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. Template:Noprint inline

Symbol  | Name  | Date of earliest use  | First author to use

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|
|

| 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
1556  | Niccolò Tartaglia

| equals sign | 1557  | Robert Recorde

| decimal separator | 1593  | Christopher Clavius

| multiplication sign | 1618  | William Oughtred

| plus–minus sign | 1628

| proportion sign

| radical symbol (for nth root)  | 1629  | Albert Girard

| strict inequality signs (less-than sign and greater-than sign)  | 1631  | Thomas Harriot

| superscript notation (for exponentiation)  | 1636 (using Roman numerals as superscripts)  | James Hume
1637 (in the modern form)  | René Descartes (La Géométrie)

| 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

| differential sign  | 1675  | Gottfried Leibniz

| integral sign

| 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

| prime symbol (for derivative)  | 1748

| 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

| factorial | 1808  | Christian Kramp

| 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]

| nabla symbol (for vector differential)  | 1846 (previously used by Hamilton as a general-purpose operator sign)  | William Rowan Hamilton

| intersection

union | 1888  | Giuseppe Peano

| aleph symbol (for transfinite cardinal numbers)  | 1893  | Georg Cantor

| membership sign (is an element of)  | 1894  | Giuseppe Peano

| Big O Notation  | 1894  | Paul Bachmann

{...}

| braces, a.k.a. curly brackets (for set notation)  | 1895  | Georg Cantor

| Blackboard bold capital N (for natural numbers set)  | 1895  | Giuseppe Peano

| Blackboard bold capital Q (for rational numbers set)

| existential quantifier (there exists)  | 1897

| middle dot (for dot product)  | 1902  | J. Willard Gibbs

| multiplication sign (for cross product)

| logical disjunction (a.k.a. OR)  | 1906  | Bertrand Russell

(...)

| matrix notation  | 1909[3] | Maxime Bôcher

[...]

| 1909[3] | Gerhard Kowalewski

| contour integral sign  | 1917  | Arnold Sommerfeld

| 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
1940 (in the present form of f: X → Y)  | Witold Hurewicz

| empty set sign  | 1939

| 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

* 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

1. ↑ Cajori, Florian (1993). A History of Mathematical Notations. Mineola, New York: Dover Publications.
2. ↑ Boyer, Carl B. (1991), A History of Mathematics (Second ed.), John Wiley & Sons, Inc., ISBN 978-0-471-54397-8, https://archive.org/details/historyofmathema00boye
3. ↑ 3.0 3.1 3.2 "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."

## External links

* RapidTables: Math Symbols List
* Jeff Miller: Earliest Uses of Various Mathematical Symbols

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