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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.
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
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
rigorousdeduction 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?
^Devlin, Keith, Mathematics: The Science of Patterns: The Search for Order in Life, Mind and the Universe (Scientific American Paperback Library) 1996, ISBN 9780716750475
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诉 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.
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.
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诉 02:11, 23 February 2024 (UTC)reply
Info to add from a source to a section of the article
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
This
edit request has been answered. Set the |answered= or |ans= parameter to no to reactivate your request.
where does the rules of math state that 1x0=0 add
Jgomezbeyondpie (
talk) 04:45, 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
Wiki Education assignment: 4A Wikipedia Assignment
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) 17:22, 22 April 2024 (UTC)reply