The following table lists many specialized symbols commonly used in mathematics, ordered by their introduction date.
|
Symbol
|
Name | Date of earliest use | First author to use |
|---|---|---|---|
|
+
− |
plus and minus signs | ca. 1360 (abbreviation for Latin et resembling the plus sign) | Nicole Oresme |
| 1489 (first appearance of plus and minus signs 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 | Nicolo Tartaglia | ||
|
=
|
equals sign | 1557 | Robert Recorde |
|
×
|
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 | ||
|
√ ̅
|
radical symbol (for square root) | 1637 (with the vinculum above the radicand) | René Descartes |
|
%
|
percent sign | ca. 1650 | unknown |
|
÷
|
division sign (a.k.a. obelus) | 1659 | Johann Rahn |
|
∞
|
infinity sign | 1655 | John Wallis |
|
≤
≥ |
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) | |
| 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 Arabs in 12th century) | Thomas Twining |
|
≠
|
inequality sign (not equal to) | unknown | Leonhard Euler |
|
∑
|
summation symbol | 1755 | |
|
∝
|
proportionality sign | 1768 | William Emerson |
|
∂
|
partial differential sign (a.k.a curly d or Jacobi's delta) | 1770 | Marquis de Condorcet |
|
x′
|
prime symbol (for derivative) | Joseph Louis Lagrange | |
|
≡
|
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 | |
|
∏
|
product symbol | 1812 | |
|
!
|
factorial | 1808 | Christian Kramp |
|
⊂
⊃ |
set inclusion signs (subset of, superset of) | 1817 | Joseph Gergonne |
| 1890 | Ernst Schröder | ||
|
|…|
|
absolute value notation | 1841 | Karl Weierstrass |
| determinant of a matrix | Arthur Cayley | ||
|
‖…‖
|
matrices notation | 1843 | |
|
∇
|
nabla symbol (for vector differential) | 1846 (previously used by Hamilton as a general-purpose operator sign) | William Rowan Hamilton |
|
∩
∪ |
intersection and union signs | 1888 | Giuseppe Peano |
|
∈
|
membership sign (is an element of) | 1894 | |
|
∃
|
existential quantifier (there exists) | 1897 | |
|
ℵ
|
aleph symbol (for cardinal numbers of transfinite sets) | 1893 | Georg Cantor |
|
{…}
|
braces, a.k.a. curly brackets (for set notation) | 1895 | |
|
ℕ
|
double-struck capital N (for natural numbers set) | Giuseppe Peano | |
|
·
|
middle dot (for dot product) | 1902 | J. Willard Gibbs? |
|
×
|
multiplication sign (for cross product) | ||
|
∨
|
logical disjunction (a.k.a. OR) | 1906 | Bertrand Russell |
|
(…)
|
matrices notation | 1909 | Gerhard Kowalewski |
|
[…]
|
1913 | Cuthbert Edmund Cullis | |
|
∮
|
contour integral sign | 1917 | Arnold Sommerfeld |
|
ℤ
|
double-struck capital Z (for integer numbers set) | 1930 | Edmund Landau |
| 1930s | Nicolas Bourbaki | ||
|
ℚ
|
double-struck capital Q (for rational numbers set) | ||
|
∀
|
universal quantifier (for all) | 1935 | Gerhard Gentzen |
|
∅
|
empty set sign | 1939 | André Weil / Nicolas Bourbaki |
|
ℂ
|
double-struck capital C (for complex numbers set) | Nathan Jacobson | |
|
→
|
arrow (for function notation) | 1936 (to denote images of specific elements) | Øystein Ore |
| 1940 (in the present form of f: X → Y) | Witold Hurewicz | ||
|
⌊x⌋
|
integral part (a.k.a. floor) | 1962 | Kenneth E. Iverson |
|
∎
|
end of proof sign (a.k.a. tombstone) | unknown | Paul Halmos |