Talk:Mathematics

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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
DateProcessResult
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

The Topic about '0'[edit]

The concept of zero is believed to have originated in the Hindu cultural and spiritual space around the 5th century CE. In Sanskrit, the word for zero is śūnya which refers to nothingness. In scientific history, astronomer and mathematician Aryabhata is often associated with inventing the number '0'. Manveermg (talk) 15:59, 28 December 2023 (UTC)[reply]

There are several concepts of zero: zero as a number, zero as a digit, zero as a placeholder in decimal representation, etc. So, it is impossible to give to zero a unique origin. D.Lazard (talk) 17:09, 28 December 2023 (UTC)[reply]

About 'Computational Mathematics'[edit]

I consider that in the areas of mathematics, Computational Mathematics should be eliminated, since it belongs, in any case, to an area of mathematics in conjunction with another science, such as Mathematical Physics or Mathematical Economics, and not to pure mathematics like the rest.

Alternatively, a section of applied mathematics could be incorporated where Computational Mathematics could be included.

Alex gnpi (talk) 09:12, 21 February 2024 (UTC)[reply]

Presently, section § Computational mathematics gives a misleading description of computational mathematics, and should be completely rewritten. Nevertheless, I strongly disagree with your suggestions.
You seem to give a strong importance to the distinction between pure and applied mathematics. There is presently a large consensus among mathematicians that this is not a classification of mathematics, but rather a point of view on mathematician motivations.
You seem also believe that most computational mathematics consist in applying mathematics to computations in another science. Ths is very much too restrictive. For example, a large part numerical analysis consist of elaborating tools for computing solutions of differential equations, which are applied to almost every science. Computational mathematics is not restricted to numerical analysis. It includes computation theory, cmputer assisted proofs such as the four color theorem, cryptography, the design of proof assistants, mathematical experimentation (computation for discoveintg and testing conjectures), etc.
In short, section § Computational mathematics deserves to be completely rewritten and expanded, not removed or dissolved in another section. D.Lazard (talk) 10:43, 21 February 2024 (UTC)[reply]

Lead[edit]

I'm in my mid-20s, and I remember reading the lead of this article as a kid and being happy with how elegant it was:

Mathematics (colloquially, maths or math) is the body of knowledge centered on such concepts as quantity, structure, space, and change, and also the academic discipline that studies them. Benjamin Peirce called it "the science that draws necessary conclusions".[1]

Other practitioners of mathematics[2][3] maintain that mathematics is the science of pattern, that mathematicians seek out patterns whether found in numbers, space, science, computers, imaginary abstractions, or elsewhere. Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.[4]

I think, broadly, this is significantly better than the present lead. There's a lot of 00s-isms there, we shouldn't consider copy-pasting it back, but would there be consensus to rewrite the lead based on a 2008 version, before the article got de-GAd?

References

  1. ^ Peirce, p.97
  2. ^ Steen, L.A. (April 29, 1988). The Science of Patterns. Science, 240: 611–616. and summarized at Association for Supervision and Curriculum Development.
  3. ^ Devlin, Keith, Mathematics: The Science of Patterns: The Search for Order in Life, Mind and the Universe (Scientific American Paperback Library) 1996, ISBN 9780716750475
  4. ^ Jourdain

Remsense 13:16, 22 February 2024 (UTC)[reply]

First paragraph: I think that the current version is better than the old version. It explicitly states how these major topics show up in current mathematics. It does not privilege Peirce's quotation.
Second paragraph: I don't love the current version. It seems overly long and detailed. The old version treats this logic/proof/axioms theme more concisely.
Third paragraph: You didn't mention this, but I hope that we agree that a paragraph about applications and utility is warranted.
Fourth paragraph: You didn't mention this. I don't love it, because it seems overly long and detailed. Mgnbar (talk) 13:50, 22 February 2024 (UTC)[reply]
I agree with your assessments of the second through fourth paragraphs, and your critique of the privileging of an individual person's quote in the first.
However, I think the important point for the first paragraph is it concretely—but not too concretely, this is math—broadly lays out the areas of experience that math usually touches. I think that's really important for an encyclopedia article on such a huge topic. The current first paragraph mentions [{em|things}}, which are for the moment undefined, but the old version deals with realms, if that makes any sense at all. It states the "purpose" of math first, before the means by which math gets there. Remsense 13:56, 22 February 2024 (UTC)[reply]
The second paragraph is unnecessarily long.

Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature or—in modern mathematics—entities that are stipulated to have certain properties, called axioms. A proof consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, and—in case of abstraction from nature—some basic properties that are considered true starting points of the theory under consideration.

Here is a proposed rewrite.

Most mathematical activity involves statements about abstract objects, known as theorems, and the use of reason to prove them. These objects may be abstractions of the natural world or entities with no relation to reality. A mathematical proof of a new theorem is formed by applying a series of deductive rules to these objects, using their known properties, which come from base assumptions known as axioms as well as previously proven theorems.

Rocfan275 (talk) 14:51, 22 February 2024 (UTC)[reply]
Here is an improved version:

Most mathematical activity involves the manipulation of abstract objects in view of proving statements called theorems. These objects may be abstractions of the natural world such as numbers and curves, or entities with no direct relation to reality such as rings, topologies and cryptographic protocols. A proof of a theorem is formed by applying a series of deductive rules starting from known properties, which may be either base assumptions known as axioms, or previously proven theorems.

D.Lazard (talk) 15:27, 22 February 2024 (UTC)[reply]
Also, I suggest to remove the last sentence of the first paragraph ("There is no general consensus among mathematicians about a common definition for their academic discipline"). The reasons are
  • Such an assertion cannot be sourced
  • Such a negative assertion could be done about many sciences, and even about Science itself : there is no general consensus among scientists about a common definition for science.
  • If this sentence should be kept in the article, this should be in § Proposed definitions
  • There is a clear consensus among mathematicians that if there is no theorems or proofs, this is not mathematics, and that any subject where theorems are proven becomes mathematics.
I have no source attesting that this is a consensus, but this is an evidence for everybody that has participated to many editorial committees of mathematical journals and conferences). So, the second paragraph can be viewed as a definition of mathematics). D.Lazard (talk) 18:52, 22 February 2024 (UTC)[reply]
Mathematics is the study of concepts such as number, structure, space, and change. These topics are broadly represented by the major mathematical disciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline.
Most mathematical activity involves the manipulation of abstract objects in view of proving statements called theorems. These objects may be abstractions of the natural world such as numbers and curves, or entities with no direct relation to reality such as rings, topologies and cryptographic protocols. A proof of a theorem is formed by applying a series of deductive rules starting from known properties, which may be either base assumptions known as axioms, or previously proven theorems.
is my synthesis of the first two paragraphs with the earlier version's opening sentence. Is this too vague? I also sense my simple use of "study" may sound too POV intuitionist for some? Though IMO describing math as a study does not imply that mathematical truths don't exist a priori. Remsense 02:11, 23 February 2024 (UTC)[reply]

Info to add from a source to a section of the article[edit]

I have seen the section "Training and practice" in the article, to which some info could be added from the following source https://www.tandfonline.com/doi/full/10.1080/01425692.2023.2240530 178.138.99.208 (talk) 16:23, 15 March 2024 (UTC)[reply]

You must say which info you want to add. Moreover, this link is an original research paper, and Wikipedia policy WP:NOR implies that, for being acceptable in Wikipedia, every original research must have been discussed in other sources. Moreover, there are thousands of articles on mathematical education, and priviledging one of them contradicts anothe fundamental policy of Wikipedia, WP:NPOV. D.Lazard (talk) 16:05, 16 March 2024 (UTC)[reply]
If you want the article mathematical education (not this article mathematics) to discuss the varying results between students based on parental involvement/disposition, you should probably try to find a survey article or the like to use as your source, rather than a particular study. –jacobolus (t) 16:46, 16 March 2024 (UTC)[reply]

Semi-protected edit request on 18 March 2024[edit]

where does the rules of math state that 1x0=0 add Jgomezbeyondpie (talk) 04:45, 18 March 2024 (UTC)[reply]

See Multiplication RudolfRed (talk) 05:02, 18 March 2024 (UTC)[reply]

Wiki Education assignment: 4A Wikipedia Assignment[edit]

This article is currently the subject of a Wiki Education Foundation-supported course assignment, between 12 February 2024 and 14 June 2024. Further details are available on the course page. Student editor(s): Not Fidel (article contribs).

— Assignment last updated by Not Fidel (talk) 06:53, 18 March 2024 (UTC)[reply]

@Not Fidel I'd recommend against choosing such high level topics as Mathematics and Astrology for an introduction to working on Wikipedia, at least if you want your contributions to be valuable and stick around. Ideally you want to find an article which is at least moderately important but currently underdeveloped or in very poor shape, for example something with 'high' priority and 'start' quality' or 'mid' priority and 'start' quality (those links go to a list of all such articles within WikiProject Mathematics). To write an effective article you need to do quite a bit of book research about a topic, and it's pretty hard to wade into a topic as large as the ones you picked without quite a lot of reading, unless you intend to pick out a particular section that seems missing, undeveloped, or otherwise problematic to focus on. –jacobolus (t) 15:10, 18 March 2024 (UTC)[reply]