View source for Wiki143:Manual of Style/Mathematics

{{MoS guideline|WP:MSM|MOS:MATH|MOS:MATHS|sortkey=Mathematics}}
{{Style|science}}

This subpage of the [[Wikipedia:Manual of Style|Manual of Style]] contains guidelines for writing and editing clear, encyclopedic, attractive, and interesting articles on [[mathematics]] and for the use of mathematical notation in Wikipedia articles on other subjects. For matters of style not treated on this subpage, follow the main Manual of Style and its other subpages to achieve consistency of style throughout Wikipedia.

==Structure==
Probably the hardest part of writing a Wikipedia article on a mathematical topic, and generally any Wikipedia article, is addressing a reader's level of knowledge. For example, when writing about a [[field (mathematics)|field]] in the context of [[abstract algebra]], is it best to assume that a reader is already familiar with [[group theory]]? A general approach to writing an article is to start simple and then move towards more abstract and technical subjects later on in the article.

===Article introduction===
{{main|Wikipedia:Manual of Style/Lead section}}

Articles should start with a short introductory section, called the "lead". The purpose of the lead is to 
*describe and define the subject,
*provide context regarding the subject,
*and summarize the article's most important points.

The lead should, as much as possible, be accessible to a general reader, so specialized terminology and symbols should be avoided.  Formulas should appear in the first paragraph only if necessary, since  they will not be displayed in the preview that pops up when hovering over a link. For having formulae displayed when hovering, they must be written in raw html (without templates {{tl|var}} or {{tl|math}}), or in [[LaTeX|{{Stylized LaTeX}}]] (inside <nowiki><math>...</math></nowiki>). In the latter case the LaTeX source is displayed without the tags <nowiki><math></nowiki> and <nowiki></math></nowiki>.

In general, the lead sentence should include the article title, or some variation thereof, in bold along with any alternate names, also in bold. The lead sentence should state that the article is about a topic in mathematics, unless the title already does so. It is safe to assume that a reader is familiar with the subjects of arithmetic, algebra, geometry, and that they may have heard of calculus, but are likely unfamiliar with it. For articles that are on these subjects, or on simpler subjects, it can be assumed that the reader is not familiar with the aforementioned subjects. A reader can be assumed to be ignorant of any topics outside of that scope or more advanced topics. 

The lead sentence should informally define or describe the subject. For example:
<blockquote>In [[mathematics]], '''topology''' (from the [[Greek language|Greek]] {{Langx|el|τόπος|lit=place|label=none}}, and {{Langx|el|λόγος|lit=study|label=none}}) is concerned with the properties of a [[mathematical object|geometric object]] that are preserved under [[Continuous function|continuous]] [[Deformation theory|deformations]], such as [[Stretch factor|stretching]], [[Twist (mathematics)|twisting]], crumpling and bending, but not tearing or [[Quotient space (topology)|gluing]].</blockquote>

<blockquote>In [[Euclidean geometry|Euclidean plane geometry]], '''Apollonius's problem''' is to construct circles that are [[tangent]] to three given circles in a plane.</blockquote>

The lead section should include, when appropriate:
*''Historical motivation'', including names and dates, especially if the article does not have a "History" section. The origin of the subject's name should be explained if it is not self-evident.
*An ''informal introduction'' to the topic, without rigor, suitable for a general audience. The appropriate audience for the overview will vary by article, but it should be as basic as reasonable. The informal introduction should clearly state that it is informal, and that it is only stated to introduce the formal approach. Include a physical or geometric analogy or diagram if it can help introduce the topic.
*''Motivation'' or ''applications'', which can illuminate the use of the topic and its connections to other areas of mathematics or other non-mathematical subjects.

===Article body===
Readers have differing levels of experience and knowledge. When in doubt, articles should define the notation they use. For example, some readers will immediately recognize that &Delta;(''K'') means the [[Discriminant of an algebraic number field|discriminant of a number field]], but others will never have encountered the notation. The latter group will be helped by an aside like "...where &Delta;(''K'') is the [[discriminant of an algebraic number field|discriminant]] of the [[field (mathematics)|field]] ''K''".

Use standard notation when possible. If an article requires non-standard or uncommon notation, they should be defined. For example, an article that uses ''x''^''n'' or ''x''**''n'' to denote exponentiation (instead of ''x<sup>n</sup>'') should define the notations. If an article requires extensive notation, consider introducing the notation as a bulleted list or separating it into a section titled "Notation".

An article about a [[mathematical object]] should provide an exact definition of the object, perhaps in a "Definition" section after section(s) of motivation. For example:
<blockquote>
Let ''S'' and ''T'' be [[topological space]]s, and let ''f'' be a [[function (mathematics)|function]] from ''S'' to ''T''. Then ''f'' is called ''continuous'' if, for every [[open set]] ''O'' in ''T'', the [[preimage]] {{itco|''f''}}<sup>−1</sup>(''O'') is an open set in ''S''.
</blockquote>
The phrase "formal definition" may help to flag the actual definition of a concept for readers unfamiliar with academic terminology, in which "definition" means formal definition, and a "proof" is always a formal proof.

When the topic is a theorem, the article should provide a precise statement of the theorem. Sometimes this statement will be in the lead, for example:
<blockquote>
'''Lagrange's theorem''', in the [[mathematics]] of [[group theory]], states that for any [[finite group]] ''G'', the [[order (group theory)|order]] (number of elements) of every [[subgroup]] ''H'' of ''G'' divides the order of ''G''.
</blockquote>
Other times, it may be better to separate the statement into its own section, as for long theorems like the [[Poincaré–Birkhoff–Witt theorem]], or to present multiple equivalent formulations, as for [[Nakayama's lemma]].

Representative examples and applications help to illustrate definitions and theorems and to provide context for why they might be interesting. Shorter examples may fit into the main exposition of the article, such as the discussion at {{section link|Algebraic number theory|Failure of unique factorization}}, while others may deserve their own section, as in {{section link|Chain rule|First example}}. Multiple related examples may also be given together, as in {{section link|Adjunction formula|Applications to curves}}. Occasionally, it is appropriate to give a large number of computationally-flavored examples, as in {{section link|Lambert W function|Applications}}. It may also be edifying to list non-examples, which almost-but-not-quite satisfy the definition. In keeping with the purpose and [[WP:TONE|tone]] of an encyclopedia, examples should be ''informative'' rather than ''instructional'' (see [[WP:NOTTEXTBOOK]] for details).

A picture can really bring home a point, and can often precede the mathematical discussion of a concept. [[Wikipedia:How to create graphs for Wikipedia articles|How to create graphs for Wikipedia articles]] contains some details on how to create graphs and other pictures as well as how to include them in articles.

Formulas tend to repel less mathematical readers, and mathematics articles should take pains to explain (or even replace) them by words if possible. In particular, the English words "for all", "exists", and "in" should be preferred to the corresponding symbols ∀, ∃, and ∈. Similarly, definitions should be highlighted with words such as "is defined by" in the text.

If not included in the introduction, a history section can provide additional context and details on the topic's motivation and connections.

===Concluding matters===
Most mathematical ideas are capable of some form of generalization. If appropriate, such material can be put under a "Generalizations" section. As an example, multiplication of the rational numbers can be generalized to other [[field (mathematics)|fields]].

It is also generally good to have a "See also" section in an article. The section should link to related subjects, or to pages which could provide more insight into the contents of the article. More details on "See also" sections can be found at {{section link|Wikipedia:Manual of Style/Layout|"See also" section}}. Lastly, a well-written and complete article should have a "References" section. This topic is discussed in detail in the section {{section link||Including literature and references}}.

==Writing style in mathematics<span class="anchor" id="TONE"></span><span class="anchor" id="NOWE"></span>==
{{shortcut|MOS:MATH#TONE|MOS:MATH#NOWE}}

There are several issues of writing style that are particularly relevant in mathematical writing.

In the interest of clarity, sentences should not begin with a symbol. Do not write:
* {{!xt|Suppose that ''G'' is a group. ''G'' can be decomposed into cosets, as follows.}}
* {{!xt|Let ''H'' be the corresponding subgroup of ''G''. ''H'' is then finite.}}

Instead, write something like:
* {{xt|A group ''G'' may be decomposed into cosets, as follows.}}
* {{xt|Let ''H'' be the corresponding subgroup of ''G''.  Then ''H'' is finite.}}

Mathematics articles are often written in a conversational style similar to a whiteboard lecture. However, a narrative pedagogical style runs counter to Wikipedia's recommended encyclopedic tone. While opinions vary on the most edifying style, authors should generally strike a balance between bare lists of facts and formulae, and relying too much on addressing the reader directly and referring to "we". Also avoid contentless clichés as {{!xt|Note that}}, {{!xt|It should be noted that}}, {{!xt|It must be mentioned that}}, {{!xt|It must be emphasized that}}, {{!xt|Consider that}}, and {{!xt|We see that}}. There is no use in imploring the reader to take note of each thing being pointed out. Rather than drawing the reader's attention to crucial information buried in the text, try to reorganize and rephrase to put the crucial part first. {{SeeAlso|MOS:NOTED}}

Articles should be as accessible as possible to readers not already familiar with the subject matter. Notations not entirely standard should be properly introduced and explained. Whenever a variable or other symbol is defined by a formula, make sure to say this is a definition introducing a notation, not an equation involving a previously known object. Also identify the nature of the entity being defined. Don't write:
* {{!xt|1=Multiplying ''M'' by ''u'' = ''v'' − ''v''<sub>0</sub>, ...}}

Instead, write:
* {{xt|1=Multiplying ''M'' by the vector ''u'' defined by ''u'' = ''v'' − ''v''<sub>0</sub>, ...}}

{{anchor|DEFSYMBOL}}
{{shortcut|MOS:DEF|MOS:MATH#DEFSYMBOL|MOS:MATH#IFF}}
In definitions, the symbol "=" is preferred over "≡" or "''':'''=".

{{anchor|IFF}}
When defining a term, do not use the phrase "if and only if".  For example, instead of
* {{!xt|1=A function ''f'' is ''even'' if and only if ''f''(&minus;''x'') = ''f''(''x'') for all ''x''}}
write
* {{xt|1=A function ''f'' is ''even'' if ''f''(&minus;''x'') = ''f''(''x'') for all ''x''.}}

If it is reasonable to do so, rephrase the sentence to avoid the use of the word "if" entirely. For example,
* {{xt|1=An ''even function'' is a function&nbsp;''f'' such that ''f''(&minus;''x'') = ''f''(''x'') for all ''x''.}}

{{anchor|OBVIOUS}}
{{shortcut|MOS:MATH#OBVIOUS}}
Avoid, as far as possible, useless phrases such as:
* {{!xt|It is easily seen that ...}}
* {{!xt|Clearly ...}}
* {{!xt|Obviously ...}}

The reader might not find what you write obvious. Instead, try to hint ''why'' something must hold, such as:
* {{xt|It follows directly from this definition that ...}}
* {{xt|By a straightforward, if lengthy, algebraic calculation, ...}}

Articles should avoid common blackboard abbreviations such as ''wrt'' (with respect to), ''wlog'' (without loss of generality), and ''iff'' (if and only if), as well as quantifier symbols ∀ and ∃ instead of ''for all'' and ''there exists''. In addition to compromising the encyclopedic tone, these abbreviations are a form of jargon that may confuse the reader.

{{anchor|ANY}}
{{shortcut|MOS:MATH#ANY}}
Avoid ''any'' when verbalizing quantifiers since it is ambiguous. Instead of {{!xt|1=if any ''x'' satisfies ''F''(''x'') = 0}}, write {{xt|1=if every ''x'' satisfies ''F''(''x'') = 0}}, or {{xt|1=if some ''x'' satisfies ''F''(''x'') = 0}}, depending on what you wish to express.

{{anchor|PLURAL}}
{{shortcut|MOS:MATH#PLURAL}}The plural of ''formula'' is either ''formulae'' or ''formulas''. Both are acceptable, but an article should be internally consistent. In an already consistent article, editors should refrain from changing one style to another.

==Mathematical conventions==
{{see also|Wikipedia:WikiProject Logic/Standards for notation}}

A number of conventions have been developed to make Wikipedia's mathematics articles more consistent with each other. These conventions cover choices of terminology, such as the definitions of ''compact'' and ''ring'', as well as notation, such as the correct symbols to use for a subset.

These conventions are suggested in order to bring some uniformity between different articles, to aid a reader who moves from one article to another. However, each article may establish its own conventions. For example, an article on a specialized subject might be more clear if written using the conventions common in that area. Thus the act of changing an article from one set of conventions to another should not be undertaken lightly.

Each article should explain its own terminology as if there are no conventions, in order to minimize the chance of confusion. Not only do different articles use different conventions, but Wikipedia's readers come to articles with widely different conventions in mind. These readers will often not be familiar with our conventions, which may differ greatly from the conventions they see outside Wikipedia. Moreover, when our articles are presented in print or on other websites, there may be no simple way for readers to check what conventions have been employed.

===Terminology conventions===

====Natural numbers====
"The [[set (mathematics)|set]] of [[natural numbers]]" has two common meanings: {{nowrap|{{mset|0, 1, 2, 3, ...}},}} which may also be called ''non-negative integers'', and {{nowrap|{{mset|1, 2, 3, ...}},}} which may also be called ''positive integers''. Use the sense appropriate to the field to which the subject of the article belongs if the field has a preferred convention. If the sense is unclear, and if it is important whether or not zero is included, consider using one of the alternative phrases rather than ''natural numbers'' if the context permits.

====Algebra====
*A [[ring (mathematics)|ring]] is assumed to be [[associative]] and [[unital algebra|unital]].  A structure satisfying all the ring axioms except the existence of a multiplicative identity is called a [[rng (algebra)|rng]].<ref>Currently, [[ring (mathematics)]] and related articles attempt to cover both unital rings and non-unital rings: they do not consistently implement this interpretation. This attempt to cover multiple meanings violates [[WP:DICT#Major differences]] ([[homograph]]s).</ref> There is an exception for rings of operators, such as [[* algebra]]s, [[B* algebra]]s, [[C* algebra]]s, which we do not assume to be unital.
*The ring with one element is called the [[zero ring]].
*A [[local ring]] is not assumed [[noetherian ring|noetherian]] (''contra'' [[Zariski]]).
*For [[Clifford algebra]]s use ''v''<sup>2</sup> = +''Q''(''v'').

====Algebraic geometry====
*An [[algebraic variety]] is assumed to be an ''irreducible'' [[algebraic set]].
*A [[scheme (mathematics)|scheme]] is not assumed to be separated. The term "prescheme" is not used.

====Topology====
*A [[compact space]] is not assumed to be [[Hausdorff space|Hausdorff]] (''contra'' [[Nicolas Bourbaki|Bourbaki]], who uses [[quasi-compact]] for our notion of [[Compact space|compactness]]).
*Separation axioms for topological spaces are as described on the [[separation axiom]] page.

====Miscellaneous====
*[[Directed set]]s are [[preordered set]]s with finite joins, not [[partially ordered set|partial orders]] as in, e.g., [[John L. Kelley|Kelley]] (''General Topology''; {{ISBN|0-387-90125-6}}).
* A [[lattice (order)|lattice]] need not be bounded. In a bounded lattice, 0 and 1 are allowed to be equal.
*[[Elliptic function]]s are written in ''ω'' = [[half-period]] style.
*A weight ''k'' [[modular form]] follows the Serre convention that ''f''(−1/''τ'') = ''τ''<sup>''k''</sup>''f''(''τ''), and ''q'' = ''e''<sup>2''πiτ''</sup>.

===Notational conventions===
*The abstract [[cyclic group]] of [[order (group theory)|order]] ''n'', when written additively, has notation Z<sub>''n''</sub>, or in contexts where there may be  confusion with [[p-adic integer|''p''-adic integers]], '''Z'''/''n'''''Z'''; when written multiplicatively, e.g. as [[roots of unity]], C<sub>''n''</sub> is used (this does not affect the notation of [[isometry group]]s called C<sub>''n''</sub>).
*The standard notation for the abstract [[dihedral group]] of order 2''n'' is D<sub>''n''</sub> in geometry and D<sub>2''n''</sub> in finite group theory. There is no good way to reconcile these two conventions, so articles using them should make clear which they are using.
*[[Bernoulli number]]s are denoted by B<sub>''n''</sub>, and are zero for ''n'' odd and greater than 1.
*In [[category theory]], write [[Hom-set]]s, or [[morphism]]s from ''A'' to ''B'', as Hom(''A'',''B'') rather than Mor(''A'',''B'') (and with the implied convention that the category is not a [[small category]] unless that is said).
*The [[semidirect product]] of groups ''K'' and ''Q'' should be written {{nowrap|''K'' ×<sub>''φ''</sub> ''Q''}} or {{nowrap|''Q'' ×<sub>''φ''</sub> ''K''}} where ''K'' is the normal subgroup and {{nowrap|''φ'' : ''Q'' → Aut(''K'')}} is the [[homomorphism]] defining the product. The semidirect product may also be written {{nowrap|''K'' ⋊ ''Q''}} or {{nowrap|''Q'' ⋉ ''K''}} (with the bar on the side of the non-normal subgroup) with or without the ''φ''.
**The context should clearly state that this is a semidirect product and should state which group is normal.
**The bar notation is discouraged because it is not supported by all browsers.
**If the bar notation is used it should be entered as <code><nowiki>{{unicode|&amp;#x22C9;}}</nowiki></code> (⋉) or <code><nowiki>{{unicode|&amp;#x22CA;}}</nowiki></code> (⋊) for maximum portability.{{update inline |date=July 2023 |reason=Template:Unicode is deprecated}}
*[[Subset]] is denoted by <math>\subseteq</math>, proper subset by <math>\subsetneq</math>. The symbol <math>\subset</math> may be used if the meaning is clear from context, or if it is not important whether it is interpreted as subset or as proper subset (for example, <math>A\subset B</math> might be given as the hypothesis of a theorem whose conclusion is obviously true in the case that <math>A=B</math>). All other uses of the <math>\subset</math> symbol should be explicitly explained in the text.
*For a matrix [[transpose]], use superscript non-italic capital letter T: ''X''<sup>T</sup>, <math>X^\mathrm T</math> or <math>X^\mathsf T</math>, and not ''X''<sup>''T''</sup>, <math>X^T</math>, or <math>X^\top</math>.
*In a [[lattice (order)|lattice]], infima are written as {{nowrap|''a'' ∧ ''b''}} or as a product ''ab'', suprema as {{nowrap|''a'' ∨ ''b''}} or as a sum {{nowrap|''a'' + ''b''}}. In a pure lattice theoretical context the first notation is used, usually without any precedence rules. In a pure engineering or "ideals in a ring" context the second notation is used and multiplication has higher precedence than addition. In any other context the confusion of readers of all backgrounds should be minimized. In an abstract bounded lattice, the smallest and greatest elements are denoted by 0 and 1.
*The scalar or [[dot product]] of vectors should be denoted with a centre-dot {{nowrap|'''a''' ⋅ '''b'''}}, as an [[inner product]] {{angle bracket|'''a''','''b'''}} or ('''a''','''b'''), or as a [[matrix product]] '''a'''<sup>T</sup>'''b''', never with juxtaposition '''ab'''.

==Proofs==
This is an encyclopedia and not a collection of mathematical texts, but we often want to include proofs to explain a theorem or definition. A downside of including proofs is that they may interrupt the flow of the article, whose goal is usually expository. Use your judgment; as a rule of thumb, include proofs when they expose or illuminate the concept or idea; don't include them when they serve only to establish the correctness of a result.

Since many readers will want to skip proofs, it is a good idea to set them apart in some way, for instance by giving them a separate section. Additional discussion and guidelines can be found at [[Wikipedia:WikiProject Mathematics/Proofs]].

==Algorithms==
{{see also|Wikipedia:WikiProject Computer science/Manual of style (computer science)#Algorithms}}

An article about an [[algorithm]] may include [[pseudocode]] or in some cases [[source code]] in some [[programming language]]. Wikipedia does not have a standard programming language or languages, and not all readers will understand any particular language even if the language is well-known and easy to read, so consider whether the algorithm could be expressed in some other way. If source code is used always choose a programming language that expresses the algorithm as clearly as possible.

Articles should not include multiple implementations of the same algorithm in different programming languages unless there is encyclopedic interest in each implementation.

Source code should always use [[MW:Extension:SyntaxHighlight GeSHi|syntax highlighting]]. For example this markup:<ref>
This example, from here [http://en.wikipedia.org/w/index.php?title=Sieve_of_Eratosthenes&oldid=347438933], is in [[Haskell]], not a well-known language so generally not a good choice when showing an algorithm.
</ref>

 <nowiki><syntaxhighlight lang="Haskell">
  primes = sieve [2..]
  sieve (p : xs) = p : sieve [x | x <- xs, x `mod` p > 0]
</syntaxhighlight></nowiki>

generates the following:

<syntaxhighlight lang="Haskell">
  primes = sieve [2..]
  sieve (p : xs) = p : sieve [x | x <- xs, x `mod` p > 0]
</syntaxhighlight>

==Including citations and literature references==
{{anchor|MATHSCITATIONS|Mathscitations|Including citations and literature references}}
Per the Wikipedia policy, [[WP:VERIFY]], it is essential for article content to have inline citations, and thus to have a well-chosen list of references and pointers to the literature. Some reasons for this are the following:
* Wikipedia articles cannot be a substitute for a textbook (that is what [[Wikibooks]] is for). Also, often one might want to find out more details (like the proof of a theorem stated in the article).
* Some notions are defined differently depending on context or author. Articles should contain some references that support the given usage.
* Important theorems should cite historical papers as an additional information (not necessarily for looking them up).
* Today many research papers or even books are freely available online and thus virtually just one click away from Wikipedia. Newcomers would greatly profit from having an immediate connection to further discussions of a topic.
* Providing further reading enables other editors to verify and to extend the given information, as well as to discuss the quality of a particular source.

The [[Wikipedia:Cite sources]] article has more information on this and also several examples for how the cited literature should look.

==Typesetting of mathematical formulae==
{{anchor|Formula|Formulae|FORMULA|FORMULAE|Typesetting of mathematical formulas}}{{shortcut|MOS:FORMULA|MOS:FORMULAE}}
{{see also|Help:Displaying a formula}}
One may set formulae using LaTeX (the {{tag|math|o}} tag, described in the next subsection) or, in certain cases, using other means of formatting that render in HTML; both are acceptable and widely used, except for ''section headings,'' which should use HTML only, as LaTeX markup might cause uneven spacing in the table of contents, as well as the appearance of illegible [[WP:ANCHOR|anchor links]] to sections. Some of the issues presented by using LaTeX or HTML are discussed below.

Large-scale formatting changes to an article or group of articles are likely to be controversial. One should not change formatting [[WP:be bold|boldly]] from LaTeX to HTML, nor from non-LaTeX to LaTeX without a clear improvement. Proposed changes should generally be discussed on the [[WP:talk pages|talk page of the article]] before implementation. If there is no positive response, or if planned changes affect more than one article, consider notifying an appropriate Wikiproject, such as [[Wikipedia:WikiProject Mathematics|WikiProject Mathematics]] for mathematical articles.

For inline formulae, such as {{math|''a''<sup>2</sup> − ''b''<sup>2</sup>}}, the community of mathematical editors of English Wikipedia currently has no consensus about preferred formatting; see [[WP:Rendering math]] for details.

For a formula ''on its own line'' the preferred formatting is the LaTeX markup, with a possible exception for simple [[string (computer science)|strings]] of Latin letters, digits, [[template:punctuation marks|common punctuation marks]], and arithmetical operators. Even for simple formulae the LaTeX markup might be preferred if required for uniformity within an article. For readability, it is also strongly preferred not to mix HTML and LaTeX markup in the same expression.

=== Using LaTeX markup ===
Wikipedia allows editors to typeset mathematical formulae in (a subset of) [[LaTeX]] markup (see also [[TeX]]); the formulae are, for a default reader, translated into [[Portable Network Graphics|PNG]] images. They may also be rendered as [[MathML]] or [[HTML]] (using [[MathJax]]), depending on user preferences. For more details on this, see [[Help:Displaying a formula]].

The LaTeX formulae can be displayed inline (like this: <math>\mathbf{x}\in\mathbb{R}^2</math>), as well as on their own line:
<math display=block>\int_0^\pi \sin x\,dx.</math>

A frequent method for displaying formulas on their own line has been to indent the line with one or more colons&nbsp;(:). Although this produces the intended visual appearance, it produces invalid html (see {{slink|Wikipedia:Manual of Style/Accessibility|Indentation}}). Instead, formulas may be placed on their own line using <syntaxhighlight lang="html" inline><math display=block></syntaxhighlight>. For instance, the formula above was typeset using <code>&lt;math display=block&gt;<syntaxhighlight lang="tex" inline>\int_0^\pi \sin x\,dx.</syntaxhighlight>&lt;/math&gt;</code>.

If you find an article which indents lines with spaces in order to achieve some formula layout effect, you should convert the formula to LaTeX markup.

Having LaTeX-based formulae inline has the following drawbacks:
* The font size can be slightly larger than that of the surrounding text on some browsers, making text containing inline formulae harder to read.
* The download speed of a page is negatively affected if it contains many formulas.
* Until bug {{phab|T263572}} is fixed, it will not work in image captions when readers click through to see full-size images.

If an inline formula needs to be typeset in LaTeX, keep the height down by using text-style or horizontal fractions: <code>&lt;math><syntaxhighlight lang="tex" inline>\tfrac12 x</syntaxhighlight>&lt;/math></code> produces <math>\tfrac12 x</math> and <code>&lt;math><syntaxhighlight lang="tex" inline>x / 2</syntaxhighlight>&lt;/math></code> produces <math>x / 2</math>, but <code>&lt;math><syntaxhighlight lang="tex" inline>\frac{x}{2}</syntaxhighlight>&lt;/math></code> is too tall to fit inline.

Often better formatting can be achieved with <syntaxhighlight lang="html" inline><math display=inline></syntaxhighlight> tag, which translates to the <code>\textstyle</code> LaTeX command. By default, LaTeX code is rendered as if it were a displayed equation (not inline), and this can frequently be too big. For example, the formula <code>&lt;math&gt;<syntaxhighlight lang="tex" inline>\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}</syntaxhighlight>&lt;/math&gt;</code> is too large to be used inline, rendering as
{{bi|left=1.6|<math>\sum_{n=1}^\infty \frac{1}{n^2} = \frac{\pi^2}{6}.</math>}}
Adding <code>display=inline</code> generates a smaller summation symbol and moves the limits to its right side. The rewritten formula <code>&lt;math display=inline&gt;<syntaxhighlight lang="tex" inline>\sum_{n=1}^\infty 1/n^2 = \pi^2/6</syntaxhighlight>&lt;/math&gt;</code> renders as {{nobr|<math display=inline>\sum_{n=1}^\infty 1/n^2 = \pi^2/6</math>,}} which fits much better inline. Adding <syntaxhighlight lang="html" inline>display=inline</syntaxhighlight> renders exponents lower, especially under square roots, often resulting in a smaller square root which fits better in inline text: compare <code>&lt;math><syntaxhighlight lang="tex" inline>\sqrt{x^2+y^2}</syntaxhighlight>&lt;/math></code> to <code>&lt;math display=inline><syntaxhighlight lang="tex" inline>\sqrt{x^2+y^2}</syntaxhighlight>&lt;/math></code> which render as <math>\sqrt{x^2+y^2}</math> and {{nowrap|<math display=inline>\sqrt{x^2+y^2}</math>}}, respectively.

HTML-generating formatting, as [[#Using HTML|described below]], is adequate for articles that use only simple inline formulae and better for text-only browsers.

==== Line wrapping ====
Directly using <code>&lt;math>...&lt;/math></code> tags results in line wrapping points that allow wrapping between it and adjacent text (typically punctuation).  Including such text within the tags to avoid this wrapping results in its font being discordant with other text.  This can be remedied by wrapping the LaTeX markup in a suitable template (optionally excluding the adjacent punctuation), e.g. <code>({{((}}nobr{{!}}&lt;math>...&lt;/math>{{))}})</code>, or by replacing the tags with a template, e.g. <code>({{((}}tmath{{!}}1=...{{))}})</code>.  Take care of some necessary substitutions documented for {{tl|tmath}}.

==== Deprecated formatting ====
{{anchor|Very simple formulae|Forcing output to be an image}}

Older versions of the MediaWiki software supported displaying simple LaTeX formulae as HTML rather than as an image. Although this is no longer an option, some formulae have formatting in them intended to force them to display as an image, such as an invisible quarter space (<code>\,</code>) added at the end of the formula, or <code>\displaystyle</code> at the beginning. Such formatting can be removed if a formula is edited and need not be added to new formulae.

==== Alt text ====
Images generated from LaTeX markup have [[WP:ALT|alt text]], which is displayed to visually impaired readers and other readers who cannot see the images. The default alt text is the LaTeX markup that produced the image. You can override this by explicitly specifying an <code>alt</code> attribute for the <code>math</code> element. For example, <code><nowiki><math alt="Square root of pi">\sqrt{\pi}</math></nowiki></code> generates an image <math alt="square root of pi">\sqrt{\pi}</math> whose alt text is "Square root of pi". Small and easily explained formulas used in less technical articles can benefit from explicitly specified alt text. More complicated formulas, or formulas used in more technical articles, are often better off with the default alt text.

===Using HTML===
The following sections cover the way of presenting simple inline formulae in HTML, instead of using LaTeX.

Templates supporting HTML formatting are listed in  [[:Category:Mathematical formatting templates]]. Not all templates are recommended for use; in particular, use of the {{tl|frac}} template to format fractions is discouraged in mathematics articles.

====Font formatting====

By default, regular text is rendered in a [[sans serif]] font. The TeX markup of {{tag|math}} uses a [[serif]] font to display a formula (whether as SVG or HTML). HTML math expressions should use the {{tlx|math}} template so they display in a serif font as well. Doing so will also ensure that the text within a formula will not line-wrap, and that the font size will closely match the surrounding text in any [[Wikipedia:Skins|skin]]. Using {{tl|math}} and {{tl|mvar}} also helps some spell checkers and screen readers treat math markup properly. Note that certain special characters (equal signs, absolute value bars) require [[Template:Math#Use_of_equals-sign_and_absolute_value_bars|special attention]].

:The relationship is defined as <syntaxhighlight lang="wikitext" inline>{{math|''x'' {{=}} −(''y''<sup>2</sup> + 2)}}</syntaxhighlight>.

will result in:

:The relationship is defined as {{math|''x'' {{=}} −(''y''<sup>2</sup> + 2)}}.

=====Variables=====
Use italic text for variables, but never for numbers or symbols. To ensure an italic serif typeface, use the {{tl|mvar}} template to enclose a simple mention of a variable by name. This helps distinguish certain characters such as {{mvar|I}} and {{mvar|l}}. Within {{tl|math}} templates (which will set a serif font but not italics), use the wikitext markup of double apostrophes to make variables italic. For example:

:<syntaxhighlight lang="wikitext" inline>{{mvar|x}} is a value on the horizontal axis</syntaxhighlight>
displays as:
:{{mvar|x}} is a value on the horizontal axis
and
:<syntaxhighlight lang="wikitext" inline>{{math|''x'' {{=}} −(''y''<sup>2</sup> + 2)}}</syntaxhighlight>
results in:
:{{math|''x'' {{=}} −(''y''<sup>2</sup> + 2)}}

While italicizing variables, things like parentheses, digits, equal and plus signs should be kept outside of the double-apostrophed sections. Using double apostrophes for math content instead of {{tl|mvar}} or without {{tl|math}} is undesirable for readers because it will render in a sans serif font; this is especially confusing when other articles or sections render the same variables or equations in a serif font. Descriptive subscripts should not be in italics, because they are not variables. For example, {{math|''m''<sub>foo</sub>}} is the mass of a foo. [[SI unit]]s are never italicized: {{math|''x'' {{=}} 5 cm}}.

=====Functions=====
Names for [[List of mathematical functions|standard functions]], such as {{math|sin}} and {{math|cos}}, are not in italic font, but we use italic names such as {{mvar| f }} for functions in other cases; for example when we define the function as in {{nobr| {{math| ''f''(''x'') {{=}} sin(''x'') cos(''x'') }} .}}

=====Sets=====
Sets are usually written in upper case italics; for example:

:{{math|''A'' {{=}} {''x'' : ''x'' > 0}}}

would be written:

:<syntaxhighlight lang="wikitext" inline>{{math|''A'' {{=}} {''x'' : ''x'' > 0}}}</syntaxhighlight>&nbsp;.

=====Greek letters=====
Italicize lower-case Greek letters when they are variables or constants (in line with the general advice to italicize variables): the example expression {{math|''λ'' + ''y'' {{=}} ''πr''<sup>2</sup>}} would then be typeset by:

<syntaxhighlight lang="wikitext" inline>{{math|''&lambda;'' + ''y'' = ''&pi;r''<sup>2</sup>}}</syntaxhighlight>

(It is also possible to enter [[Greek_alphabet#Greek_in_Unicode|Greek letters]] directly.)

For consistency with the LaTeX style, do not italicize ''capital'' Greek letters; e.g.  {{nobr| {{math| ''n''! {{=}} [[Gamma function|&Gamma;]](''n'' + 1) }}.}}

According to the Unicode Consortium,<ref>[https://www.unicode.org/reports/tr25/tr25-6.html Unicode Technical Report #25: Unicode Support for Mathematics], §2.5 Duplicated Characters</ref> the characters {{unichar|00B5|micro sign}} and {{unichar|2126|OHM}} are intended for compatibility with legacy character sets, and Unicode-capable environments (like Wikipedia) should use the Greek letters instead ({{unichar|03BC|GREEK LETTER SMALL MU}} and {{unichar|03A9|GREEK LETTER CAPITAL OMEGA}}). This is also required for "micro" by [[MOS:UNITSYMBOLS]].

=====Common sets of numbers=====
Commonly used sets of numbers are typeset in boldface, as in the set of real numbers {{math|'''R'''}}. Again, typically we use wiki markup: three apostrophes (<syntaxhighlight lang="wikitext" inline>'''</syntaxhighlight>) rather than the HTML <syntaxhighlight lang="wikitext" inline><b></syntaxhighlight> tag for making text bold. On chalkboards and increasingly in printed publications, mathematicians alternately use blackboard bold for sets such as the real numbers, which may be encoded in LaTeX as <syntaxhighlight lang="wikitext" inline><math>\mathbb{R}</math></syntaxhighlight> (preferred shortcut: {{nobr|<syntaxhighlight lang="wikitext" inline><math>\R</math></syntaxhighlight>),}} which renders as <math>\mathbb{R}.</math> However, the special [[Unicode]] characters, such as {{nobr|U+211D}} (plain text ℝ or math font {{math|ℝ}}) and its adjacent characters should be avoided at present, since these characters are not yet universally supported and may have an inconsistent appearance. Either bold or blackboard bold is acceptable in Wikipedia articles, but should be consistent within each article.

{{further|#Blackboard bold}}

=====Superscripts and subscripts=====
{{main article|Wikipedia:Manual of Style (superscripts and subscripts)}}

Superscripts and subscripts should be wrapped in <code>&lt;sup></code> and <code>&lt;sub></code> tags, respectively, with no other formatting info. Font sizes and such should be entrusted to be handled with stylesheets.<!--see discussion on [[Template talk:Sup]]--> For example, to write {{math|''c''<sub>3+5</sub>}}, use

:<syntaxhighlight lang="wikitext" inline>{{math|''c''<sub>3+5</sub>}}</syntaxhighlight>.

Do not use special characters like <code>[[Unicode_subscripts_and_superscripts|²]]</code> (<code>&amp;sup2;</code>) for squares. This does not combine well with other powers, as the following comparison shows:

: {{math|1 + ''x'' + ''x''² + ''x''<sup>3</sup> + ''x''<sup>4</sup>}} (with <code>&amp;sup2;</code>) versus
: {{math|1 + ''x'' + ''x''<sup>2</sup> + ''x''<sup>3</sup> + ''x''<sup>4</sup>}} (with <code>&lt;sup>2&lt;/sup></code>).

Moreover, the TeX engine used on Wikipedia may format simple superscripts using <syntaxhighlight lang="wikitext" inline><sup>...</sup></syntaxhighlight> depending on user preferences. Thus, for some users <math>x^2</math> will be an image, and for others it will be HTML like {{math|''x''<sup>2</sup>}}. Formulae formatted without using TeX should use the same syntax to maintain the same appearance.

====Special symbols====
{{shortcut|MOS:MATHSPECIAL}}
The [[list of mathematical symbols]], [[list of mathematical symbols by subject]] and the list at [[Wikipedia:Mathematical symbols]] may be useful when editing mathematics articles. [[Mathematical operators and symbols in Unicode|Almost all mathematical operator symbols]] have their specific [[code point]]s in [[Unicode]] outside both [[ASCII]] and [[General Punctuation]] (with notable exception of "+", "=", "|", as well as ",", ":", and three sorts of [[bracket]]s). The [[list of mathematical symbols by subject]] includes markup for LaTeX and HTML, and Unicode code points.

Keep in mind:
# Not all of the symbols in these lists are displayed correctly on all browsers (see [[Help:Special characters]]). Although the symbols that correspond to [[List of XML and HTML character entity references|named entities]] are very likely to be displayed correctly, a significant number of viewers will have problems seeing all the characters listed at [[Mathematical operators and symbols in Unicode]]. One way to guarantee that an uncommon symbol is rendered correctly for all readers is to [[#Forcing output to be an image|force the symbol to display as an image]], using the {{tag|math}} with LaTeX markup.
# Not all readers will be familiar with mathematical notation. Thus, to maximize the size of the audience who can read an article, it is better to be conservative in using symbols. For example, writing "''a'' divides ''b''" rather than "{{nowrap|''a'' {{!}} ''b''}}" in an elementary article may make it more accessible.


{{shortcut|MOS:ROMANNUM}}
* For [[Roman numerals]], [[Basic Latin (Unicode block)|Basic Latin]] (ASCII) letters should be used instead of the equivalent [[Numerals in Unicode#Roman numerals|Unicode characters in the U+21XX range]]. For example, {{xt|L}} and {{xt|VI}}, not {{!xt|Ⅼ}}, and not precomposed characters like {{!xt|Ⅵ}}. (The only exception is when discussing the Unicode characters themselves.)
*:{{for|when to use or not use Roman numerals|Wikipedia:Manual of Style/Dates and numbers}}
* Use {{unichar|2032|PRIME}} or {{unichar|2033|DOUBLE PRIME}} where the [[Prime (symbol)|prime symbol]] is appropriate; do not use the ASCII apostrophe (') or double quote (") in these cases. {{tl|prime}} and {{tl|pprime}} can be useful to prevent overlap with italicized characters.
* Use {{unichar|002A|ASTERISK}} when the character should render like a [[superscript]], and is typical when used as a postfix. This character also appears on keyboards, and is thus easier to type and search for. Example: {{xt|C*-algebra}}. Use {{unichar|2217|ASTERISK OPERATOR}} (&amp;lowast;) for subscripts and when the bottom of the character should roughly align with the [[typeface anatomy|baseline]] of neighboring characters, which is typical when used as a prefix or infix operator, or a standalone character. Usage should be consistent across articles covering the same subfield of mathematics; see [[Asterisk#Mathematics]] for a canonical list.
* Use {{unichar|002F|SOLIDUS}} instead of {{unichar|2215|DIVISION SLASH}}
* Use {{unichar|003A|COLON}} instead of {{unichar|2236|RATIO}}
* Use {{unichar|007E|TILDE}} instead of {{unichar|223C|TILDE OPERATOR}}. Use [[Approximation#Typography|other symbols]] to mean "approximately" (and {{char|¬}} for [[negation]]) in mathematical expressions, because [[Tilde#Mathematics|tilde has other mathematical meanings]].
* Use <code><nowiki><math>... \setminus ...</math></nowiki></code> or <code><nowiki><math>... \smallsetminus ...</math></nowiki></code> instead of {{unichar|2216|SET MINUS}} or {{unichar|005C|REVERSE SOLIDUS}} for set substraction. (Either Unicode character can be used where {{tag|math}} markup cannot be used for technical reasons.)
* Use <code><nowiki><math>... \circ ...</math></nowiki></code> (<math>\circ</math>) instead of {{unichar|2218|RING OPERATOR}} (which on some systems is too small and can be confused with [[interpunct]]) or {{unichar|25CB|WHITE CIRCLE}} (which on some systems is too large).
* Use <code><nowiki><math>...  \ngtr ...</math></nowiki></code> (<math>\ngtr</math>) instead of {{unichar|226F|NOT GREATER-THAN}}, which on some systems renders as two separate characters.<!-- Reported on Chrome version 123.0.6312.106 on Windows 10 version 22H2 -->


{{see also|Wikipedia:Manual of Style/Abbreviations#Unicode abbreviation ligatures}}

====Less-than sign====
Although the MediaWiki markup engine is fairly smart about differentiating between unescaped "&lt;" characters that are used to denote the start of an embedded HTML or HTML-like tag and those that are just being used as literal less-than symbols, it is ideal to use <code>&amp;lt;</code> when writing the less-than sign, just like in HTML and XML. For example, to write {{math|''x'' &lt; 3}}, use

:<syntaxhighlight lang="wikitext" inline>{{math|''x'' &lt; 3}}</syntaxhighlight>,
not
:<syntaxhighlight lang="wikitext" inline>{{math|''x'' < 3}}</syntaxhighlight>.

==== Multiplication sign ====
{{shortcut|WP:&sdot;}}

Standard algebraic notation is best for formulae, so two variables ''q'' and ''d'' being multiplied are best written as ''qd'' when presented in a formula. That is, when ''citing'' a formula, don't use <code>×</code>.

However, when ''explaining'' the formula for a general audience (not just mathematicians), or giving examples of its application, it is prudent to use the [[multiplication sign]]: "×", coded as <code>&amp;times;</code> in HTML or accessed via {{tlx|times}}. Do not use the letter "x" to indicate multiplication.

* When [[division (mathematics)|dividing]] 26 by 4, 6 is the [[quotient]] and 2 is the [[remainder]], because {{nowrap|26 {{=}} 6 × 4 + 2.}}
* {{nowrap|−42 {{=}} 9 × (−5) + 3}}

An alternative to <code>×</code> is the [[dot operator]] <code>&amp;sdot;</code> (also encoded <syntaxhighlight lang="wikitext" inline><math>\cdot</math></syntaxhighlight> and reachable in the "Math and logic" drop-down list below the edit box or via template {{tlx|sdot}}), which produces a symmetrically spaced centered dot: "''a''{{sdot}}''b''".

Do not use the ASCII [[asterisk]]&nbsp;(*) as a multiplication sign outside of [[source code]]. It is not used for this purpose in professionally published mathematics, and most fonts render it in an inappropriate vertical position (above the midline of the text rather than centered on it). For the dot operator, do not use punctuation symbols, such as a simple interpunct <code>&amp;middot;</code> (the choice offered in the "Wiki markup" drop-down list below the edit box), as in many fonts it does not kern properly. The use of {{unichar|2022|bullet|nlink=}} as an operator symbol is also discouraged except in abstract contexts (e.g. to denote an unspecified operator).

Metric units often embed the notion of multiplication and division. [[NIST]] endorses the half-high dot (⋅) or a bare space for this purpose.

====Minus sign====
The correct encoding of the minus sign "−" is different from all varieties of [[hyphen]]&nbsp;"-‐‑",<ref>Note that, aside of &lt;math>, many [[Help:template|templates]] and [[Help:parser|parser functions]] accept the [[hyphen-minus]]&nbsp;"-" as a valid representation of the minus sign. Except situations where "-" has to represent the minus sign in a [[source code]] (including wiki code), it should not be seen in a rendered page, though.</ref> as well as from en-[[dash]]&nbsp;"–". To really get a minus sign, use the "minus" character "−" (reachable via selecting "Math and logic" in the drop-down list below the edit box or using <code>{{tls|minus}}</code>) or use the "<code>&amp;minus;</code>" entity.

====Square brackets====
Square brackets have two problems; they can occasionally cause problems with wiki markup, and editors sometimes 'fix' the brackets in asymmetrical [[interval (mathematics)|intervals]]  to make them symmetrical. The nowiki tag can be used as a general solution to problems like this, as in <code>&lt;nowiki&gt;]&lt;/nowiki&gt;</code> to have the <nowiki>]</nowiki> treated as literal text.

The use of intervals for the range or domain of a function is very common. A solution which makes the reason for the different brackets around an interval more plain is to use one of the templates {{tl|open-closed}}, {{tl|closed-open}}, {{tl|open-open}}, {{tl|closed-closed}}. For instance:

:<syntaxhighlight lang="wikitext" inline>{{open-closed|−π, π}}</syntaxhighlight>

produces

:{{open-closed|−π, π}}.

These templates use the {{tl|math}} template to avoid line breaks and use the TeX font.

====Function symbol====
{{shortcut|MOS:FNOF}}
Functions are conventionally denoted by the lowercase italic letters {{tmath|f}}, {{tmath|g}}, and {{tmath|h}}, often with a serif font whose ''f'' extends below the baseline. Many readers see Wikipedia body copy in a sans-serif font whose italic ''f'' has a different appearance without a "tail". Circa 2010, some editors proposed using the Unicode symbol {{unichar|0192|LATIN SMALL LETTER F WITH HOOK|html=}} as a replacement function symbol; however, this symbol should not be used, because the mathematical function symbol is nothing more or less than an ordinary italic ''f'', and its appearance should be consistent with the font otherwise used for mathematical notation in the same article. Furthermore, some screen readers, such as [[JAWS (screen reader)|JAWS]] and [[NonVisual Desktop Access]], pronounce the Unicode &fnof; symbol as "florin" (it can be used as a [[Florin sign|Florin currency symbol]]<ref>Latin Extended-B, [http://www.unicode.org/charts/PDF/U0180.pdf]</ref>) or a numerical code, which can be confusing.

An ordinary italicized letter should be used instead, as in {{code|''f''}}, {{code|<nowiki>{{mvar|f}}</nowiki>}}, or <code><nowiki><math>f</math></nowiki></code>, which render as ''f'', {{mvar|f}}, or {{nobr|<math>f</math>,}} respectively.<ref>[[Wikipedia talk:WikiProject Mathematics/Archive 68#ƒ or f?]]</ref>

====Radical symbol====
{{shortcut|MOS:RADICAL}}
The [[radical symbol]] √ can be used when written on its own, but when part of a larger expression, can be problematic. {{tl|radic}} (often seen as {{tl|sqrt}}) is the best way to write such expressions in HTML, but the result is unattractive due to the hole between the overline and the radical symbol in many web browsers:
:{{radical|9}}, {{radical|27|3}}
This method should be avoided whenever technically possible to do so. Instead, use {{tag|math}} tags and \sqrt{}, even if inline.  For example:
:<math>\sqrt{9}, \sqrt[3]{27}</math>

Because of Mediawiki bug {{phab|T263572}}, {{tag|math}} markup is incompatible with the Media Viewer (used for full-screen image viewing on mobile devices), so until that is fixed, the {{tl|radic}} method or √ with no overline should be used in image captions.

The use of √ with no overline is acceptable for simple expressions, as long as the operand is unambiguous.<ref>[[Special:Permalink/987584665#Radical_RFC_comments|October 2020 RfC]].</ref>

===Explanation of symbols in formulae===
{{shortcut|MOS:EXPLAINSYMBOLS}}
A list as in
<blockquote>
Example 1: The foocity is given by

:<math>\mathbf{F} = \mathbf{b} \times a\mathbf{r},</math>

where

* <math>\mathbf{b}</math> is the barness vector,
* <math>a</math> is the bazness coefficient,
* <math>\mathbf{r}</math> is the quuxance vector.
</blockquote>

should be written as prose, to avoid using more vertical space than necessary:

<blockquote>
Example 2: The foocity is given by

:<math>\mathbf{F} = \mathbf{b} \times a\mathbf{r},</math>

where <math>\mathbf{b}</math> is the barness vector, <math>a</math> is the bazness coefficient, and <math>\mathbf{r}</math> is the quuxance vector.
</blockquote>

An exception would be if some of the definitions are very long (as in [[Heat equation#Three-dimensional problem|Heat equation]], for example).  In any case, each definition should end with a comma or semicolon, and the last one should end with a period if it terminates a sentence.

===Punctuation after formulae<span class="anchor" id="PUNC"></span>===
{{shortcut|MOS:MATH#PUNC}}

Just as in mathematics publications, a sentence which ends with a formula must have a period at the end of the formula.<ref>This style, adopted by Wikipedia, is shared by Higham (1998), Halmos (1970), the Chicago Manual of Style, and many mathematics journals.</ref> This equally applies to displayed formulae (that is, formulae that take up a line by themselves). Similarly, if the conventional punctuation rules would require a question mark, comma, semicolon, or other punctuation at that place, the formula must have that punctuation at the end.

If the formula is written in [[LaTeX]], that is, surrounded by the <syntaxhighlight lang="wikitext" inline><math></syntaxhighlight> and <syntaxhighlight lang="wikitext" inline></math></syntaxhighlight> tags, then the punctuation should also be inside the tags, because otherwise the punctuation could wrap to a new line if the formula is at the edge of the browser window. Alternatively—since the previous result can be unaesthetic, especially for inlined formulae presented as an image whose baseline does not line up with that of the running text—the punctuation can be placed after the <syntaxhighlight lang="wikitext" inline></math></syntaxhighlight> tag and then the whole formula (including the punctuation) can be enclosed with the {{tl|nowrap}} template, as in <syntaxhighlight lang="wikitext" inline>This shows that {{nowrap|<math>\tfrac{1}{2} = 0.5</math>.}}</syntaxhighlight>.<ref>It is technically possible to use a [[word joiner]] before the punctuation instead, but it's [http://jkorpela.fi/html/nobr.html#prevent seldom respected by browsers].</ref>

Also, for simple inline formulae, the template {{tl|tmath}} may be useful, especially when punctuation is followed by a footnote.

===Font usage===

====Multi-letter names====
Functions that have multi-letter names should always be in an upright font. The most well-known functions—trigonometric functions, logarithms, etc.—can be written without parentheses for as long as the result does not become ambiguous. For example:

: <math>2\sin x</math>   (parentheses may be omitted here, as the argument consists of a single term only; typeset from <syntaxhighlight lang="tex" inline><math>2\sin x</math></syntaxhighlight>)
:<math>2\sin(x+1)</math> (parentheses are required to clarify the intended argument)
but not
: <math>2sin x</math>   (''incorrect''—typeset from <syntaxhighlight lang="tex" inline><math>2sin x</math></syntaxhighlight>).

: Note: For potential pitfalls of forms not understood consistently across the board, see [[order of operations]] and [[implied multiplication]]; if there is any risk that a term could become ambiguous for our readership, use parentheses.

When operator (function) names do not have a pre-defined abbreviation,  we may use <syntaxhighlight lang="tex" inline>\operatorname</syntaxhighlight>:
: <math>2\operatorname{csch}x</math>   (typeset from <syntaxhighlight lang="tex" inline><math>2\operatorname{csch}x</math></syntaxhighlight>).
: <math>a\operatorname{tr}(A)</math>   (typeset from <syntaxhighlight lang="tex" inline><math>a\operatorname{tr}(A)</math></syntaxhighlight>).
<code>\operatorname</code> includes correct spacing that would not be present with other means such as <code>\rm</code>:
: <math>2{\rm sin} x</math>   (''incorrect''—typeset from <syntaxhighlight lang="tex" inline><math>2{\rm sin} x</math></syntaxhighlight>).

Special care is needed with subscripted labels to distinguish the purpose of the subscript (as this is a common error): variables and constants in subscripts should be italic, while textual labels should be in normal text font (Roman, upright). For example:

: <math> x_\text{this one} = y_\text{that one}</math>   (correct—typeset from <syntaxhighlight lang="tex" inline><math> x_\text{this one} = y_\text{that one}</math></syntaxhighlight>),
and
: <math>\sum_{i=1}^n { y_i^2 }</math>   (correct—typeset from <syntaxhighlight lang="tex" inline><math>\sum_{i=1}^n { y_i^2 }</math></syntaxhighlight>),
but not
: <math>r = x_{predicted} - x_{observed}</math>   (''incorrect''—typeset from <syntaxhighlight lang="tex" inline><math>r = x_{predicted} - x_{observed}</math></syntaxhighlight>).

For several years this manual recommended <code>\mbox</code> as a workaround for lack of <code>\text</code>, but this is now considered undesirable.  See ''[[/Why you should never use \mbox within Wikipedia|An opinion: Why you should never use \mbox within Wikipedia]].''

====Roman versus italic====
For single-letter variables, constants, and operators such as the [[derivative|differential]], [[imaginary unit]], and [[e (mathematical constant)|Euler's number]], Wikipedia articles usually use an italic font. One writes
:<math>\int_0^\pi \sin x \, dx ,</math>   (typeset from <syntaxhighlight lang="tex" inline><math>\int_0^\pi \sin x \, dx ,</math></syntaxhighlight>—note the thin space (<syntaxhighlight lang="tex" inline>\,</syntaxhighlight>) before <syntaxhighlight lang="tex" inline>dx</syntaxhighlight>),
:<math>\frac{dz}{dx} = \frac{dz}{dy} \cdot \frac{dy}{dx} ,</math>   (typeset from <syntaxhighlight lang="tex" inline><math>\frac{dz}{dx} = \frac{dz}{dy} \cdot \frac{dy}{dx} ,</math></syntaxhighlight>),
:<math>x+iy,</math>   (typeset from <syntaxhighlight lang="tex" inline><math>x+iy,</math></syntaxhighlight>), and
:<math>e^{i\theta} .</math>   (typeset from <syntaxhighlight lang="tex" inline><math>e^{i\theta} .</math></syntaxhighlight>).
Some authors prefer to use an upright (Roman) font for operators, as in {{math|d}}, for the differential operator, as opposed to {{mvar|d}} for a variable. Upright fonts are sometimes used for standard, nearly universal constants, as in {{math|i}}, {{math|e}}, and {{math|&pi;}}; other authors use Roman boldface, as in '''{{math|i}}'''.  Changes from one style to another should be done only to make an article consistent with itself.  Formatting changes should ''not'' be made solely to make articles consistent with each other, nor to make articles conform to a particular style guide or standards body.  It is inappropriate for an editor to go through articles doing mass changes from one style to another.  When there is dispute over the correct style to use, follow the same principles as [[MOS:STYLERET]].  

Generally, one way to determine which usage is appropriate on Wikipedia is to look at prevalence in reliable sources in addition to relevant style guides, per [[WP:WEIGHT]].  For example, the ISO&nbsp;80000-2 recommends that the mathematical constant {{math|''e''}} should be typeset in an upright Roman font: {{math|e}}.  But this guide is rarely followed in reliable mathematical sources, and it is contradicted by other style guides, like [[Donald Knuth]]'s ''TeXbook''.  This makes the more common practice to use an italic face for the constant {{math|''e''}}.

====Blackboard bold====
{{Shortcut|MOS:BBB}}
The [[blackboard bold]] letter style originated in the 1960s to distinguish bold letters from ordinary letters on a blackboard or using a typewriter; in professionally typeset documents, bold fonts were used for the same purpose. Since then, blackboard bold has gradually gained currency, and is now commonly used in mathematical printing to denote certain common objects in a style distinct from other uses of bold letters.

Today, either blackboard bold or ordinary bold letters can be used interchangeably to represent the standard [[number system]]s (<math>\mathbb N,</math> <math>\mathbb Z,</math> <math>\mathbb Q,</math> <math>\mathbb R,</math> <math>\mathbb C,</math> <math>\mathbb H,</math> <math>\mathbb F_q,</math> <math>\mathbb Z_p,</math> <math>\mathbb Q_p</math>) and for certain other mathematical objects, including [[affine space]] <math>\mathbb{A}^n</math>, [[projective space]] <math>\mathbb{P}^n</math>, [[adele ring]]s <math>\mathbb{A}_K</math>, the additive and multiplicative [[group scheme]]s (<math>\mathbb{G}_a</math> and <math>\mathbb{G}_m</math>), and [[hypercohomology]] (e.g., <math>\mathbb{H}^i(X,\Omega_X^\bullet)</math>). Font preferences vary from one mathematical author or publisher to another.

A particular concern for the use of blackboard bold on Wikipedia is that the Unicode symbols for blackboard bold characters are not supported by all systems, and font substitution in browsers often renders these symbols in discordant fonts. The use of Unicode characters for blackboard bold is discouraged in English Wikipedia; instead, either the LaTeX rendering (for example <code><nowiki><math>\mathbb{Z}</math></nowiki></code> or <code><nowiki><math>\Z</math></nowiki></code>) or standard bold fonts should be used. As with all such choices, each article should be consistent with itself, and editors should not change articles from one choice of typeface to another, except to maintain internal consistency. When there is dispute, follow [[MOS:STYLERET]].

Due to [[phab:T279805|a rendering bug]], LaTeX blackboard bold currently does not work with numerals. Use bold instead (e.g. <nowiki>{{math|'''1'''}} or <math>\bold{1}</math></nowiki>), which is more common anyway. If absolutely necessary (e.g. when discussing the notation itself), use the Unicode character (e.g. 𝟙).
 	
Due to bug {{phab|T263572}}, {{tag|math}} markup should not be used in image captions.

===Fractions===
{{see also|Wikipedia:Manual of Style/Dates and numbers#Fractions}}

In mathematics articles, fractions should always be written either with a horizontal fraction bar (as in <math>\textstyle\frac{1}{2}</math>), or with a forward [[slash (punctuation)|slash]] and with the baseline of the numbers aligned with the baseline of the surrounding text (as in 1/2). The use of {{tlx|frac}} (such as {{frac|1|2}}) is discouraged in mathematics articles.  The use of [[Unicode]] [[precomposed fraction]]s (such as ½) is discouraged entirely, for [[Web accessibility|accessibility]] reasons<ref>Characters in [[ISO/IEC 8859-1]] (¼, ½, and ¾) work with screen readers, but others, like ⅐, might not.</ref> among others.<ref>Not all fractions are available precomposed.</ref>  Metric units are given in decimal fractions (e.g., {{val|5.2|u=cm}}); non-metric units can be either type of fraction, but the fraction style should be consistent throughout the article.<!--This section needs to be checked periodically for consistency with MOSNUM#Fractions.-->

Only "/" is used for [[quotient object]]s in abstract algebra: {{math|''R'' / ''A''}} or <math>R / A</math> {{snd}}markup: {{tlx|math|<nowiki>''R'' / ''A''</nowiki>}} or {{xtag|math|p|content=R / A}}

For simple fractional subscripts or superscripts, the horizontal style is visually the least confusing: {{tlx|math|<nowiki>x<sup>1/2</sup></nowiki>}} ({{math|x<sup>1/2</sup>}}) or {{xtag|math|p|content=x^{1/2} }} (<math>x^{1/2}</math>).

==Graphs and diagrams==
[[File:MOS triangle.svg|thumb|right|The angle {{mvar|CAB}} is {{mvar|α}}.<br>The length of {{mvar|CA}} is {{mvar|b}}.]]
{{See also|Wikipedia:How to create charts for Wikipedia articles}}

There is no general agreement on what fonts to use in graphs and diagrams. In geometrical diagrams points are normally labelled using upper case letters, sides with lower case and angles with lower case Greek letters.

Recent{{when}} geometry books tend to use an italic serif font in diagrams as in <math>A</math> for a point. This allows easy use in LaTeX markup. However, older books tend to use upright letters as in <math>\mathrm{A}</math> and many diagrams in Wikipedia use sans-serif upright A instead. Graphs in books tend to use LaTeX conventions, but yet again there are wide variations.

For ease of reference diagrams and graphs should use the same conventions as the text that refers to them. If there is a better illustration with a different convention, though, the better illustration should normally be used.
{{clear}}

==See also==

===Help for those writing a formula===
*[[Help:Displaying a formula]]
*[[Wikipedia:Mathematical symbols]]
*[[Wikipedia:Rendering math]]

===General information===
*[[Wikipedia:WikiProject Mathematics]]
*[[Wikipedia:Scientific citation guidelines]]—advice on providing references for mathematical and scientific articles

==Notes==
{{Reflist}}

==Further reading==
A style guide specifically written for mathematics:
* {{ citation | first = Nicholas J. | last = Higham | author-link = Nicholas Higham | title = Handbook of Writing for the Mathematical Sciences | edition = second | publisher = SIAM (Society for Industrial and Applied Mathematics) | date = 1998 | doi = 10.1137/1.9780898719550 | isbn = 0-89871-420-6 | url = http://epubs.siam.org/doi/book/10.1137/1.9780898719550}}.
More style guidance:
* {{ citation | first = P.R. | last = Halmos | author-link = Paul Halmos | title = How to Write Mathematics | journal = Enseignements Mathématiques | doi=10.5169/seals-43857 | volume = 16 | pages = 123–152 | date = 1970 }}. Reprinted in {{ISBN|0821800558}}
Some finer points of typography are discussed in:
* {{ citation | first = Donald E. | last = Knuth | author-link = Donald Knuth | title = The TeXbook | publisher = Addison-Wesley | location = Reading, Massachusetts | date = 1984 | isbn = 0-201-13448-9 }}.
General style manuals often include advice on mathematics, including
* {{citation
 | editor = University of Chicago Press Staff
 | year = 2010
 | title = The Chicago Manual of Style
 | edition = 16th
 | url = http://www.chicagomanualofstyle.org/home.html
 | publisher = University of Chicago Press
 | isbn = 9780226104201
}}

{{Manual of Style}}

[[Category:WikiProject Mathematics]]
[[Category:Wikipedia how-to|{{PAGENAME}}]]
[[Category:Wikipedia Manual of Style (science)|Mathematics]]