Table of mathematical symbols by introduction date

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

Symbol	Name	Date of earliest use	First author to use
—	horizontal bar for division	14th century (approx.)	Nicole Oresme^[1]
+	plus sign	1360 (approx.), 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
(...)	parentheses (for precedence grouping)	1556	Niccolò Tartaglia
=	equals sign	1557	Robert Recorde
.	decimal separator	1593	Christopher Clavius
×	multiplication sign	1618	William Oughtred
±	plus–minus sign	1628
∷	proportion sign	1628
ⁿ√	radical symbol (for nth root)	1629	Albert Girard
< >	strict inequality signs (less-than sign and greater-than sign)	1631	Thomas Harriot
x^y	superscript notation (for exponentiation)	1636 (using Roman numerals as superscripts)	James Hume
x^y	superscript notation (for exponentiation)	1637 (in the modern form)	René Descartes (La Géométrie)
x	Use of the letter x for an independent variable or unknown value. See History of algebra: The symbol x.	1637^[2]	René Descartes (La Géométrie)
√ ̅	radical symbol (for square root)	1637 (with the vinculum above the radicand)	René Descartes (La Géométrie)
%	percent sign	1650 (approx.)	unknown
∞	infinity sign	1655	John Wallis
÷	division sign (a repurposed obelus variant)	1659	Johann Rahn
≤ ≥	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
d	differential sign	1675	Gottfried Leibniz
∫	integral sign	1675
:	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 Abu Bakr al-Hassar in the 12th century)	Thomas Twining
≠	inequality sign (not equal to)	unknown	Leonhard Euler
x′	prime symbol (for derivative)	1748
Σ	summation symbol	1755
∝	proportionality sign	1768	William Emerson
∂	partial differential sign (a.k.a. curly d or Jacobi's delta)	1770	Marquis de Condorcet
≡	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	Carl Friedrich Gauss
!	factorial	1808	Christian Kramp
Π	product symbol	1812	Carl Friedrich Gauss
⊂ ⊃	set inclusion signs (subset of, superset of)	1817	Joseph Gergonne
⊂ ⊃	set inclusion signs (subset of, superset of)	1890	Ernst Schröder
\|...\|	absolute value notation	1841	Karl Weierstrass
\|...\|	determinant of a matrix	1841	Arthur Cayley
‖...‖	matrix notation	1843^[3]	Arthur Cayley
∇	nabla symbol (for vector differential)	1846 (previously used by Hamilton as a general-purpose operator sign)	William Rowan Hamilton
∩ ∪	intersection union	1888	Giuseppe Peano
ℵ	aleph symbol (for transfinite cardinal numbers)	1893	Georg Cantor
∈	membership sign (is an element of)	1894	Giuseppe Peano
O	Big O Notation	1894	Paul Bachmann
{...}	braces, a.k.a. curly brackets (for set notation)	1895	Georg Cantor
$\mathbb {N}$	Blackboard bold capital N (for natural numbers set)	1895	Giuseppe Peano
$\mathbb {Q}$	Blackboard bold capital Q (for rational numbers set)	1895
∃	existential quantifier (there exists)	1897
·	middle dot (for dot product)	1902	J. Willard Gibbs
×	multiplication sign (for cross product)	1902	J. Willard Gibbs
∨	logical disjunction (a.k.a. OR)	1906	Bertrand Russell
(...)	matrix notation	1909^[3]	Maxime Bôcher
[...]	matrix notation	1909^[3]	Gerhard Kowalewski
∮	contour integral sign	1917	Arnold Sommerfeld
$\mathbb {Z}$	Blackboard bold capital Z (for integer numbers set)	1930	Edmund Landau
∀	universal quantifier (for all)	1935	Gerhard Gentzen
→	arrow (for function notation)	1936 (to denote images of specific elements)	Øystein Ore
→	arrow (for function notation)	1940 (in the present form of f: X → Y)	Witold Hurewicz
∅	empty set sign	1939	André Weil / Nicolas Bourbaki^[4]
$\mathbb {C}$	Blackboard bold capital C (for complex numbers set)	1939	Nathan Jacobson
∎	end of proof sign (a.k.a. tombstone)	1950^[5]	Paul Halmos
⌊x⌋ ⌈x⌉	greatest integer ≤ x (a.k.a. floor) smallest integer ≥ x (a.k.a. ceiling)	1962^[6]	Kenneth E. Iverson

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Sources

^ Cajori, Florian (1993). A History of Mathematical Notations. Mineola, New York: Dover Publications.
^ Boyer, Carl B. (1991), A History of Mathematics (Second ed.), John Wiley & Sons, Inc., ISBN 978-0-471-54397-8
^ ^a ^b ^c "Earliest Uses of Symbols for Matrices and Vectors". jeff560.tripod.com. Retrieved 18 December 2016.
^ Weil, André (1992), The Apprenticeship of a Mathematician, Springer, p. 114, ISBN 9783764326500.
^ Halmos, Paul (1950). Measure Theory. New York: Van Nostrand. pp. vi. 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.
^ Kenneth E. Iverson (1962), A Programming Language, Wiley, retrieved 20 April 2016

External links

Common mathematical notation, symbols, and formulas

Lists of Unicode and LaTeX mathematical symbols
List of mathematical symbols by subject Glossary of mathematical symbols List of logic symbols

Lists of Unicode symbols

General	List of Unicode characters Unicode block
Alphanumeric	Mathematical Alphanumeric Symbols Blackboard bold Letterlike Symbols Symbols for zero
Arrows and Geometric Shapes	Arrows Miscellaneous Symbols and Arrows Geometric Shapes (Unicode block)
Operators	Mathematical operators and symbols Mathematical Operators (Unicode block)
Supplemental Math Operators	Supplemental Mathematical Operators Number Forms
Miscellaneous	A B Technical ISO 31-11 (Mathematical signs and symbols for use in physical sciences and technology)

Typographical conventions and notations

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Letters	Diacritic Letters in STEM Greek letters in STEM Latin letters in STEM
Notation	Mathematical notation Abbreviations Notation in probability and statistics List of common physics notations

Meanings of symbols
Glossary of mathematical symbols List of mathematical constants Physical constants Table of mathematical symbols by introduction date List of typographical symbols and punctuation marks

This page was last edited on 26 February 2024, at 23:10

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