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 | ||
|---|---|---|---|---|---|
| bgcolor=#d0f0d0 align=center | — | horizontal bar for division | 14th century (approx.) | Nicole Oresme[1] | |
| bgcolor=#d0f0d0 align=center | + | plus sign | 1360 (approx.), abbreviation for Latin et resembling the plus sign | Nicole Oresme | |
| bgcolor=#d0f0d0 align=center | − | minus sign | 1489 (first appearance of minus sign, and also first appearance of plus sign in print) | Johannes Widmann | |
| bgcolor=#d0f0d0 align=center | √ | 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 | ||||
| bgcolor=#d0f0d0 align=center | = | equals sign | 1557 | Robert Recorde | |
| bgcolor=#d0f0d0 align=center | . | decimal separator | 1593 | Christopher Clavius | |
| bgcolor=#d0f0d0 align=center | × | multiplication sign | 1618 | William Oughtred | |
| bgcolor=#d0f0d0 align=center | ± | plus–minus sign | 1628 | ||
| bgcolor=#d0f0d0 align=center | ∷ | proportion sign | |||
| bgcolor=#d0f0d0 align=center | n√ | radical symbol (for nth root) | 1629 | Albert Girard | |
| bgcolor=#d0f0d0 align=center | < > | strict inequality signs (less-than sign and greater-than sign) | 1631 | Thomas Harriot | |
xy | superscript notation (for exponentiation) | 1636 (using Roman numerals as superscripts) | James Hume | ||
| style=border-bottom:none | 1637 (in the modern form) | René Descartes (La Géométrie) | |||
| bgcolor=#d0f0d0 align=center | x | Use of the letter x for an independent variable or unknown value. See History of algebra: The symbol x. | 1637 | René Descartes (La Géométrie) | |
| bgcolor=#d0f0d0 align=center | √ ̅ | radical symbol (for square root) | style=border-bottom:none | 1637 (with the vinculum above the radicand) | René Descartes (La Géométrie) |
| bgcolor=#d0f0d0 align=center | % | percent sign | 1650 (approx.) | unknown | |
| bgcolor=#d0f0d0 align=center | ∞ | infinity sign | 1655 | John Wallis | |
| bgcolor=#d0f0d0 align=center | ÷ | 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 | ||||
| bgcolor=#d0f0d0 align=center | d | differential sign | 1675 | Gottfried Leibniz | |
| bgcolor=#d0f0d0 align=center | ∫ | integral sign | |||
| bgcolor=#d0f0d0 align=center | colon (for division) | 1684 (deriving from use of colon to denote fractions, dating back to 1633) | |||
| bgcolor=#d0f0d0 align=center | · | middle dot (for multiplication) | 1698 (perhaps deriving from a much earlier use of middle dot to separate juxtaposed numbers) | ||
| bgcolor=#d0f0d0 align=center | ⁄ | division slash (a.k.a. solidus) | 1718 (deriving from horizontal fraction bar, invented by Abu Bakr al-Hassar in the 12th century) | Thomas Twining | |
| bgcolor=#d0f0d0 align=center | ≠ | inequality sign (not equal to) | unknown | Leonhard Euler | |
| bgcolor=#d0f0d0 align=center | x | prime symbol (for derivative) | 1748 | ||
| bgcolor=#d0f0d0 align=center | Σ | summation symbol | 1755 | ||
| bgcolor=#d0f0d0 align=center | ∝ | proportionality sign | 1768 | William Emerson | |
| bgcolor=#d0f0d0 align=center | ∂ | partial differential sign (a.k.a. curly d or Jacobi's delta) | 1770 | Marquis de Condorcet | |
| bgcolor=#d0f0d0 align=center | ≡ | identity sign (for congruence relation) | 1801 (first appearance in print; used previously in personal writings of Gauss) | Carl Friedrich Gauss | |
| bgcolor=#d0f0d0 align=center | [''x''] | integral part (a.k.a. floor) | 1808 | ||
| bgcolor=#d0f0d0 align=center | ! | factorial | 1808 | Christian Kramp | |
| bgcolor=#d0f0d0 align=center | 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 | |||
| bgcolor=#d0f0d0 align=center | ‖...‖ | matrix notation | 1843[2] | ||
| bgcolor=#d0f0d0 align=center | ∇ | nabla symbol (for vector differential) | 1846 (previously used by Hamilton as a general-purpose operator sign) | William Rowan Hamilton | |
| bgcolor=#d0f0d0 align=center | ∩ | 1888 | Giuseppe Peano | ||
| bgcolor=#d0f0d0 align=center | ℵ | aleph symbol (for transfinite cardinal numbers) | 1893 | Georg Cantor | |
| bgcolor=#d0f0d0 align=center | ∈ | membership sign (is an element of) | 1894 | Giuseppe Peano | |
| bgcolor=#d0f0d0 align=center | O | Big O Notation | 1894 | Paul Bachmann | |
| bgcolor=#d0f0d0 align=center | braces, a.k.a. curly brackets (for set notation) | 1895 | Georg Cantor | ||
| bgcolor=#d0f0d0 align=center | N | Blackboard bold capital N (for natural numbers set) | 1895 | Giuseppe Peano | |
| bgcolor=#d0f0d0 align=center | Q | Blackboard bold capital Q (for rational numbers set) | |||
| bgcolor=#d0f0d0 align=center | ∃ | existential quantifier (there exists) | 1897 | ||
| bgcolor=#d0f0d0 align=center | · | middle dot (for dot product) | 1902 | J. Willard Gibbs | |
| bgcolor=#d0f0d0 align=center | × | multiplication sign (for cross product) | |||
| bgcolor=#d0f0d0 align=center | ∨ | logical disjunction (a.k.a. OR) | 1906 | Bertrand Russell | |
| bgcolor=#d0f0d0 align=center | (...) | matrix notation | 1909 | Maxime Bôcher | |
| bgcolor=#d0f0d0 align=center | [...] | 1909 | Gerhard Kowalewski | ||
| bgcolor=#d0f0d0 align=center | ∮ | contour integral sign | 1917 | Arnold Sommerfeld | |
| bgcolor=#d0f0d0 align=center | Z | Blackboard bold capital Z (for integer numbers set) | 1930 | Edmund Landau | |
| bgcolor=#d0f0d0 align=center | ∀ | 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 | ||||
| bgcolor=#d0f0d0 align=center | ∅ | empty set sign | 1939 | André Weil / Nicolas Bourbaki[3] | |
| bgcolor=#d0f0d0 align=center | C | Blackboard bold capital C (for complex numbers set) | 1939 | Nathan Jacobson | |
| bgcolor=#d0f0d0 align=center | ∎ | end of proof sign (a.k.a. tombstone) | 1950[4] | Paul Halmos | |
| bgcolor=#d0f0d0 align=center | ⌊x⌋ | greatest integer ≤x (a.k.a. floor) smallest integer ≥x (a.k.a. ceiling) | 1962 | Kenneth E. Iverson |