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

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
radical symbol (for nth root) 1629 Albert Girard
strict inequality signs (less-than sign and greater-than sign) 1631 Thomas Harriot
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
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
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
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
aleph symbol (for cardinal numbers of transfinite sets) 1893 Georg Cantor
braces, a.k.a. curly brackets (for set notation) 1895
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
double-struck capital Z (for integer numbers set) 1930 Edmund Landau
1930s Nicolas Bourbaki
double-struck capital Q (for rational numbers set)
universal quantifier (for all) 1935 Gerhard Gentzen
empty set sign 1939 André Weil / Nicolas Bourbaki
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
integral part (a.k.a. floor) 1962 Kenneth E. Iverson
end of proof sign (a.k.a. tombstone) unknown Paul Halmos

See also

History of mathematical notation
History of the Hindu-Arabic numeral system
Table of mathematical symbols


Jeff Miller: Earliest Uses of Various Mathematical Symbols

Mathematics Encyclopedia

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