is ill-defined, the concept is defined clearly enough for the purposes of a lede paragraph in an encyclopedia. Power~enwiki (talk) 20:47, 20 May 2017 (UTC)

Perhaps a second-rate encyclopedia, but I would hope that our aspirations are higher than that. The problem is not that we can not identify areas that are clearly mathematics, but rather where do we stop and how fine should the distinctions be made? Courant and Robbins book What Is Mathematics? spends 566 pages attempting to do this and Reuben Hersh gives it another 334 pages in What Is Mathematics Really?. To think that this can be distilled down to a couple of meaningful sentences seems to me to be the height of hubris. --Bill Cherowitzo (talk) 21:57, 20 May 2017 (UTC)
It would take time to distill the 900 pages into a few sentences: "I would have written a shorter letter, but I did not have the time." —Blaise Pascal. I personally took a year on Imre Lakatos' Proofs and Refutations article. As Lakatos put it, "mathematicians are imperfect personifications of Mathematics". --Ancheta Wis   (talk | contribs) 09:43, 21 May 2017 (UTC)
Wow! Probably useless for this article, but quite a pleasure anyway (this phrase of Lakatos); thanks. Boris Tsirelson (talk) 16:17, 21 May 2017 (UTC)

Semi-protected edit request on 2 July 2017[edit]

hey dawg. Wanna make some repairings round here. Hope you dont mind dawg. This incorrectly written article may miseducate few other daaaawgs. Better repair it all up Jasmína Hajdúková (talk) 08:20, 2 July 2017 (UTC)

Not done: dawg this is not the right page to request additional user rights. You may reopen this request with the specific changes to be made and some dawg will add them for you, or you can wait until you are autoconfirmed and edit the page yourself. DRAGON BOOSTER 08:54, 2 July 2017 (UTC)