# Table of mathematical symbols by introduction date

The following table lists many specialized symbols commonly used in modern mathematics, ordered by their introduction date. The table can also be ordered alphabetically by clicking on the relevant header title.

Symbol Name Date of earliest use First author to use
horizontal bar for division 14th century (approx.) Nicole Oresme[1]
+
plus sign 1360 (approx.), abbreviation for Latin et resembling the plus sign Nicole Oresme
minus sign 1489 (first appearance of minus sign, and also first appearance of plus sign in print) Johannes Widmann
radical symbol (for square root) 1525 (without the vinculum above the radicand) Christoff Rudolff
(...)
parentheses (for precedence grouping) 1544 (in handwritten notes) Michael Stifel
1556 Niccolò Tartaglia
=
equals sign 1557 Robert Recorde
.
decimal separator 1593 Christopher Clavius
×
multiplication sign 1618 William Oughtred
±
plus–minus sign 1628
proportion sign
n

radical symbol (for nth root) 1629 Albert Girard
<
>
strict inequality signs (less-than sign and greater-than sign) 1631 Thomas Harriot
xy

superscript notation (for exponentiation) 1636 (using Roman numerals as superscripts) James Hume
1637 (in the modern form) René Descartes (La Géométrie)
x

Use of the letter x for an independent variable or unknown value. See History of algebra: The symbol x. 1637[2] René Descartes (La Géométrie)
√ ̅
radical symbol (for square root) 1637 (with the vinculum above the radicand) René Descartes (La Géométrie)
%
percent sign 1650 (approx.) unknown
infinity sign 1655 John Wallis
÷
division sign (a repurposed obelus variant) 1659 Johann Rahn

unstrict inequality signs (less-than or equals to sign and greater-than or equals to sign) 1670 (with the horizontal bar over the inequality sign, rather than below it) John Wallis
1734 (with double horizontal bar below the inequality sign) Pierre Bouguer
d
differential sign 1675 Gottfried Leibniz
integral sign
:
colon (for division) 1684 (deriving from use of colon to denote fractions, dating back to 1633)
·
middle dot (for multiplication) 1698 (perhaps deriving from a much earlier use of middle dot to separate juxtaposed numbers)
division slash (a.k.a. solidus) 1718 (deriving from horizontal fraction bar, invented by Abu Bakr al-Hassar in the 12th century) Thomas Twining
inequality sign (not equal to) unknown Leonhard Euler
x
prime symbol (for derivative) 1748
Σ
summation symbol 1755
proportionality sign 1768 William Emerson
partial differential sign (a.k.a. curly d or Jacobi's delta) 1770 Marquis de Condorcet
identity sign (for congruence relation) 1801 (first appearance in print; used previously in personal writings of Gauss) Carl Friedrich Gauss
[x]
integral part (a.k.a. floor) 1808
!
factorial 1808 Christian Kramp
Π
product symbol 1812 Carl Friedrich Gauss

set inclusion signs (subset of, superset of) 1817 Joseph Gergonne
1890 Ernst Schröder
|...|
absolute value notation 1841 Karl Weierstrass
determinant of a matrix 1841 Arthur Cayley
‖...‖
matrix notation 1843[3]
nabla symbol (for vector differential) 1846 (previously used by Hamilton as a general-purpose operator sign) William Rowan Hamilton

intersection

union
1888 Giuseppe Peano
aleph symbol (for transfinite cardinal numbers) 1893 Georg Cantor
membership sign (is an element of) 1894 Giuseppe Peano
O
Big O Notation 1894 Paul Bachmann
{...}
braces, a.k.a. curly brackets (for set notation) 1895 Georg Cantor
${\displaystyle \mathbb {N} }$
Blackboard bold capital N (for natural numbers set) 1895 Giuseppe Peano
${\displaystyle \mathbb {Q} }$
Blackboard bold capital Q (for rational numbers set)
existential quantifier (there exists) 1897
·
middle dot (for dot product) 1902 J. Willard Gibbs
×
multiplication sign (for cross product)
logical disjunction (a.k.a. OR) 1906 Bertrand Russell
(...)
matrix notation 1909[3] Maxime Bôcher
[...]

1909[3] Gerhard Kowalewski
contour integral sign 1917 Arnold Sommerfeld
${\displaystyle \mathbb {Z} }$
Blackboard bold capital Z (for integer numbers set) 1930 Edmund Landau
universal quantifier (for all) 1935 Gerhard Gentzen
arrow (for function notation) 1936 (to denote images of specific elements) Øystein Ore
1940 (in the present form of f: XY) Witold Hurewicz
empty set sign 1939 André Weil / Nicolas Bourbaki[4]
${\displaystyle \mathbb {C} }$
Blackboard bold capital C (for complex numbers set) 1939 Nathan Jacobson
end of proof sign (a.k.a. tombstone) 1950[5] Paul Halmos
x
x
greatest integer ≤x (a.k.a. floor)

smallest integer ≥x (a.k.a. ceiling)
1962[6] Kenneth E. Iverson