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.

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.
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
ℕ
 Blackboard bold capital N (for natural numbers set) 1895 Giuseppe Peano
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
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
ℂ
 Blackboard bold capital C (for complex numbers set) 1939 Nathan Jacobson
∎
 end of proof sign (a.k.a. tombstone) 1950[4] Paul Halmos
⌊x⌋
⌈x⌉
 greatest integer ≤ x (a.k.a. floor)

smallest integer ≥ x (a.k.a. ceiling) 		Kenneth E. Iverson

See also

Sources

  1. ↑ 1.0 1.1 Cajori, Florian (1993). A History of Mathematical Notations. Mineola, New York: Dover Publications. 
  2. ↑ 2.0 2.1 Cite error: Invalid <ref> tag; no text was provided for refs named boyer1991
  3. ↑ 3.0 3.1 "Earliest Uses of Symbols for Matrices and Vectors". http://jeff560.tripod.com/matrices.html. Retrieved 18 December 2016. 
  4. ↑ 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." 



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