Multiplication sign

The multiplication sign (×), also known as the times sign or the dimension sign, is a mathematical symbol used to denote the operation of multiplication, which results in a product. While similar to a lowercase X (x), the form is properly a four-fold rotationally symmetric saltire.

The symbol is also used in botany, in botanical hybrid names and the heavy goods vehicle industry, to calculate the amount of powered wheels.

History
The earliest known use of the × symbol to represent multiplication appears in an anonymous appendix to the 1618 edition of John Napier's Mirifici Logarithmorum Canonis Descriptio. This appendix has been attributed to William Oughtred, who used the same symbol in his 1631 algebra text, Clavis Mathematicae, stating:"Multiplication of species [i.e. unknowns] connects both proposed magnitudes with the symbol 'in' or ×: or ordinarily without the symbol if the magnitudes be denoted with one letter."

An earlier use of the symbol from the 1500s appears in The Ground of Arts, where it is used in the context of a mental arithmetic method for computing simple, single-digit multiplications. Rob Eastaway theorizes that this may have been the original influence for John Napier's more general usage.

Two even earlier uses of a ✕ notation have been identified, but do not stand critical examination.

Uses
In mathematics, the symbol × has a number of uses, including
 * Multiplication of two numbers, where it is read as "times" or "multiplied by"
 * Cross product of two vectors, where it is usually read as "cross"
 * Cartesian product of two sets, where it is usually read as "cross"
 * Geometric dimension of an object, such as noting that a room is 10 feet × 12 feet in area, where it is usually read as "by" (e.g., "10 feet by 12 feet")
 * Screen resolution in pixels, such as 1920 pixels across × 1080 pixels down. Read as "by".
 * Dimensions of a matrix, where it is usually read as "by"
 * A statistical interaction between two explanatory variables, where it is usually read as "by"

In biology, the multiplication sign is used in a botanical hybrid name, for instance Ceanothus papillosus × impressus (a hybrid between C. papillosus and C. impressus) or Crocosmia × crocosmiiflora (a hybrid between two other species of Crocosmia). However, the communication of these hybrid names with a Latin letter "x" is common, when the actual "×" symbol is not readily available.

The multiplication sign is also used by historians for an event between two dates. When employed between two dates – for example 1225 and 1232 –  the expression "1225×1232" means "no earlier than 1225 and no later than 1232".

A monadic × symbol is used by the APL programming language to denote the sign function.

Similar notations
The lower-case Latin letter x is sometimes used in place of the multiplication sign. This is considered incorrect in mathematical writing.

In algebraic notation, widely used in mathematics, a multiplication symbol is usually omitted wherever it would not cause confusion: "$a$ multiplied by $b$" can be written as $ab$ or $a b$.

Other symbols can also be used to denote multiplication, often to reduce confusion between the multiplication sign × and the common variable $x$. In some countries, such as Germany, the primary symbol for multiplication is the "dot operator" ⋅ (as in $a⋅b$). This symbol is also used in compound units of measurement, e.g., N⋅m (see International System of Units). In algebra, it is a notation to resolve ambiguity (for instance, "b times 2" may be written as $b⋅2$, to avoid being confused with a value called $b_{2}$). This notation is used wherever multiplication should be written explicitly, such as in "$ab = a⋅2$ for $b = 2$"; this usage is also seen in English-language texts. In some languages, the use of full stop as a multiplication symbol, such as $a.b$, is common when the symbol for decimal point is comma.

Historically, computer language syntax was restricted to the ASCII character set, and the asterisk * became the de facto symbol for the multiplication operator. This selection is reflected in the numeric keypad on English-language keyboards, where the arithmetic operations of addition, subtraction, multiplication and division are represented by the keys +, -, * and /, respectively.

Unicode and HTML entities
Other variants and related characters:
 * (a zero-width space indicating multiplication)
 * (the interpunct, may be easier to type than the dot operator)
 * (intended to explicitly denote the cross product of two vectors)
 * (intended to explicitly denote the cross product of two vectors)
 * (intended to explicitly denote the cross product of two vectors)
 * (intended to explicitly denote the cross product of two vectors)
 * (intended to explicitly denote the cross product of two vectors)
 * (intended to explicitly denote the cross product of two vectors)
 * (intended to explicitly denote the cross product of two vectors)