Wikipedia:Manual of Style/Mathematics

Wikipedia:Manual of Style/Mathematics

This subpage of the Manual of Style contains guidelines for writing and editing clear, encyclopedic, attractive, and interesting articles on mathematics. 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.


Suggested structure of a mathematics article


Article introduction


In general, the lead sentence should include the article title in bold along with alternate names, establish context by linking to a more general subject, and informally define or describe the subject. For example:

Topology (from the Greek τόπος, “place”, and λόγος, “study”) is a major area of mathematics concerned with spatial properties that are preserved under continuous deformations of objects, for example, deformations that involve stretching, but no tearing or gluing.


The lead section should include, where appropriate:


Article body

If you want to introduce some notation, it should be in its own section. You should remember that not everyone understands that, for example, x^n or x**n mean xn; so it is good to use standard notation if you can. If you need to use non-standard notations, or if you introduce new notations, define them in your article.

There should be an exact definition, in mathematical terms; often in a Definition(s) section, for example:


Using the term formal definition may seem rather empty to a mathematician (a formal definition is a mathematician's definition, as a formal proof is just a proof); but it may help to flag where the actual definition is to be found, after some sections of motivation. (Cf. rigged Hilbert space.)

Some representative examples would be nice to have, in a separate section, which could serve to both expand on the definition, and also provide some context as to why one might want to use the defined entity. You might also want to list non-examples—things which come close to satisfying the definition but do not—in order to refine the reader's intuition more precisely. It is important to remember when composing examples, however, that the purpose of an encyclopedia is to inform rather than instruct (see WP:NOT#TEXTBOOK). Examples should therefore strive to maintain an encyclopedic tone, and should be informative rather than merely instructional.




Concluding matters




Writing style in mathematics


Instead, one could write this:
  • A group G may be decomposed into cosets as follows.
  • Let H be the corresponding subgroup of G. Then H must be finite.
    • "Note that…" / "It should be noted that…"
    • "It must be mentioned that…" / "It must be emphasized that…"
    • "Consider that…"
    • "We see that…"
  • Multiplying M by u = vv0, ...
Instead, write:
  • Avoid, as far as possible, phrases such as
    • "It is easily seen that ..."
    • "Clearly ..."
    • "Obviously ..."
  • "It follows directly from this definition that ..."
  • "By a straightforward, if lengthy, algebraic calculation, ..."
  • The plural of formula is either formulae or formulas. Both are acceptable, but articles should be consistent with themselves. If an article is consistent, then editors should not change the article from one style to another.

Mathematical conventions




Terminology conventions

Natural numbers


Notational conventions

  • The semidirect product of groups K and Q should be written K ×φ Q or Q ×φ K where K is the normal subgroup and φ : Q → Aut(K) is the homomorphism defining the product. The semidirect product may also be written K Q or Q K (with the bar on the side of the non-normal subgroup) with or without the φ.
    • If the bar notation is used it should be entered as {{unicode|&#x22C9;}} () or {{unicode|&#x22CA;}} () for maximum portability.
  • Subset is denoted by \subseteq, proper subset by \subsetneq. The symbol \subset 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, A\subset B might be given as the hypothesis of a theorem whose conclusion is obviously true in the case that A = B). All other uses of the \subset symbol should be explicitly explained in the text.
  • For a matrix transpose, use superscript non-italic capital letter T: XT, XT or X^\mathrm T\,, and not XT, XT, X^T\, or X^\top.
  • In a lattice, infima are written as a ∧ b or as a product ab, suprema as a ∨ b or as a sum 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.


This is an encyclopedia, not a collection of mathematical texts; but we often want to include proofs, as a way of really exposing the meaning of some theorem, definition, etc. A downside of including proofs is that they may interrupt the flow of the article, whose goal is usually expository. Use your judgement; 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.





Source code should always use syntax highlighting. For example this markup:[1]

<source lang="Haskell">
  primes = sieve [2..]

generates the following:

  primes = sieve [2..]

Including literature and references




Typesetting of mathematical formulae

One may set formulae using LaTeX or, for simple formulae, using HTML; both are acceptable and widely used, though there are issues, as discussed below. However, for section headings, use HTML only, as LaTeX markup does not appear in the table of contents.

Using LaTeX markup

Wikipedia allows editors to typeset mathematical formulas in (a subset of) LaTeX markup (see also TeX); the formulae are normally translated into PNG images, but may be rendered as HTML or MathML, depending on user preferences. For more details on this, see meta:Help:Formula.

The LaTeX formulae can be displayed in-line (like this: \mathbf{x}\in\mathbb{R}^2), as well as on their own line:


When displaying formulae on their own line, one should indent the line with one or more colons (:); the above was typeset from

:<math>\int_0^\infty e^{-x^2}\,dx.</math>


Having LaTeX-based formulae in-line which render as PNG under the default user settings, as above, is generally discouraged, for the following reasons.

  • The font size is larger than that of the surrounding text on some browsers, making text containing in-line formulae hard to read.
  • The download speed of a page is negatively affected if it contains many images.
  • HTML (as described below) is adequate for most simple in-line formulae and better for text-only browsers.

If an in-line formula needs to be typeset in LaTeX, often better formatting can be achieved with the \textstyle LaTeX command. By default, LaTeX code is rendered as if it were a displayed equation (not in-line), and this can frequently be too big. For example, the formula <math>\sum_{n=1}^\infty 1/n^2 = \pi^2/6 </math>, which displays as \sum_{n=1}^\infty 1/n^2 = \pi^2/6, is too large to be used in-line. \textstyle generates a smaller summation sign and moves the limits on the sum to the right side of the summation sign. The code for this is <math>\textstyle\sum_{n=1}^\infty 1/n^2 = \pi^2/6</math>, and it renders as the much more aesthetic \textstyle\sum_{n=1}^\infty 1/n^2 = \pi^2/6. However, the default font for \textstyle is larger than the surrounding text on many browsers.

If you plan on editing LaTeX formulae, it is helpful if you leave your preference settings (link in the upper right corner of this page, underneath your user name) in the "rendering math" section at the default "HTML if very simple or else PNG"; that way, you'll see the page like most users will see it.

Very simple formulae

If you enter a very simple formula using the mathematical notations like <math>L^p</math> this will (in the default used by most users) not be displayed using a PNG image but using HTML, like this: Lp. This is different from typesetting it as ''L''<sup>''p''</sup>. Compare:

LaTeX rendered as HTML: Lp 
Regular HTML: Lp .

Either form is acceptable, but do not change one form to the other in other people's writing. They are likely to get annoyed since this seems to be a highly emotional issue. Changing to make an entire article consistent is acceptable.

However, still try to avoid in-line PNG images. Even if you use <math>L^p</math> throughout the article, use ''L''<sup>&infin;</sup> to get L rather than using the LaTeX-based <math>L^\infty</math> to get L^\infty, which doesn't always look good.

Forcing output to be an image

If you want to force a formula to be displayed as an image, put, for example, a \, (one quarter space in LaTeX) at the end of the formula. This should usually only be done for formulae displayed on their own line. Adding \displaystyle at the beginning of the formula has the same effect.

Alt text


Using HTML

The following sections cover the way of presenting simple in-line formulae in HTML, instead of using LaTeX.


Font formatting

''x'' = (''y''<sup>2</sup> + 2)

will result in:

x = (y2 + 2) .


{{math|''x'' {{=}} (''y''<sup>2</sup> + 2)}}

will result in:

x = (y2 + 2) .

To start with, we generally use italic text for variables (but never for numbers or symbols). Most editors prefer to use ''x'' in the edit box to refer to the variable x. Some prefer using the HTML "variable" tag, <var>, since it provides semantic meaning to the text contained within. Which method you choose is entirely up to you, but in order to keep with convention, we recommend the wiki markup method of enclosing the variable name between repeated single quotes. Thus we write:


which results in:

x = (y2 + 2) .

While italicizing variables, things like parentheses, digits, equal and plus signs should be kept outside of the double-quoted sections. In particular, do not use double quotes as if they are <math> tags; they merely denote italics. Descriptive subscripts should not be in italics, because they are not variables. For example, mfoo is the mass of a foo. SI units are never italicized: x = 5 cm.




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

A = {x : x > 0 }

would be written:

Greek letters

Some editors italicize lower-case Greek letters when they are variables (in line with the general advice to italicize variables): the example expression λ + y = πr2 would then be typeset as ''&lambda;'' + ''y'' = ''&pi;r''<sup>2</sup>. However the examples in the other sections of this guide do not specify italic formatting of Greek letters.

Common sets of numbers

Commonly used sets of numbers are typeset in boldface, as in the set of real numbers R; see blackboard bold for the types in use. Again, typically we use wiki markup: three single quotes (''') rather than the HTML <b> tag for making text bold.

Superscripts and subscripts





Moreover, the TeX engine used on Wikipedia may format simple superscripts using <sup>...</sup> depending on user preferences. Thus, instead of the image x^2\,, many users see x2. Formulae formatted without using TeX should use the same syntax to maintain the same appearance.

Special symbols

There is a table of mathematical symbols and a list at Wikipedia:Mathematical symbols that may be useful when editing mathematics articles. There are two caveats to keep in mind, however.


Less-than sign


''x'' &lt; 3,


''x'' < 3.

Multiplication sign


However, when explaining, for a general audience (not just mathematicians), the formula or giving examples of its application, it is prudent to use the multiplication sign: "×", coded as &times; in HTML. Do not use the letter "x" as a substitute for "×". For example:

  • When dividing 26 by 4, 6 is the quotient and 2 is the remainder, because 26 = 6 × 4 + 2.
  • −42 = 9 × (−5) + 3

Another alternative to the &times; markup is &middot;, which will produce a center dot: " · ".

Minus sign

The typographically correct representation of the minus sign "−" is different from the hyphen "-" and en-dash "–". To really render a minus sign, use the "minus" character "−" (reachable via selecting "Math and logic" in the "Choose character subset" drop down list below the edit box), or use the "&minus;" entity.

Square brackets

Square brackets have two problems; they can occasionally cause problems with wiki markup, and editors sometimes 'fix' the brackets in asymmetrical intervals to make them symmetrical. A general solution to problems like this is to use the nowiki tag as in for example <nowiki>]<nowiki> to show ] is special.




(−π, π].


Function symbol

There is a special Unicode function symbol for functions, U+0192, "LATIN SMALL LETTER F WITH HOOK = script f = Florin currency symbol (Netherlands) = function symbol"[2], which looks like ƒ. As of December 2010, this character is not interpreted correctly by screen readers such as JAWS and NonVisual Desktop Access[3]. An italicized letter f should be used instead.

Explanation of symbols in formulae

A list such as:

Example 1: The foocity is given by

\mathbf{F} = \mathbf{b} \times a\mathbf{r},
  • b is the barness vector,
  • a is the bazness coefficient,
  • r is the quuxance vector.

has no reason to be bulleted, and it should be written as prose:

Example 2: The foocity is given by



Punctuation after formulae



If the formula is written in LaTeX, that is, surrounded by the <math> and </math> tags, then the punctuation needs to also be inside the tags, because otherwise it can be displayed on a new line if the formula is at the edge of the browser window. Alternatively—the 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 formula can be enclosed using the {{nowrap}} template, as in This shows that {{nowrap|<math>\tfrac{1}{2} = 0.5</math>.}}.

Choice of type style

In mathematics notation, functions that have multi-letter names should always be in an upright font. The most well-known functions—trigonometric functions, logarithms, etc.—have no parentheses. For example:

\sin x \,\!   (correct typeset from <math>\sin x \,\!</math>)

but not

sin x \,\!   (incorrect—typeset from <math>sin x \,\!</math>).

Some operator (function) names do not have a pre-defined abbreviation; for these we may use \operatorname:

\operatorname{Tr}(M) \,\!   (typeset from <math>\operatorname{Tr}(M) \,\!</math>).


 x_\text{this one} = y_\text{that one} \,\!   (correct—typeset from <math> x_\text{this one} = y_\text{that one} \,\!</math>),


\sum_{i=1}^n { y_i^2 }\!   (correct—typeset from <math>\sum_{i=1}^n { y_i^2 }\!</math>),

but not


On the other hand, for the differential, imaginary unit, and Euler's number, Wikipedia articles usually use an italic font, so one writes

\int_0^\pi \sin x \, dx , \,\!   (typeset from <math>\int_0^\pi \sin x \, dx , \,\!</math>—note the thin space (\,) before dx),
x+iy, \,\!   (typeset from <math>x+iy, \,\!</math>), and
e^{i\theta} . \,\!   (typeset from <math>e^{i\theta} . \,\!</math>).

Some authors prefer to use an upright (Roman) font for dx, and Roman boldface for i. Both forms are correct; what is most important is consistency within an article, with deference to previous editors. It is considered inappropriate for an editor to go through articles doing mass changes from one style to another. This is much the same principle as the guidelines in the Manual of Style for the colour/color spelling choice, etc.

Blackboard bold


An article may use either boldface type or blackboard bold for objects traditionally printed in boldface. As with all such choices, the article should be consistent. Editors should not change articles from one choice of typeface to another except for consistency.


In mathematics articles, fractions should always be written either with a horizontal fraction bar (as in \textstyle\frac{1}{2}), or with a forward slash and with the baseline of the numbers aligned with the baseline of the surrounding text (as in 1/2). The use of {{frac}} (such as 12) is discouraged in mathematics articles. The use of Unicode symbols (such as ½) is discouraged entirely, for accessibility reasons among others. Metric units are given in decimal fractions (e.g., 5.2 cm); non-metric units can either type of fraction, but the fraction style should be consistent throughout the article.

Graphs and diagrams

The angle CAB is α.
The length of CA is b.


Recent geometry books tend to use an italic serif font in diagrams as in A for a point. This allows easy use in LaTeX markup. However older books tend to use upright letters as in A 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.

See also

Help for those writing a formula

General information

  • Wikipedia:WikiProject Mathematics
  • Wikipedia:Scientific citation guidelines—advice on providing references for mathematical and scientific articles


  2. ^ Latin Extended-B, [2]
  3. ^ Wikipedia talk:WikiProject Mathematics/Archive 68#ƒ or f?
  4. ^ This style, adopted by Wikipedia, is shared by Higham (1998), the Chicago Manual of Style, and many mathematics journals.

Further reading

A style guide specifically written for mathematics:

  • Higham, Nicholas J. (1998), Handbook of Writing for the Mathematical Sciences (second ed.), SIAM, ISBN 0-89871-420-6 .

More style guidance:

Some finer points of typography are discussed in:

  • Knuth, Donald E. (1984), The TeXbook, Reading, Massachusetts: Addison-Wesley, ISBN 0-201-13448-9 .

General style manuals often include advice on mathematics, including

Wikimedia Foundation. 2010.

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