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 sign | ca. 1360 (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 |
× | 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 the 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) | 1748 | Leonhard Euler |
≡ | 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 |
‖…‖ | matrix notation | 1843[1] |
∇ | nabla symbol (for vector differential) | 1846 (previously used by Hamilton as a general-purpose operator sign) | William Rowan Hamilton |
∩
∪ | intersection
union | 1888 | Giuseppe Peano |
∈ | membership sign (is an element of) | 1894 |
∃ | existential quantifier (there exists) | 1897 |
ℵ | aleph symbol (for transfinite cardinal numbers) | 1893 | Georg Cantor |
{…} | braces, a.k.a. curly brackets (for set notation) | 1895 |
ℕ | Blackboard bold 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 |
(…) | matrix notation | 1909[1] | Maxime Bôcher |
[…]
| 1909[1] | Gerhard Kowalewski |
∮ | contour integral sign | 1917 | Arnold Sommerfeld |
ℤ | Blackboard bold capital Z (for integer numbers set) | 1930 | Edmund Landau |
ℚ | Blackboard bold capital Q (for rational numbers set) | 1895 | Giuseppe Peano |
∀ | universal quantifier (for all) | 1935 | Gerhard Gentzen |
∅ | empty set sign | 1939 | André Weil / Nicolas Bourbaki[2] |
ℂ | Blackboard bold capital C (for complex numbers set) | 1939 | 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 |
∎ | end of proof sign (a.k.a. tombstone) | 1950[3] | Paul Halmos |
⌊x⌋
⌈x⌉ | greatest integer ≤ x (a.k.a. floor)
smallest integer ≥ x (a.k.a. ceiling) | 1962[4] | Kenneth E. Iverson |
1. ^1 2 {{cite web|title=Earliest Uses of Symbols for Matrices and Vectors|url=http://jeff560.tripod.com/matrices.html|website=jeff560.tripod.com|accessdate=18 December 2016}}
2. ^{{citation|title=The Apprenticeship of a Mathematician|first=André|last=Weil|authorlink=André Weil|publisher=Springer|year=1992|isbn=9783764326500|page=114|url=https://books.google.com/books?id=73REHmJ9JNUC&pg=PA114}}.
3. ^{{Cite book | last = Halmos | first = Paul | authorlink = | year = 1950 | title = Measure Theory | publisher = Van Nostrand | location = New York | quote = The symbol ∎ is used throughout the entire book in place of such phrases as "Q.E.D." or "This completes the proof of the theorem" to signal the end of a proof. | pages = vi}}
4. ^{{citation|author=Kenneth E. Iverson|title=A Programming Language|date=1962|publisher=Wiley|url=http://www.jsoftware.com/papers/APL.htm|accessdate=20 April 2016}}