View source for Table of mathematical symbols by introduction date

{{Short description|None}}
{{Use dmy dates|date=August 2023}}
{{Contains special characters
| special    = [[Unicode]] [[mathematical symbols]]
| fix        = Help:Special characters
| characters = [[mathematical symbols]]
}}
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.}}
{{clear}}
{| class="wikitable sortable"
|-
! Symbol
! Name
! Date of earliest use
! First author to use
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">—</div>
| [[obelus|horizontal bar for division]]
| 14th century (approx.)
| [[Nicole Oresme]]<ref>{{Cite book |last=Cajori |first=Florian |title=A History of Mathematical Notations |publisher=Dover Publications |year=1993 |location=Mineola, New York}}</ref>
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">+</div>
| [[plus and minus signs|plus sign]]
| 1360 (approx.), abbreviation for Latin ''et'' resembling the plus sign
| [[Nicole Oresme]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">−</div>
| [[plus and minus signs|minus sign]]
| 1489 (first appearance of minus sign, and also first appearance of plus sign in print)
| [[Johannes Widmann]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">√</div> 
| radical symbol (for [[square root]])
| 1525 (without the [[vinculum (symbol)|vinculum]] above the [[radicand]])
| [[Christoff Rudolff]]
|-
| rowspan=2 bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">(...)</div>
| rowspan=2| [[Bracket#Parentheses|parentheses]] (for precedence grouping)
| 1544 (in handwritten notes)
| [[Michael Stifel]]
|-
| 1556
| [[Niccolò Fontana Tartaglia|Niccolò Tartaglia]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">=</div> 
| [[equals sign]]
| 1557
| [[Robert Recorde]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">.</div> 
| [[decimal separator]]
| 1593
| [[Christopher Clavius]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">×</div> 
| [[multiplication sign]]
| 1618
| rowspan=3| [[William Oughtred]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">±</div> 
| [[plus–minus sign]]
| rowspan=2| 1628
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">∷</div> 
| [[proportion sign]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;"><sup>''n''</sup>√<br />&nbsp;</div> 
| radical symbol (for [[nth root|''n''th root]])
| 1629
| [[Albert Girard]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;"><<br />></div>
| [[strict inequality]] signs (''less-than sign'' and ''greater-than sign'')
| 1631
| [[Thomas Harriot]]
|-
| rowspan=2 bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">''x<sup>y</sup>''<br />&nbsp;</div> 
| rowspan=2| [[superscript]] notation (for [[exponentiation]])
| 1636 (using [[Roman numerals]] as superscripts)
| [[James Hume (mathematician)|James Hume]]
|-
| style=border-bottom:none| 1637 (in the modern form)
| [[René Descartes]] ([[La Géométrie]])
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">''x''<br />&nbsp;</div> 
| Use of the letter ''x'' for an [[independent variable]] or unknown value. See [[History of algebra#The symbol x|History of algebra: The symbol ''x'']].
| 1637<ref>{{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
 }}</ref>
| [[René Descartes]] ([[La Géométrie]])
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">√ ̅  </div> 
| radical symbol (for [[square root]])
| style=border-bottom:none| 1637 (with the [[vinculum (symbol)|vinculum]] above the [[radicand]])
| [[René Descartes]] ([[La Géométrie]])
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">%</div> 
| [[percent sign]]
| 1650 (approx.)
| unknown
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">∞</div> 
| [[infinity]] sign
| 1655
| [[John Wallis]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">÷</div> 
| [[division sign]] (a repurposed [[obelus]] variant)
| 1659
| [[Johann Rahn]]
|-
| rowspan=2 bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">≤<br /><br />≥</div> 
| rowspan=2| [[inequality (mathematics)|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]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">d</div> 
| [[differential (calculus)|differential]] sign
| rowspan=2| 1675
| rowspan=4| [[Gottfried Leibniz]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">∫</div> 
| [[integral sign]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">:</div> 
| [[colon (punctuation)|colon]] (for [[division (mathematics)|division]])
| 1684 (deriving from use of colon to denote fractions, dating back to 1633)
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">·</div> 
| [[middle dot]] (for [[multiplication]])
| 1698 (perhaps deriving from a much earlier use of middle dot to separate juxtaposed numbers)
|-
| bgcolor=#d0f0d0 align=center|<div style="font-size:200%;">⁄</div> 
| [[slash (punctuation)|division slash]] (a.k.a. ''solidus'')
| 1718 (deriving from horizontal fraction bar, invented by [[Abu Bakr al-Hassar]] in the 12th century)
| [[Thomas Twining (merchant)|Thomas Twining]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">≠</div> 
| [[inequality (mathematics)|inequality]] sign (''not equal to'')
| unknown
| rowspan=3| [[Leonhard Euler]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">''x''{{prime}}</div>  
| [[prime symbol]] (for [[derivative]])
| 1748
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">Σ</div> 
| [[summation]] symbol
| 1755
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">∝</div> 
| [[proportionality (mathematics)|proportionality]] sign
| 1768
| [[William Emerson (mathematician)|William Emerson]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">∂</div> 
| [[partial differential]] sign (a.k.a. ''curly d'' or ''[[Carl Gustav Jacob Jacobi|Jacobi]]'s delta'')
| 1770
| [[Marquis de Condorcet]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">≡</div> 
| [[Identity (mathematics)|identity]] sign (for [[congruence relation]])
| 1801 (first appearance in print; used previously in personal writings of Gauss)
| rowspan=2| [[Carl Friedrich Gauss]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">[''x'']</div> 
| ''integral part'' (a.k.a. [[floor and ceiling functions|floor]])
| 1808
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">!</div> 
| [[factorial]]
| 1808
| [[Christian Kramp]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">Π</div> 
| [[multiplication|product]] symbol
| 1812
| [[Carl Friedrich Gauss]]
|-
| rowspan=2 bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">⊂<br />⊃</div>
| rowspan=2| [[set inclusion]] signs (''subset of'', ''superset of'')
| 1817
| [[Joseph Gergonne]]
|-
| 1890
| [[Ernst Schröder (mathematician)|Ernst Schröder]]
|-
| rowspan=2 bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">|...|</div> 
| [[absolute value]] notation
| 1841
| [[Karl Weierstrass]]
|-
| [[determinant]] of a matrix
| 1841
| rowspan=2| [[Arthur Cayley]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%; white-space:nowrap;">‖...‖</div> 
| [[matrix (mathematics)|matrix]] notation
| 1843<ref name="matrix">{{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}}</ref>
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">∇</div> 
| [[nabla symbol]] (for [[vector differential]])
| 1846 (previously used by Hamilton as a general-purpose operator sign)
| [[William Rowan Hamilton]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">∩<br />∪</div> 
| [[intersection (set theory)|intersection]] <br /><br /> [[union (set theory)|union]] 
| 1888
| [[Giuseppe Peano]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;" class="Unicode">ℵ</div> 
| [[aleph number|aleph]] symbol (for [[transfinite cardinal number]]s)
| 1893
| [[Georg Cantor]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">∈</div> 
| [[membership sign]] (''is [[element (mathematics)|an element]] of'')
| 1894
| [[Giuseppe Peano]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">O</div> 
| [[Big O Notation]]
| 1894
| [[Paul Bachmann]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">{...}</div>
| braces, a.k.a. [[curly bracket]]s (for [[Set (mathematics)|set]] notation)
| 1895
| [[Georg Cantor]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;"  class="Unicode"><math>\mathbb{N}</math></div> 
| [[Blackboard bold]] capital N (for [[natural number]]s set)
| rowspan=2| 1895
| rowspan=3|[[Giuseppe Peano]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;"  class="Unicode"><math>\mathbb{Q}</math></div> 
| [[Blackboard bold]] capital Q (for [[rational number]]s set)
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">∃</div> 
| [[existential quantifier]] (''there exists'')
| 1897
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">·</div> 
| [[middle dot]] (for [[dot product]])
| rowspan=2| 1902
| rowspan=2| [[J. Willard Gibbs]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">×</div> 
| [[multiplication sign]] (for [[cross product]])
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">∨</div>
| [[logical disjunction]] (a.k.a. ''OR'')
| 1906
| [[Bertrand Russell]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">(...)</div> 
| rowspan=2| [[matrix (mathematics)|matrix]] notation
| 1909<ref name="matrix" />
| [[Maxime Bôcher]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">[...]<br />&nbsp;</div> 
| 1909<ref name="matrix" />
| [[Gerhard Kowalewski]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">∮</div>
| [[line integral|contour integral]] sign
| 1917
| [[Arnold Sommerfeld]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;"  class="Unicode"><math>\mathbb{Z}</math></div> 
| [[Blackboard bold]] capital Z (for [[integer]] numbers set)
| 1930
| [[Edmund Landau]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">∀</div> 
| [[universal quantifier]] (''for all'')
| 1935
| [[Gerhard Gentzen]]
|-
| rowspan=2 bgcolor=#d0f0d0 align=center| <div style="font-size:200%;">→</div>
| rowspan=2| [[arrow]] (for [[function (mathematics)|function]] notation)
| 1936 (to denote images of specific elements)
| [[Øystein Ore]]
|-
| 1940 (in the present form of ''f'': ''X'' → ''Y'')
| [[Witold Hurewicz]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;" class="Unicode">∅</div>
| [[empty set]] sign
| 1939
| [[André Weil]] / [[Nicolas Bourbaki]]<ref>{{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}}.</ref>
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;"  class="Unicode"><math>\mathbb{C}</math></div> 
| [[Blackboard bold]] capital C (for [[complex number]]s set)
| 1939
| [[Nathan Jacobson]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;" class="Unicode">∎</div>
| [[end of proof]] sign (a.k.a. [[tombstone (typography)|tombstone]])
| 1950<ref>{{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
}}</ref>
| [[Paul Halmos]]
|-
| bgcolor=#d0f0d0 align=center| <div style="font-size:200%;" class="Unicode">⌊''x''⌋<br />⌈''x''⌉</div> 
| ''greatest integer ≤{{thin space}}x'' (a.k.a. [[floor and ceiling functions|floor]]) <br /> <br /> ''smallest integer ≥{{thin space}}x'' (a.k.a. [[floor and ceiling functions|ceiling]])
| 1962<ref>{{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}}</ref>
| [[Kenneth E. Iverson]]
|}

==See also==
* [[History of mathematical notation]]
* [[History of the Hindu–Arabic numeral system]]
* [[Glossary of mathematical symbols]]
* [[List of mathematical symbols by subject]]
* [[Mathematical notation]]
* [[Mathematical operators and symbols in Unicode]]

==Sources==
{{Reflist}}

==External links==
* [https://www.rapidtables.com/math/symbols/Basic_Math_Symbols.html RapidTables: Math Symbols List]
* [https://mathshistory.st-andrews.ac.uk/Miller/mathsym/ Jeff Miller: ''Earliest Uses of Various Mathematical Symbols'']

{{Mathematical symbols notation language}}

[[Category:Mathematical notation|*]]
[[Category:Mathematics-related lists|Symbols by introduction date]]
[[Category:Mathematical symbols| ]]
[[Category:Mathematics timelines|Symbols]]