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

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| 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

| 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  | James Hume  | Using Roman numerals as superscripts.
René Descartes | In La Géométrie. In the modern form.

| 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.

| 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.

| 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 (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

| prime symbol (for derivative)  | 1748  | Leonhard Euler

| summation symbol  | 1755  | Leonhard Euler

| proportionality sign  | 1768  | William Emerson

| partial differential sign  | 1770  | Marquis de Condorcet

| 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

| 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

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

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

| Big O Notation  | 1894  | Paul Bachmann

{...}

| curly brackets or braces (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)  | 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

| 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

| 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. ↑ 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."

## External links

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

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