Table of mathematical symbols by introduction date

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

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Symbol	Name	Date of earliest use	First author to use	Notes
—	horizontal bar for division	14th century c. 14th century	Nicole Oresme[1]
+	plus sign	1360 c. 1360	Nicole Oresme[1]	From a ligature of Latin et.
−	minus sign	1489	Johannes Widmann	Appears in work that includes the first use of the plus sign in print.
√	radical symbol (for square root)	1525	Christoff Rudolff	Without the vinculum above the radicand.
(...)	parentheses (for precedence grouping)	1544	Michael Stifel	In handwritten notes.
		1556	Nicolo Tartaglia
=	equals sign	1557	Robert Recorde
.	decimal separator	1593	Christopher Clavius
×	multiplication sign	1618	William Oughtred
±	plus–minus sign	1628	William Oughtred
∷	proportion sign	1628	William Oughtred
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	James Hume	Using Roman numerals as superscripts.
		1637[2]	René Descartes	In La Géométrie. In the modern form.
x	Use of the letter x for an independent variable or unknown value.	1637[2]	René Descartes	In La Géométrie.
√ ̅	radical symbol (for square root)	1637[2]	René Descartes	In La Géométrie. With the vinculum above the radicand.
%	percent sign	1650 c. 1650	unknown
∞	infinity sign	1655	John Wallis
÷	division sign	1659	Johann Rahn or John Pell	Originated as a repurposed obelus variant.
∴	therefore sign	1659	Johann Rahn or John Pell
≤ ≥	unstrict inequality signs (less-than or equals to sign and greater-than or equals to sign)	1670	John Wallis	With the horizontal bar above the inequality sign.
		1734	Pierre Bouguer	With double horizontal bar below the inequality sign.
d	differential sign	1675	Gottfried Leibniz
∫	integral sign	1675	Gottfried Leibniz
:	colon (for division)	1684	Gottfried Leibniz	Derives from the use of the colon to denote fractions, dating back to 1633.
·	middle dot (for multiplication)	1698	Gottfried Leibniz	Perhaps derives from a much earlier use of the middle dot to separate juxtaposed numbers.
π	pi (ratio of a circle's circumference to its diameter)	1706	William Jones	Believed to have been used because p (π) is the first letter in perimetron (perimeter).
⁄	division slash (a.k.a. solidus)	1718	Thomas Twining	Derives from the horizontal fraction bar.
e	e (the base of the natural logarithm)	1727–1728	Leonhard Euler	Unpublished. First published appearance was in Euler's Mechanica (1736).
≠	inequality sign (not equal to)	unknown	Leonhard Euler
x′	prime symbol (for derivative)	1748	Leonhard Euler
Σ	summation symbol	1755	Leonhard Euler
∝	proportionality sign	1768	William Emerson
∂	partial differential sign	1770	Marquis de Condorcet
i	imaginary number	1777	Leonhard Euler	Used in a memoir. First publisher by Euler in 1794 in his Institutionum calculi integralis.
≡	identity sign (for congruence relation)	1801	Carl Friedrich Gauss	First appearance in print, used previously in personal writings of 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
		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	William Rowan Hamilton	Previously used by Hamilton as a general-purpose operator sign.
∩ ∪	intersection and union signs	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
{...}	curly brackets or braces (for set notation)	1895	Georg Cantor
${\displaystyle \mathbb {N} }$	Blackboard bold capital N (for natural numbers set)	1895	Giuseppe Peano
${\displaystyle \mathbb {Q} }$	Blackboard bold capital Q (for rational numbers set)	1895	Giuseppe Peano
∃	existential quantifier (there exists)	1897	Giuseppe Peano
·	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
			Gerhard Kowalewski
∮	contour integral sign	1917	Arnold Sommerfeld
${\displaystyle \mathbb {Z} }$	Blackboard bold capital Z (for integer numbers set)	1930	Edmund Landau
∀	universal quantifier (for all)	1935	Gerhard Gentzen
→	arrow (for function notation)	1936	Øystein Ore	To denote images of specific elements.
		1940	Witold Hurewicz	In the present form of f: X → Y.
∅	empty set sign	1939	André Weil (Nicolas Bourbaki)[4]
${\displaystyle \mathbb {C} }$	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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