Mathematical notation consists of using symbols for representing operations, unspecified numbers, relations, and any other mathematical objects and assembling them into expressions and formulas.
Mathematical notation is widely used in mathematics, science, and engineering for representing complex concepts and properties in a concise, unambiguous, and accurate way.
is the quantitative representation in mathematical notation of mass–energy equivalence.
[1] Mathematical notation was first introduced by François Viète at the end of the 16th century and largely expanded during the 17th and 18th centuries by René Descartes, Isaac Newton, Gottfried Wilhelm Leibniz, and overall Leonhard Euler.
They play a similar role as words in natural languages.
, Cyrillic Ш, and Hiragana よ. Uppercase and lowercase letters are considered as different symbols.
[2] In order to have more symbols, and for allowing related mathematical objects to be represented by related symbols, diacritics, subscripts and superscripts are often used.
may denote the Fourier transform of the derivative of a function called
Some symbols are similar to Latin or Greek letters, some are obtained by deforming letters, some are traditional typographic symbols, but many have been specially designed for mathematics.
An expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
In general, an expression denotes or names a mathematical object, and plays therefore in the language of mathematics the role of a noun phrase in the natural language.
Although the resulting expression contains the operators of division, subtraction and exponentiation, it cannot be evaluated further because a and b denote unspecified numbers.
It is believed that a notation to represent numbers was first developed at least 50,000 years ago.
[3] Early mathematical ideas such as finger counting[4] have also been represented by collections of rocks, sticks, bone, clay, stone, wood carvings, and knotted ropes.
The tally stick is a way of counting dating back to the Upper Paleolithic.
The Census Quipu of the Andes and the Ishango Bone from Africa both used the tally mark method of accounting for numerical concepts.
It was used as a placeholder by the Babylonians and Greek Egyptians, and then as an integer by the Mayans, Indians and Arabs (see the history of zero).
Until the 16th century, mathematics was essentially rhetorical, in the sense that everything but explicit numbers was expressed in words.
The first systematic use of formulas, and, in particular the use of symbols (variables) for unspecified numbers is generally attributed to François Viète (16th century).
Later, René Descartes (17th century) introduced the modern notation for variables and equations; in particular, the use of
The 18th and 19th centuries saw the standardization of mathematical notation as used today.
[6] Since then many new notations have been introduced, often specific to a particular area of mathematics.
One of the reasons is that, in mathematical notation, the symbols are often arranged in two-dimensional figures, such as in: TeX is a mathematically oriented typesetting system that was created in 1978 by Donald Knuth.
It is widely used in mathematics, through its extension called LaTeX, and is a de facto standard.
More recently, another approach for mathematical typesetting is provided by MathML.
In addition to Arabic notation, mathematics also makes use of Greek letters to denote a wide variety of mathematical objects and variables.
On some occasions, certain Hebrew letters are also used (such as in the context of infinite cardinals).
Some mathematical notations are mostly diagrammatic, and so are almost entirely script independent.
Examples are Penrose graphical notation and Coxeter–Dynkin diagrams.