Table of mathematical symbols by introduction date

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{{Use dmy dates|date=August 2023}}

{{Contains special characters

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

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class="wikitable sortable"
Symbol

! Name

! Date of earliest use

! First author to use

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| horizontal bar for division

| 14th century (approx.)

| Nicole Oresme{{Cite book |last=Cajori |first=Florian |title=A History of Mathematical Notations |publisher=Dover Publications |year=1993 |location=Mineola, New York}}

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+

| plus sign

| 1360 (approx.), abbreviation for Latin et resembling the plus sign

| Nicole Oresme

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| minus sign

| 1489 (first appearance of minus sign, and also first appearance of plus sign in print)

| Johannes Widmann

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| radical symbol (for square root)

| 1525 (without the vinculum above the radicand)

| Christoff Rudolff

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(...)

| rowspan=2| parentheses (for precedence grouping)

| 1544 (in handwritten notes)

| Michael Stifel

1556

| Niccolò Tartaglia

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=

| equals sign

| 1557

| Robert Recorde

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.

| decimal separator

| 1593

| Christopher Clavius

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×

| multiplication sign

| 1618

| rowspan=3| William Oughtred

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±

| plus–minus sign

| rowspan=2| 1628

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| proportion sign

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n
 

| radical symbol (for nth root)

| 1629

| Albert Girard

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<
>

| strict inequality signs (less-than sign and greater-than sign)

| 1631

| Thomas Harriot

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xy
 

| rowspan=2| superscript notation (for exponentiation)

| 1636 (using Roman numerals as superscripts)

| James Hume

style=border-bottom:none| 1637 (in the modern form)

| René Descartes (La Géométrie)

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x
 

| Use of the letter x for an independent variable or unknown value. See History of algebra: The symbol x.

| 1637{{Citation

| first=Carl B.

| last=Boyer

| author-link=Carl Benjamin Boyer

| title=A History of Mathematics

| edition=Second

| publisher=John Wiley & Sons, Inc.

| year=1991

| isbn=978-0-471-54397-8

| url=https://archive.org/details/historyofmathema00boye

}}

| René Descartes (La Géométrie)

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√ ̅

| radical symbol (for square root)

| style=border-bottom:none| 1637 (with the vinculum above the radicand)

| René Descartes (La Géométrie)

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%

| percent sign

| 1650 (approx.)

| unknown

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| infinity sign

| 1655

| John Wallis

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÷

| division sign (a repurposed obelus variant)

| 1659

| Johann Rahn

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| rowspan=2| 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

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d

| differential sign

| rowspan=2| 1675

| rowspan=4| Gottfried Leibniz

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| integral sign

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:

| colon (for division)

| 1684 (deriving from use of colon to denote fractions, dating back to 1633)

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·

| middle dot (for multiplication)

| 1698 (perhaps deriving from a much earlier use of middle dot to separate juxtaposed numbers)

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| division slash (a.k.a. solidus)

| 1718 (deriving from horizontal fraction bar, invented by Abu Bakr al-Hassar in the 12th century)

| Thomas Twining

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| inequality sign (not equal to)

| unknown

| rowspan=3| Leonhard Euler

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x{{prime}}

| prime symbol (for derivative)

| 1748

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Σ

| summation symbol

| 1755

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| proportionality sign

| 1768

| William Emerson

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| partial differential sign (a.k.a. curly d or Jacobi's delta)

| 1770

| Marquis de Condorcet

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| identity sign (for congruence relation)

| 1801 (first appearance in print; used previously in personal writings of Gauss)

| rowspan=2| Carl Friedrich Gauss

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[x]

| integral part (a.k.a. floor)

| 1808

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!

| factorial

| 1808

| Christian Kramp

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Π

| product symbol

| 1812

| Carl Friedrich Gauss

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| rowspan=2| set inclusion signs (subset of, superset of)

| 1817

| Joseph Gergonne

1890

| Ernst Schröder

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|...|

| absolute value notation

| 1841

| Karl Weierstrass

determinant of a matrix

| 1841

| rowspan=2| Arthur Cayley

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‖...‖

| matrix notation

| 1843{{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}}

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| nabla symbol (for vector differential)

| 1846 (previously used by Hamilton as a general-purpose operator sign)

| William Rowan Hamilton

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| intersection

union

| 1888

| Giuseppe Peano

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| aleph symbol (for transfinite cardinal numbers)

| 1893

| Georg Cantor

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| membership sign (is an element of)

| 1894

| Giuseppe Peano

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O

| Big O Notation

| 1894

| Paul Bachmann

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{...}

| braces, a.k.a. curly brackets (for set notation)

| 1895

| Georg Cantor

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\mathbb{N}

| Blackboard bold capital N (for natural numbers set)

| rowspan=2| 1895

| rowspan=3|Giuseppe Peano

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\mathbb{Q}

| Blackboard bold capital Q (for rational numbers set)

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| existential quantifier (there exists)

| 1897

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·

| middle dot (for dot product)

| rowspan=2| 1902

| rowspan=2| J. Willard Gibbs

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×

| multiplication sign (for cross product)

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| logical disjunction (a.k.a. OR)

| 1906

| Bertrand Russell

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(...)

| rowspan=2| matrix notation

| 1909

| Maxime Bôcher

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[...]
 

| 1909

| Gerhard Kowalewski

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| contour integral sign

| 1917

| Arnold Sommerfeld

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\mathbb{Z}

| Blackboard bold capital Z (for integer numbers set)

| 1930

| Edmund Landau

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| universal quantifier (for all)

| 1935

| Gerhard Gentzen

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| rowspan=2| arrow (for function notation)

| 1936 (to denote images of specific elements)

| Øystein Ore

1940 (in the present form of f: XY)

| Witold Hurewicz

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| empty set sign

| 1939

| André Weil / Nicolas Bourbaki{{citation|title=The Apprenticeship of a Mathematician|first=André|last=Weil|author-link=André Weil|publisher=Springer|year=1992|isbn=9783764326500|page=114|url=https://books.google.com/books?id=73REHmJ9JNUC&pg=PA114}}.

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\mathbb{C}

| Blackboard bold capital C (for complex numbers set)

| 1939

| Nathan Jacobson

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| end of proof sign (a.k.a. tombstone)

| 1950{{Cite book

| last = Halmos

| first = Paul

| 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

}}

| Paul Halmos

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x
x

| greatest integer ≤{{thin space}}x (a.k.a. floor)

smallest integer ≥{{thin space}}x (a.k.a. ceiling)

| 1962{{citation|author=Kenneth E. Iverson|author-link=Kenneth E. Iverson|title=A Programming Language|date=1962|publisher=Wiley|url=http://www.jsoftware.com/papers/APL.htm|accessdate=20 April 2016}}

| Kenneth E. Iverson

See also

Sources

{{Reflist}}