Table of mathematical symbols by introduction date


The following table lists many specialized symbols commonly used in mathematics, ordered by their introduction date.


SymbolNameDate of earliest useFirst author to use
+
plus sign1360, abbreviation for Latin et resembling the plus signNicole Oresme
−
minus sign1489 Johannes Widmann
√
radical symbol 1525 Christoff Rudolff
parentheses 1544 Michael Stifel
parentheses 1556Niccolò Tartaglia
=
equals sign1557Robert Recorde
.
decimal separator1595Bartholomaeus Pitiscus
×
multiplication sign1618William Oughtred
±
plus-minus sign1628William Oughtred
∷
proportion sign1628William Oughtred
n√
radical symbol 1629Albert Girard
<
>
strict inequality signs 1631Thomas Harriot
xy
superscript notation 1636 James Hume
xy
superscript notation 1637 René Descartes
√ ̅
radical symbol 1637 René Descartes
%
percent sign1650 unknown
∞
infinity sign1655John Wallis
÷
division sign 1659Johann Rahn
≤

≥
unstrict inequality signs 1670 John Wallis
≤

≥
unstrict inequality signs 1734 Pierre Bouguer
d
differential sign1675Gottfried Leibniz
∫
integral sign1675Gottfried Leibniz
:
colon 1684 Gottfried Leibniz
·
middle dot 1698 Gottfried Leibniz
⁄
division slash 1718 Thomas Twining
≠
inequality sign unknownLeonhard Euler
x′
prime symbol 1748Leonhard Euler
∑
summation symbol1755Leonhard Euler
∝
proportionality sign1768William Emerson
∂
partial differential sign 1770Marquis de Condorcet
≡
identity sign 1801 Carl Friedrich Gauss
integral part 1808Carl Friedrich Gauss
!
factorial1808Christian Kramp
∏
product symbol1812Carl Friedrich Gauss
⊂
⊃
set inclusion signs 1817Joseph Gergonne
⊂
⊃
set inclusion signs 1890Ernst Schröder
absolute value notation1841Karl Weierstrass
determinant of a matrix1841Arthur Cayley
‖...‖
matrix notation1843Arthur Cayley
∇
nabla symbol 1846 William Rowan Hamilton
∩
∪
intersection

union		1888Giuseppe Peano
ℵ
aleph symbol 1893Georg Cantor
∈
membership sign 1894Giuseppe Peano
braces, a.k.a. curly brackets 1895Georg Cantor
ℕ
Blackboard bold capital N 1895Giuseppe Peano
ℚ
Blackboard bold capital Q 1895Giuseppe Peano
∃
existential quantifier 1897Giuseppe Peano
·
middle dot 1902J. Willard Gibbs
×
multiplication sign 1902J. Willard Gibbs
∨
logical disjunction 1906Bertrand Russell
matrix notation1909Maxime Bôcher

matrix notation1909Gerhard Kowalewski
∮
contour integral sign1917Arnold Sommerfeld
ℤ
Blackboard bold capital Z 1930Edmund Landau
∀
universal quantifier 1935Gerhard Gentzen
→
arrow 1936 Øystein Ore
→
arrow 1940 Witold Hurewicz
∅
empty set sign1939André Weil / Nicolas Bourbaki
ℂ
Blackboard bold capital C 1939Nathan Jacobson
∎
end of proof sign 1950Paul Halmos
⌊x⌋
⌈x⌉
greatest integer ≤ x

smallest integer ≥ x 		1962Kenneth E. Iverson