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 Nicole Oresme + plus sign Nicole Oresme From a ligature of Latin . − 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 René Descartes In La Géométrie. In the modern form. x Use of the letter x for an independent variable or unknown value. 1637 René Descartes In La Géométrie. √ ̅ radical symbol (for square root) 1637 René Descartes In La Géométrie. With the vinculum above the radicand. % percent sign 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 e e (the base of the natural logarithm) 1727–1728 Leonhard Euler Unpublished.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 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 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 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 André Weil (Nicolas Bourbaki). Blackboard bold capital C (for complex numbers set) 1939 Nathan Jacobson ∎ end of proof sign (a.k.a. tombstone) 1950 Paul Halmos ⌊x⌋⌈x⌉ greatest integer ≤x (a.k.a. floor) smallest integer ≥x (a.k.a. ceiling) 1962 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

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