Talk:Mathematics

Greek origin of the word "Mathematics"

Hi, I propose to promote the first line by this footnote:

From the Greek μάθημα (máthema), meaning "science, knowledge, or learning"

Yielding:

Mathematics is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities.

Such etymology improves the definition and first line of article. Thanks, Rais-Ali Delvari (talk) 06:36, 26 July 2026 (UTC)

References

Seems fine to leave this to § Etymology. –jacobolus (t) 07:25, 26 July 2026 (UTC)

@Jacobolus Hi and thanks. In my opinion an abstract "footnote version" is really helpful for the first line. In simple English article here, it is correctly mentioned, making the article more understandable. Rais-Ali Delvari (talk) 07:29, 26 July 2026 (UTC)

First line can have a summary for Mathematics#Etymology. Rais-Ali Delvari (talk) 07:31, 26 July 2026 (UTC)

I agree with Jacobolus: We may safely suppose that most readers have already heard of mathematics, and come here for knowing more on the topic. Since the meaning of the word is not exactly the same as in Ancient Greece, etymology is a minor aspect of the topic that needs not to be emphasized in the lead when there is no place in the lead for much more important aspects. D.Lazard (talk) 10:51, 26 July 2026 (UTC)

Pedagogy began with pedagogy teaching of Jesuits

@D.Lazard you removed part of a sentence stating that the formal instruction in pedagogy began with members of the Jesuits. You state that you did this since it was unsourced in your edit summary. But it was sourced, the source in reference is currently labeled 201: Jones, Phillip S. (1967). "The History of Mathematical Education". The American Mathematical Monthly. 74 (1). Taylor & Francis, Ltd.: 38–55. doi:10.2307/2314867. JSTOR 2314867. EulerianTrail (talk) 17:16, 7 August 2026 (UTC)

Yes, Jesuits seem to be the first to teach pedagogy of mathematics. But this section is about mathematical education, not pedagocical education. SO, the sentence about Jesuits is confusing and out of scope. IMO, it should be removed. Nevertheless, I'll not do this, and, as a compromise, I'll edit the sentence for making clear that it is about the formation of future teachers. D.Lazard (talk) 21:03, 7 August 2026 (UTC)

I acceded to Jones' article The History of Mathematical Education. It is clearly not a WP:reliable source for mathematical education in the 16th and 17th century, since the article contains only one or two sentences on the subject and does not provide its sources. Therefore, I edited the article by beginning the sentence with "According to Phillip S. Jones". However, as Jones does not nave a Wikipedia page, and pedagogy is not the subject of the article, my opinion is that this sentence must be removed. Indeed, we do not even know what is contained in Jesuit courses, and whether it was pedagogy (in the modern sense) or simply a detailed course program).

Moreover, the next sentence asserting "Most mathematical curricula remained at a basic and practical level ..." is blatantly wrong (it is not in Jones' paper), as Euclidean geometry is neither basic nor practical, and was commonly taught from centuries.

So, I'll remove the two sentences. D.Lazard (talk) 10:06, 10 August 2026 (UTC)

Mysterious of Maths

In the Wikipedia text they could possibly add three of the main mysteries of maths such as the Yang mill’s theory the Riemann hypothesis and odd perfect number theory making the text more interesting for readers. Mathworkofpast (talk) 00:39, 23 August 2026 (UTC)

No links in first paragraph

Could we revisit § Hyperlinks missed in the first paragraph? There's a comment in the article:

<!-- Please, do not add any wikilink to this paragraph: On June-July 2026, there was a consensus on the talk page to not link any term in the first paragraph -->

However, in that discussion, I'm only seeing @D.Lazard strongly against linking while the other commenters seem to be for a modest amount of links.

Here's my first thought about what should be linked:

−

'''Mathematics''' is a field of knowledge concerned with abstract concepts such as numbers, geometric shapes, sets, functions, and probabilities. It uses logical reasoning and proof to study and establish their properties, often expressed as theorems, formulas, and equations. Mathematics is used to model and solve problems in science, engineering, technology, economics, and everyday life.

+

'''Mathematics''' is a field of knowledge concerned with abstract concepts such as [[number]]s, [[geometric shape]]s, [[Set (mathematics)|set]]s, [[Function (mathematics)|function]]s, and [[Probability|probabilities]]. It uses logical reasoning and proof to study and establish their properties, often expressed as [[theorem]]s, [[formula]]s, and [[equation]]s. Mathematics is used to model and solve problems in [[science]], [[engineering]], [[technology]], [[economics]], and everyday life.

Each of the sentences here is formulated with a list at the end, so I'm only linking terms in those lists.

The only other things I might link are "proof" → Mathematical proof and "model" → Mathematical model, but that might open up a can of worms to add things like "solve" → Mathematical solution and logical reasoning, and at that point the number of links would start making readers dizzy, so it's probably best to avoid linking any of those.

And we should revise the comment if we're going to go through with this:

−

<!-- Please, do not add any wikilink to this paragraph: On June-July 2026, there was a consensus on the talk page to not link any term in the first paragraph -->

+

<!-- Please do not add any additional wikilinks to this paragraph: As of August 2026, there is consensus on the talk page to keep the number of links minimal in the first paragraph. -->

All the best — W.andrea (talk) 13:29, 30 August 2026 (UTC)

Please, explain to which sort of readers these links could be more useful than distracting, and why do you think they could be useful. D.Lazard (talk) 16:09, 30 August 2026 (UTC)

High schoolers, for example.

Regarding usefulness, what kind of explanation are you looking for? I mean, I assume you're familiar with the general principles of linking, e.g. MOS:LINKING and MOS:UL:

Appropriate links ... increase readers' understanding of the topic at hand [... and] help the reader find related information

links should be created for: ... Articles with relevant information, ... Articles explaining words of technical terms

In the lead, "set" and "function" are the most technical terms, so at bare minimum they should be linked. But then I would argue that all the other items listed with them should be linked too, for symmetry.

— W.andrea (talk) 16:23, 30 August 2026 (UTC)

First line on French Wikipedia

Hi, I investigated first line of this article on other Wikis, and this definition on French Wikipedia (this article) attracted me:

Les mathématiques sont un ensemble de connaissances abstraites résultant de raisonnements logiques appliqués à des objets divers tels que les ensembles mathématiques, les nombres, les formes, les structures, les transformations, etc. ; ainsi qu'aux relations et opérations mathématiques qui existent entre ces objets. Elles sont aussi le domaine de recherche développant ces connaissances, ainsi que la discipline qui les enseigne.

translated to English as:

Mathematics is a body of abstract knowledge resulting from logical reasoning applied to diverse objects such as mathematical sets, numbers, shapes, structures, transformations, etc.; as well as to the mathematical relationships and operations that exist between these objects. It is also the field of research that develops this knowledge, as well as the discipline that teaches it.

In my opinion this definition on French Wikipedia for mathematics is really powerful and is sufficient and contains all necessity parts. Please discuss. Thanks, Rais-Ali Delvari (talk) 14:09, 7 September 2026 (UTC)

This is very similar in spirit with the current English article. However, it lacks a necessary part, the fact that mathematics applies to every science, to engineering and everyday life. Moreover, it is more jargonning, and almost circular, using twice "mathematical". It is also possibly confusing for people who are not mathematicians (who knows what are "structures", "transformations", "operations on objects"). Also who knows that "object" means here a type of abstract concept manipulated by mathematicians.

The current first paragraph is the result of many discussions on this talk page, and is certainly more adapted to a general audience than the French version. D.Lazard (talk) 15:06, 7 September 2026 (UTC)

Using "custom infobox" for this article

@D.Lazard Hi, What is your opinion about this "custom infobox" for this article? In my opinion an improved version of this Infobox is really helpful. Thanks,

Mathematics

Overview
Definition	The study of numbers, quantities, structures, spaces, and patterns.
Type	Academic discipline
Major branches
Pure mathematics	Algebra, number theory, mathematical analysis, geometry, topology, logic, and set theory
Applied mathematics	Statistics, probability, optimization, numerical analysis, and mathematical modelling
Foundations
Formal foundations	Mathematical logic and set theory
Applications
Related disciplines	Physics, computer science, engineering, economics, and cryptography
History
Origins	Ancient civilizations
Notable concepts	Number, function, proof, symmetry, infinity, and mathematical structure

Rais-Ali Delvari (talk) 13:26, 12 October 2026 (UTC)

Sidebars are discouraged in article leads. Sławomir Biały (talk) 14:09, 12 October 2026 (UTC)

Please read the code of Infobox. It is not a sidebar, it uses Template:Infobox. Please mention:

In general, this template is not meant for use directly in an article, but can be used on a one-off basis if required.

Rais-Ali Delvari (talk) 14:16, 12 October 2026 (UTC)

Where would you put this "infobox"? In the lead, as a bar, on the side? That makes it a sidebar, and consensus is against those. Sławomir Biały (talk) 15:09, 12 October 2026 (UTC)

There ia a longstanding consensus to not have infoboxes in articles about areas of mathematics and Mathematics itselk. The reason is that infoboxes require an oversimplification hat is generally misleading. In this particular case, the proposed infobox contradicts the article at almost evey line:

• "Definition": the article says that there is no definition that is commonly accepted.
• "Type": the article says that mathematics is much more than an academic discipline, and has many non-academic uses.
• "Pure and applied mathematics": the article says that they are not major divisions of mathemtics
• "Notable concepts": The lead says that proofs and theorems are amoongs the most notable concepts of mathematics (since they occur in all areas of mathematics)
• "Applications": everyday life, all engineering domains and all science are mentioned in the lead and not in your infobox.

Infoboxes are for facts that can be summarized in one or two words. There no such facts in this article. D.Lazard (talk) 14:50, 12 October 2026 (UTC)

There is no need for such an "infobox". Please do not add such a thing to any article. –jacobolus (t) 15:59, 12 October 2026 (UTC)

change in word spelling

subarea can be made as sub-area ~2026-55474-54 (talk) 06:12, 16 October 2026 (UTC)

Missing comma

The last sentence of the article, "To date, only one of these problems, the Poincaré conjecture, has been solved by the Russian mathematician Grigori Perelman." is missing a comma. It reads as if from the sidelines we are cheering GP on for the other six! It should be "To date, only one of these problems, the Poincaré conjecture, has been solved, by the Russian mathematician Grigori Perelman." Even better, the solver should be identified parenthetically "To date, only one of these problems, the Poincaré conjecture, has been solved (by the Russian mathematician Grigori Perelman)." And I see no reason to include the words "the Russian mathematician". That's what the link is for. ~2026-55701-75 (talk) 14:36, 18 October 2026 (UTC)

I've edited the text down, to a version that avoids the objection entirely.

In the future, please Wikipedia:Be bold and make such changes yourself. :) Mgnbar (talk) 15:17, 18 October 2026 (UTC)

As an anon, I do not get to edit protected articles. ~2026-55701-75 (talk) 17:28, 18 October 2026 (UTC)

Barely any good discussion of mathematicians

Shouldn't this article at least briefly discuss the people who actually do mathematics? The only place mathematician is linked to is in the education section, with the display text "careers". Wreaderick (talk) 08:58, 28 October 2026 (UTC)

In his article, "mathematician" is used for someone who practices mathematics. As an everiday word, it needs not to be linked per WP:OVERLINK. The only link to Mathematician occurs as a WP:SUBMARINE link through another everyday word that should not be linked either. Nevertheless,I see two problems here.

The article Mathematician is very poor, misleading and contradicts Mathematics on many aspects. In particular, the emphasis on the distinction between pure and applied mathematics. Also, although research is an important activity of mathematicians, it is not presented as a common mathematical activity. This page is not the place for discussing here all the issues of Mathematician, but, presently, linking to it would be a disimprovement.

I agree that Mathematics lacks of a section § As a human activity. The current § Training and practice could be a starting point for that, although it requires to be rewritten. In the future, it could contain the template {{main article|Mathematician}}, but none article is ready for that. D.Lazard (talk) 10:45, 28 October 2026 (UTC)