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The notation of mathematics: operators, relations, set and logic symbols, and the conventions that let an expression be read the same way by two people who share no language.
Here when the symbol carries mathematical meaning. A Greek letter used as a mathematical variable is here; the same letter as a letter of an alphabet is filed under scientific notation, where its role as a designator is the point.
Standardised and commonly used in near-equal measure, with a documented history behind most of it — mathematical notation is one of the few areas where the inventor of a symbol is often known by name.
All 355symbols in this domain, A–Z.
A number held in beads.
Letters standing for numbers.
A raised star marking a conjugate transpose or dual.
The first Hebrew letter with a zero subscript, counting the whole numbers.
A capital F marking points on every face.
The first Greek letter, used across science for angles, rates and particles.
A capital A with a subscript, the even permutations only.
A capital H with a subscript one, naming the hypothesis accepted if the null is rejected.
A flat-backed D shape, outputting true only when every input is true.
A small wedge open to the right, prefixing the name of an angle.
A capital A with a small ring above it, marking a length of 10⁻¹⁰ metres.
Curly braces around two operators separated by a comma.
Two stacked wavy strokes, meaning 'roughly equal to'.
A comma-like mark splitting a number.
Per cent, drawn differently.
The digits used in Arabic script.
Coordinate ranges bounding the smallest unique part.
A capital N with subscript A, the number of entities in a mole.
A dashed line marking a glide along an axis.
A flag for twenty, a feather for eight thousand.
The second Greek letter, used for beta particles, coefficients and angles.
A capital Greek B of two variables, an integral of two powers.
A Hebrew beth with a subscript, the tower of power sets.
An enlarged upside-down U with limits, intersecting a family.
A capital O with a bracketed expression, bounding a growth rate from above.
A capital omega bounding a growth rate from below.
A capital theta bounding a growth rate from both sides.
An enlarged sideways U with limits, taking the union of a family.
Two numbers stacked inside tall brackets, counting selections without order.
Double-struck capitals naming the standard number systems.
A name, a definition sign and alternatives.
A capital I marking a lattice point at the cell centre.
An italic k, often subscripted B, relating temperature to energy.
A curled ∂ applied to a chain or a region.
Angle brackets and a bar denoting quantum states.
The ancestor of the digits.
Strands crossing in order.
Four figures used for hexagonal crystals.
The two letters cd, the SI unit symbol for the candela.
Vertical bars around a set, counting its members.
A multiplication cross between sets, forming ordered pairs.
An integral sign struck through with a short bar, meaning a symmetric limit around a singularity.
A knot built on a hidden grid.
A Greek letter chi raised to the power two, naming a distribution and its test.
Two beads above and five below a bar.
Four digits in one figure.
An overline on a set, adding its limit points.
A capital H with a raised degree, the dual of homology.
Square brackets around two operators separated by a comma.
An overbar on a set name, meaning everything outside it.
Square brackets around a species, meaning its concentration.
A capital P with two events separated by a vertical bar.
A pair of bounds, giving a range of plausible values for an estimate.
A number in square brackets, naming a whole class of numbers.
Three stacked horizontal bars, marking congruence rather than equality.
An integral sign with a circle, integrating around a closed path.
A small six-pointed star set between two functions, combining them by sliding one across the other.
An upside-down capital pi, the dual of a product.
Greek letters counting in Egypt.
A lower-case r, reporting how closely two variables move together.
Rods laid out in place columns.
Three figures in angle brackets naming equivalent directions.
Three figures in square brackets naming a direction.
Three figures in curly brackets naming equivalent planes.
A symbol naming one of thirty-two symmetry classes.
Wedges counted in sixties.
Del followed by a cross, measuring rotation about a point.
A capital Z or C with a subscript, naming the group generated by one element.
A square operator combining space and time derivatives.
A point or a comma, depending on the country.
A colon before an equals sign, marking a definition rather than a claim.
A small raised circle marking degrees of temperature, angle or arc.
The letters df, or a Greek nu, counting the values free to vary.
The fourth Greek letter, meaning change or difference in almost every field.
Straight vertical bars around a square grid, denoting its determinant.
A dash-dot line marking a diagonal glide.
A circle with a diagonal stroke, marking a dimension as a diameter.
A dash-dot line with arrows for a quarter glide.
The dot patterns on a die, and the rule that opposite faces total seven.
A capital D applied to a function, meaning differentiation as an operation in its own right.
A Greek psi of a variable, the gamma function's logarithmic derivative.
A capital D with a subscript, the symmetries of a regular polygon.
A lowercase delta of a variable, infinitely tall and infinitely narrow.
A circled plus joining structures into one that splits cleanly.
A subscripted del or a dotted gradient, giving the rate of change along one chosen direction.
A union sign with a dot or a squared form, tagging each element by origin.
Del followed by a dot, measuring outward flow from a point.
A vertical stroke asserting one number divides another exactly.
A horizontal stroke with a dot above and below, indicating division.
A Greek sigma with a subscript, summing powers of divisors.
A struck-through vertical stroke, denying exact division.
A rectangle split into two halves, each carrying nought to six pips.
Two exclamation marks, skipping every other factor.
Two integral signs side by side, integrating over an area.
A vertical stroke with two bars, meaning 'entails' or 'models'.
Square brackets marking an optional part.
Braces marking a repeatable part.
A repeated index, meaning a sum with no sigma written.
An italic lower-case e, the magnitude of the charge on a proton.
A circle crossed by a diagonal stroke, denoting the set with no members.
A Greek epsilon or lambda standing for a string of no characters.
A capital delta before an H, denoting heat absorbed or released.
An arrow with two heads, a surjection.
The fifth Greek letter, conventionally a very small positive quantity.
Two short horizontal parallel lines (=), denoting that the values on either side are equal.
Barred letters standing for numbers.
The numerals Rome inherited.
A Greek chi of a space, a single whole number invariant.
A Greek phi of a number, counting coprime predecessors.
A plus inside a circle, true when exactly one operand is.
A capital E with a variable in brackets, meaning the long-run average.
An exclamation mark after a number, multiplying it down to one.
A base with a bracketed or underlined superscript, a product of descending terms.
An upside-down T standing for a contradiction.
Lines that stand for an integral.
One field over another separated by a slash, with no quotient implied.
Square brackets with the top or bottom serifs removed, marking rounding direction.
An inverted capital A, the universal quantifier of formal logic.
A filled square marking a fourfold axis.
Three fractions locating an atom in a cell.
A plain right arrow naming a function's domain and codomain.
A small raised ring between two functions.
A Greek pi with subscript one, a space and a base point.
Gal with a field extension in brackets, the symmetries of a polynomial's roots.
The third Greek letter, used for gamma rays, functions and display response.
A capital Greek gamma of a variable, the factorial extended.
Letters counted as numbers.
The letters GL with a size and a field in brackets, the invertible matrices.
An italic capital G, the constant in Newton's law of gravitation.
An angle bracket opening to the left, stating that the left value is larger.
A greater-than wedge with a bar beneath it, allowing equality as well.
Two numbers in brackets, or the letters gcd, naming their largest shared divisor.
A group name inside vertical bars, counting its elements.
A small circle between two matrices, multiplying them entry by entry.
A t with subscript one-half, the time for half a quantity to decay.
A scripted or hatted H standing for a system's total energy.
A caret over a letter, marking an estimate or a unit vector.
A capital H or theta of a variable, zero then one.
Symmetry named by axis order and plane letter.
A capital H of second partial derivatives, testing whether a stationary point is a maximum or a minimum.
A tilde over an equals sign, or a plain tilde, between two spaces.
A capital H with a degree subscript and a space in brackets.
A single wavy line, a weaker equivalence than homeomorphism.
A generator inside angle or round brackets, naming everything it multiplies into.
Three horizontal bars, asserting equality in every case.
The letters id with an object subscript, the map that changes nothing.
A double-shafted arrow with heads at both ends, denoting logical equivalence.
A double-shafted arrow pointing right, denoting logical implication.
A doubled upright stroke pair, denying any statistical relation.
A blackboard-bold 1 with a set subscript, one inside and zero outside.
inf, the greatest lower bound of a set, which need not belong to the set.
A sideways figure-eight (∞) denoting an unbounded quantity in mathematics, and used more broadly as a symbol of endlessness.
Angle brackets around two vectors, giving a number.
An elongated S indicating integration in calculus.
A small circle raised after a set, or the word int.
An inverted rounded U, denoting what two sets have in common.
Mixed square and round brackets marking whether an endpoint is included.
A small open circle marking a centre of symmetry.
A wave over an equals sign, saying two structures are the same.
An element symbol with mass number above and atomic number below, to its left.
The Legendre symbol's glyph extended to composite denominators.
A ∂ over a ∂ with parenthesised lists, the determinant of a matrix of partial derivatives.
A capital J, the SI unit symbol for the joule.
A grid ordered so neighbours differ by one.
A capital K, the SI unit symbol for the kelvin.
A stroke turning a letter into a number.
Numbers from the Gandharan north-west.
A lower-case k, the SI prefix for a factor of one thousand.
The two-letter symbol kg, the SI unit symbol for the kilogram.
An asterisk repeating the preceding element any number of times.
A break in a line showing which passes under.
Another letter kept only for counting.
A lowercase delta with two indices, one when they match and zero otherwise.
An apostrophe after a function name, meaning its derivative.
The eleventh Greek letter, used for wavelength, eigenvalues and anonymous functions.
A triangle or squared nabla, summing second derivatives.
A point group symbol with inversion added.
The letters lcm with a bracketed list, or square brackets alone.
Two numbers stacked in tall brackets with no dividing line.
A d over a d, naming both the function and the variable differentiated against.
An angle bracket opening to the right, stating that the left value is smaller.
A less-than wedge with a bar beneath it, allowing equality as well.
A lowercase epsilon with three indices, valued minus one, zero or one.
Square brackets around two vector fields or Lie algebra elements.
lim inf, the smallest value a sequence returns to infinitely often.
The letters lim with an arrow beneath, naming a value approached.
lim sup, the largest value a sequence returns to infinitely often.
An integral sign whose limits name a curve rather than two numbers.
A picture standing beside a count.
A lowercase o asserting negligible growth.
Shapes standing for boolean functions.
A pointed caret, denoting conjunction in formal logic.
A pointed V, denoting inclusive disjunction in formal logic.
Fractions with their own glyphs.
An arrow with a tail bar, naming what a function does to an element.
Three dots standing for an omitted, obvious continuation.
Square or round brackets enclosing a grid of numbers, marking a matrix.
Dots for ones, bars for fives.
A shell standing for nothing.
A lower-case m, the SI unit symbol for the metre.
A lower-case Greek mu with a straight descender, used as the SI prefix for one millionth.
Three figures in round brackets naming a plane.
A bar above a figure marking a negative index.
The mathematical sign for subtraction, written as a single horizontal stroke.
A heavy solid line marking a mirror.
A Greek mu of a number, valued minus one, zero or one.
The three letters mol, the SI unit symbol for the mole.
An arrow with a hooked tail, an injection.
The twelfth Greek letter, and the SI prefix for one millionth.
Two nested greater-than signs, marking dominance of scale.
Two nested less-than signs, marking a difference of scale.
A stacked column of numbers in tall brackets, several rows deep.
The diagonal cross used to indicate multiplication.
Burmese digits, round by design.
An inverted solid triangle, denoting the vector differential operator.
A double-shafted arrow between functors.
An open square before a proposition, meaning 'necessarily'.
A horizontal bar with a short downward tick at its right end, denoting logical not.
A two-cell form for equality in the Nemeth code.
Cells opening and closing a fraction.
A braille cell for subtraction in the Nemeth code.
A braille cell for addition in the Nemeth code.
Cells opening and closing a root expression.
A cell lowering what follows below the baseline.
A cell raising what follows to an exponent.
A capital N, the SI unit symbol for the newton.
A dot above a variable, meaning its derivative with respect to time.
Three scales and a straight edge.
Doubled vertical bars measuring the size of a vector.
A capital N with a mean and variance in brackets, naming a bell-shaped distribution.
A triangle on its side, marking a subgroup closed under conjugation.
A struck-through epsilon, denying membership of a set.
An equals sign struck through by a diagonal stroke, meaning inequality.
A capital H with a subscript zero, naming the hypothesis being tested.
The last Greek letter, used for angular velocity — and the source of the ohm sign.
A superscript plus or minus on the limit point, approaching from one side only.
A capital B with a centre and a radius in brackets.
A curved-back shield shape, outputting true when any input is true.
A rounded double-cupped Greek omega, the first infinite ordinal.
A lower-case p followed by a probability, reporting how surprising a result would be.
Two vertical strokes side by side, stating that two lines never meet.
A rounded d with a curled top, marking differentiation in one variable.
The two letters Pa, the SI unit symbol for the pascal.
A downward arrow between propositions, meaning 'neither'.
Tensors drawn as shapes with legs.
A percent sign with an extra circle, meaning 'per thousand'.
Two small circles either side of a diagonal stroke, meaning 'per hundred'.
A capital P with two subscripts, counting ordered arrangements.
An upright T shape with the crossbar at the foot, stating that two lines meet at a right angle.
Tokens moving between places.
The twenty-first Greek letter, used for the golden ratio and magnetic flux.
The Greek letter used for the ratio of a circle's circumference to its diameter.
An italic lower-case h, denoting the quantum of action.
The mathematical sign for addition, written as an upright cross.
A plus sign above a minus stroke, giving a tolerance or two possible values.
A pair of curved curly braces around two functions in classical mechanics.
Letters addressed by row and column.
A ring name with a variable in square brackets, the polynomials over it.
An open diamond before a proposition, meaning 'possibly'.
Peaks labelled with plane indices.
A script capital P applied to a set, naming all of its subsets.
Straight slanted ticks for feet, inches, minutes and seconds.
A Greek pi of a number, counting primes rather than measuring circles.
A capital P opening a space group symbol.
A large capital pi, denoting the product of a sequence of terms.
A sideways U with a struck-through bar, excluding the case of equality.
A looped form resembling an open alpha, stating a constant ratio.
A small right-angle bracket in a square diagram's corner, marking a fibre product.
A right-angle bracket in the opposite corner, marking an amalgamated sum.
A filled or hollow square ending a proof.
Dyed cords carrying category.
The knot that means one.
Turns counted to give the digit.
A cord hanging from the main line.
One knot, one unit, in the tens and above.
A cord hanging off a cord.
One group name over another separated by a slash, collapsing a subgroup to a point.
A capital R giving agreement as a fraction.
A capital R before a dimension, marking it as a radius.
A struck-through h, Planck's constant divided by two pi.
A vertical bar with a subscript, cutting a function down to part of its domain.
The seventeenth Greek letter, used for density and resistivity.
A capital R marking a rhombohedral setting.
A Greek zeta of a complex variable.
Z over nZ, the integers wrapped round at a fixed size.
A base with a raised bracket or overline, a product of ascending terms.
A rotation symbol with an open circle inside.
The last of the numeral-only signs.
A letter x with a horizontal bar above it, standing for the average of a sample.
Symmetry named by a letter and a subscript.
A rotation symbol carrying tails.
A lower-case s, the SI unit symbol for the second.
A product sign with a short vertical bar on one side, marking which factor is normal.
Letters stacked by information.
A backslash between two sets, removing one from the other.
Braces enclosing a variable, a separator and a condition, defining a set by a rule.
A vertical bar between two propositions, meaning 'not both'.
A capital A, B or C marking one centred face pair.
The eighteenth Greek letter, used for standard deviation and stress.
How a number is written to state how well it is known.
A point group symbol with dots for missing directions.
A filled hexagon marking a sixfold axis.
A stroke multiplying by a thousand.
Numbers spaced by logarithm.
A line drawn without lifting the finger.
One bead above, four below.
A lattice letter followed by symmetry elements.
The letters SO with a dimension in brackets, the rotations of a space.
An italic lower-case c, denoting the speed of light in vacuum.
A hooked stroke with a horizontal bar, indicating a root of a number.
A lower-case sigma, or a letter s, standing for the spread of a distribution.
A letter that is only a number.
A capital F carrying three indices.
An exclamation mark before a number instead of after it.
A sideways U with a bar beneath, allowing the two sets to be identical.
A rounded bracket opening right, stating that one set is contained in another.
A vertical bar or colon separating a variable from its condition.
Small candidate numbers written in a cell's corners or centre.
The capital Greek sigma, used to indicate a sum over a series.
A sideways U opening leftwards, saying one set contains another.
sup, the least upper bound of a set, which need not belong to the set.
A rod-derived shorthand for numbers.
A triangle between two sets, taking what is in one but not both.
A capital S with a subscript, the group of all rearrangements of that many things.
Letters written above and below a symbol, marking a tensor's components.
A circled multiplication cross joining two structures.
Thailand's own digits.
A backwards E with an exclamation mark, asserting a unique solution.
A mirrored capital E, the existential quantifier of formal logic.
Three dots in an upward-pointing triangle, introducing a conclusion.
An ellipsoid drawn for atomic displacement.
The eighth Greek letter, the default name for an angle.
A filled triangle marking a threefold axis.
A single wave-shaped stroke marking equivalence, similarity or distribution.
An upright d drawn with a straight stroke, against the curled ∂ of a partial derivative.
A raised capital T flipping a matrix about its diagonal.
Three stacked lines, each solid or broken.
Three integral signs side by side, integrating over a three-dimensional region.
Every case, written out.
A vertical stroke with a bar to its right, meaning 'proves'.
A matrix or plane naming a twin relation.
A filled lens shape marking a twofold axis.
A rounded U shape, denoting everything in either of two sets.
A capital U with a dimension in brackets, the complex analogue of rotation.
The letters Var, or a squared sigma, measuring spread.
A short arrow written above a letter, marking it as a vector.
A T standing for a proposition true in every case.
A Greek psi standing for a quantum state's amplitude.
A Greek lambda, denoting the distance between successive wave peaks.
A short vertical line with two side strokes, combining a group with a permutation action.
A capital W of a set of functions, testing whether they are linearly independent.
A multiplicity figure with a letter.
A diagram built to a construction.
A stylised h or よ, embedding a category into its functor category.
A lowercase z counting standard deviations from the mean.