How do you say that?

Series: Explain
Summary: A visual, beginner-first guide to saying Greek letters and common mathematical symbols, distinguishing a symbol's name from the way it is naturally read inside an expression.
Math Level: GENERAL
Index Excerpt: Greek letter pronunciation; mathematical symbols; how to say epsilon; xi; theta; nabla; partial derivative; infinity; set symbols; read equations aloud; UK US pronunciation

You can understand a piece of mathematics for years without ever discovering how part of it is pronounced.

Perhaps you have seen

\xi(s)

a hundred times.

You know what the function does. You recognise the symbol. You may even be perfectly comfortable manipulating it on a page.

Then somebody asks you to read the equation aloud.

What do you call that little curl?

Or perhaps the mystery is

\partial,\qquad \nabla,\qquad \equiv,\qquad \in,\qquad \sum.

Mathematics has an enormous written vocabulary.

Much of it is rarely taught as a spoken vocabulary.

This guide is for that moment.

It is a guide to recognising mathematical symbols, saying their names, reading them naturally inside expressions, and typing them when the symbol itself is inconvenient to enter.

It is also, deliberately, a chance simply to look at them.

Mathematical symbols are beautiful objects.

So throughout this guide, each symbol is given room of its own.

Look at the symbols

The symbol itself is the largest element in each entry.

Not the name.

Not the pronunciation.

Not the explanation.

The symbol.

The specimen boxes are deliberately identical in size. The characters use the same mathematical typeface, the same nominal size and the same positioning rules.

We do not enlarge a small-looking symbol or shrink a large-looking one just to make everything fill its box.

That would spoil the comparison.

Some mathematical characters are narrow. Some are wide. Some sit high. Some descend. Some occupy surprisingly little of the space around them. Others seem to fill it.

Those differences are part of the typography of mathematics.

(The boxes are the same size on purpose. The symbols are not individually stretched to fill them, so their natural differences in size and proportion remain visible.)

Longer constructions such as

\frac{d}{dx}

are slightly different. They are expressions rather than single glyphs, so they can be shown as expression specimens rather than being squeezed into the same comparative box.

How to use this guide

Every entry answers the same questions.

NAME tells you what the symbol is called.

SAY tells you how that name is pronounced.

Where British and American English differ, both are shown. Where they do not, they are combined as UK / US. Where more than one pronunciation is genuinely established, we show that too.

Capital letters in our friendly pronunciation spelling show the stressed part:

AL-fuh

BEE-tuh

EP-si-lon

ep-SIGH-lon

READ ALOUD is different.

It tells you what to say when you actually encounter the symbol inside mathematics.

That distinction becomes important very quickly.

A symbol may be called a right arrow, for example, while

x\to0

is normally read “x tends to zero”.

And a vertical bar may be called a vertical bar, while

P(A\mid B)

contains the spoken word “given”.

The aim is to leave as little as possible for you to guess.

A note about language

Riemann Console is an English-language website, so this is an English-language guide to saying and reading mathematical notation aloud.

The notation itself travels much more widely than the language used to speak it. A mathematician in Tokyo, Paris, Berlin, Athens or Buenos Aires may write exactly the same symbols while using quite different words for them.

Japanese mathematics, for example, commonly reads $\sqrt{x}$ using rūto — “root” — while multiplication with $\times$ can be read using kakeru and division with $\div$ using waru. Greek-letter names acquire their own established Japanese forms too. [1, 2]

So there is no single worldwide spoken pronunciation hiding behind every mathematical symbol.

What is remarkably international is the written notation.

In the entries that follow, SAY describes established English pronunciation. Where British and American English differ, we show both. Where more than one English pronunciation is accepted, we show that too.

The aim is not to declare one accent correct.

It is to tell an English-speaking reader what they are likely to hear — and what they can confidently say themselves.

This is a practical field guide, not a catalogue of every mathematical character Unicode can encode. It concentrates on common notation from school and undergraduate mathematics, plus symbols that appear especially often around analysis and number theory.

The Greek alphabet

The pronunciations in this section have been checked against current Cambridge Dictionary pronunciation entries, with Collins used where it records additional established English variants. The friendly spellings below are deliberately easier to read than IPA; the dictionaries remain the more exact phonetic reference.

Greek letters occur everywhere in mathematics, physics, engineering, statistics and computing.

Sometimes a Greek letter acquires a particularly famous mathematical role. $\pi$ , for example, immediately suggests the ratio of a circle's circumference to its diameter.

But Greek letters are still letters.

There is no universal mathematical law saying that $\alpha$ must always mean an angle, or that $\lambda$ must always mean an eigenvalue.

A mathematician is free to define them.

The meanings below are therefore common uses, not permanent definitions.

\boxed{\hspace{6em}\mathclap{\Huge Α\qquad α}\hspace{6em}\vphantom{\Huge \int}}

NAME Alpha

SAY

UK / US AL-fuh

READ ALOUD

\alpha=0.05

“Alpha equals zero point zero five.”

PLAIN TEXT \alpha\

LATEX \\\alpha\

COMMONLY USED FOR Angles, parameters, coefficients and significance levels.

Alpha is the first Greek letter.

In mathematics it often denotes an angle, a parameter, a coefficient or some first object in a family. In statistics, $\alpha$ commonly denotes a significance level.

\boxed{\hspace{6em}\mathclap{\Huge Β\qquad β}\hspace{6em}\vphantom{\Huge \int}}

NAME Beta

SAY

UK BEE-tuh

US BAY-tuh

PRONUNCIATION NOTE The UK/US difference is completely normal. Both forms are standard English pronunciations. [3]

READ ALOUD

\beta_1

“Beta one.”

Or, where the indexing needs to be explicit:

“Beta sub one.”

PLAIN TEXT \beta\

LATEX \\\beta\

COMMONLY USED FOR Parameters, coefficients and angles.

The pronunciation changes.

The mathematics does not.

\boxed{\hspace{6em}\mathclap{\Huge Γ\qquad γ}\hspace{6em}\vphantom{\Huge \int}}

NAME Gamma

SAY

UK / US GAM-uh

READ ALOUD

\Gamma(s)

“Gamma of s.”

PLAIN TEXT \gamma\

LATEX \\\gamma\ Capital: \\\Gamma\

COMMONLY USED FOR Parameters, curves, distributions and special functions.

Capital gamma, $\Gamma$ , famously appears in the gamma function.

\boxed{\hspace{6em}\mathclap{\Huge Δ\qquad δ}\hspace{6em}\vphantom{\Huge \int}}

NAME Delta

SAY

UK / US DEL-tuh

READ ALOUD

\Delta x

“Delta x.”

Depending on the context, a mathematician might instead say:

“The change in x.”

PLAIN TEXT \delta\

LATEX \\\delta\ Capital: \\\Delta\

COMMONLY USED FOR Change, difference and small positive quantities.

Delta is strongly associated with change or difference, although that is not its only use.

\boxed{\hspace{6em}\mathclap{\Huge Ε\qquad ε\qquad ϵ}\hspace{6em}\vphantom{\Huge \int}}

NAME Epsilon

SAY

UK EP-si-lon · ep-SIGH-lon

US EP-suh-lahn · EP-suh-luhn

PRONUNCIATION NOTE Both British forms are established. EP-si-lon is not a mistaken or merely informal pronunciation; ep-SIGH-lon is another standard British form. [4, 5]

READ ALOUD

\varepsilon>0

“Epsilon is greater than zero.”

\forall\varepsilon>0

“For every epsilon greater than zero.”

PLAIN TEXT \epsilon\

LATEX \\\epsilon\ Variant: \\\varepsilon\

COMMONLY USED FOR Small positive quantities, errors and tolerances.

Epsilon deserves a little more room because both its pronunciation and its written lowercase form vary.

The two forms

\epsilon \qquad \varepsilon

are conventional glyph variants of the same Greek letter.

They do not automatically represent different mathematical objects.

An author may deliberately use both for different quantities, but if so the distinction exists because the author defines it.

DON'T CONFUSE A different-looking epsilon glyph does not mean a different Greek letter.

\boxed{\hspace{6em}\mathclap{\Huge Ζ\qquad ζ}\hspace{6em}\vphantom{\Huge \int}}

NAME Zeta

SAY

UK ZEE-tuh

US ZAY-tuh

READ ALOUD

\zeta(s)

“Zeta of s.”

PLAIN TEXT \zeta\

LATEX \\\zeta\

COMMONLY USED FOR Functions and variables.

On Riemann Console, this is one of the important ones.

The Riemann zeta function is written

\zeta(s).

For the longer story, see What is the Riemann zeta function?.

\boxed{\hspace{6em}\mathclap{\Huge Η\qquad η}\hspace{6em}\vphantom{\Huge \int}}

NAME Eta

SAY

UK EE-tuh

US AY-tuh

READ ALOUD

\eta=1

“Eta equals one.”

PLAIN TEXT \eta\

LATEX \\\eta\

COMMONLY USED FOR Parameters, efficiencies and functions.

Look closely at the capital form.

Greek capital eta can look essentially identical to a Latin capital H.

The identity of a mathematical letter therefore sometimes comes from its context, not merely its silhouette.

\boxed{\hspace{6em}\mathclap{\Huge Θ\qquad θ\qquad ϑ}\hspace{6em}\vphantom{\Huge \int}}

NAME Theta

SAY

UK THEE-tuh

US THAY-tuh

READ ALOUD

\sin\theta

“Sine theta.”

PLAIN TEXT \theta\

LATEX \\\theta\ Variant: \\\vartheta\

COMMONLY USED FOR Angles and parameters.

Theta is one of the most familiar angle symbols in mathematics.

The lowercase forms $\theta$ and $\vartheta$ are conventional glyph variants.

\boxed{\hspace{6em}\mathclap{\Huge Ι\qquad ι}\hspace{6em}\vphantom{\Huge \int}}

NAME Iota

SAY

UK / US eye-OH-tuh

READ ALOUD

\iota(x)

“Iota of x.”

PLAIN TEXT \iota\

LATEX \\\iota\

COMMONLY USED FOR Maps, embeddings, indices and parameters.

Capital iota is another Greek letter that may look indistinguishable from an ordinary Latin capital I.

\boxed{\hspace{6em}\mathclap{\Huge Κ\qquad κ}\hspace{6em}\vphantom{\Huge \int}}

NAME Kappa

SAY

UK / US KAP-uh

READ ALOUD

\kappa=2

“Kappa equals two.”

PLAIN TEXT \kappa\

LATEX \\\kappa\

COMMONLY USED FOR Curvature, condition numbers and parameters.

\boxed{\hspace{6em}\mathclap{\Huge Λ\qquad λ}\hspace{6em}\vphantom{\Huge \int}}

NAME Lambda

SAY

UK / US LAM-duh

READ ALOUD

Av=\lambda v

“A v equals lambda v.”

PLAIN TEXT \lambda\

LATEX \\\lambda\ Capital: \\\Lambda\

COMMONLY USED FOR Eigenvalues, wavelengths, measures, parameters and functions.

Lambda has an extraordinary number of mathematical lives.

In linear algebra it is especially familiar as an eigenvalue.

\boxed{\hspace{6em}\mathclap{\Huge Μ\qquad μ}\hspace{6em}\vphantom{\Huge \int}}

NAME Mu

SAY

UK MYOO

US MOO

READ ALOUD

\mu=0

“Mu equals zero.”

PLAIN TEXT \mu\

LATEX \\\mu\

COMMONLY USED FOR Means, measures, coefficients and parameters.

The same symbol also appears in the SI prefix micro-.

\boxed{\hspace{6em}\mathclap{\Huge Ν\qquad ν}\hspace{6em}\vphantom{\Huge \int}}

NAME Nu

SAY

UK NYOO

US NOO

READ ALOUD

\nu=3

“Nu equals three.”

PLAIN TEXT \nu\

LATEX \\\nu\

COMMONLY USED FOR Parameters, frequencies and degrees.

DON'T CONFUSE

Lowercase nu,

\nu,

can look remarkably like an italic Latin $v$ .

\boxed{\hspace{6em}\mathclap{\Huge Ξ\qquad ξ}\hspace{6em}\vphantom{\Huge \int}}

NAME Xi

SAY

UK SIGH · ZIGH · K-SIGH · KSEE

US SIGH · ZIGH

PRONUNCIATION NOTE Xi has unusually broad established variation in English. You may hear speakers preserve the initial consonant sound, soften or omit it, or use a different final vowel. [6, 7]

Riemann Console generally uses SIGH in its explanatory prose.

READ ALOUD

\xi(s)

“Xi of s.”

\Xi(t)

“Capital xi of t.”

PLAIN TEXT \xi\

LATEX \\\xi\ Capital: \\\Xi\

COMMONLY USED FOR Variables and special functions.

Xi is especially important on Riemann Console.

The completed xi function is commonly written

\xi(s),

while the corresponding real-variable form is often written

\Xi(t).

(Xi is a useful warning against assuming that every mathematical word has one internationally fixed English pronunciation. It does not.)

See What is the Riemann xi function?.

\boxed{\hspace{6em}\mathclap{\Huge Ο\qquad ο}\hspace{6em}\vphantom{\Huge \int}}

NAME Omicron

SAY

UK oh-MY-kron · OM-i-kron

US Common forms include AH-mi-krahn and OH-mi-krahn

PRONUNCIATION NOTE Omicron has substantial variation in ordinary English. Mathematical usage does not require one unique English pronunciation. [8]

READ ALOUD

If an author genuinely uses omicron as a variable,

o_n

might be read:

“Omicron sub n.”

PLAIN TEXT \omicron\

LATEX There is normally no need for a distinct mathematical omicron command because its glyphs coincide with Latin O and o.

COMMONLY USED FOR Comparatively uncommon as a distinct mathematical variable.

That rarity has a practical reason.

Its capital and lowercase forms look essentially like Latin O and o.

\boxed{\hspace{6em}\mathclap{\Huge Π\qquad π\qquad ϖ}\hspace{6em}\vphantom{\Huge \int}}

NAME Pi

SAY

UK / US PIE

READ ALOUD

\pi=3.14159265\ldots

“Pi equals three point one four one five nine two six five, and so on.”

PLAIN TEXT \pi\

LATEX \\\pi\ Capital: \\\Pi\ Variant: \\\varpi\

COMMONLY USED FOR The circle constant, variables and related notation.

Lowercase $\pi$ is one of the most famous symbols in mathematics.

Capital pi also gives its shape to the product operator

\prod,

which we will meet later.

\boxed{\hspace{6em}\mathclap{\Huge Ρ\qquad ρ\qquad ϱ}\hspace{6em}\vphantom{\Huge \int}}

NAME Rho

SAY

UK / US ROH

READ ALOUD

\rho=0.9

“Rho equals zero point nine.”

PLAIN TEXT \rho\

LATEX \\\rho\ Variant: \\\varrho\

COMMONLY USED FOR Density, correlation and parameters.

DON'T CONFUSE

Capital rho resembles a Latin capital P.

\boxed{\hspace{6em}\mathclap{\Huge Σ\qquad σ\qquad ς}\hspace{6em}\vphantom{\Huge \int}}

NAME Sigma

SAY

UK / US SIG-muh

READ ALOUD

\sigma=2

“Sigma equals two.”

PLAIN TEXT \sigma\

LATEX \\\sigma\ Capital: \\\Sigma\

COMMONLY USED FOR Standard deviation, parameters and sums.

The form $\varsigma$ , corresponding to Greek final sigma, is the form used at the end of a word in ordinary Greek. It is not normally treated as a separate mathematical letter.

Capital sigma also gives us one of the great mathematical operators:

\sum.

That symbol is no longer merely a letter.

It is an instruction to add.

\boxed{\hspace{6em}\mathclap{\Huge Τ\qquad τ}\hspace{6em}\vphantom{\Huge \int}}

NAME Tau

SAY

UK / US TOW, rhyming with “cow”

READ ALOUD

\tau=2\pi

“Tau equals two pi.”

PLAIN TEXT \tau\

LATEX \\\tau\

COMMONLY USED FOR Time constants, parameters and variables.

Tau has also been proposed as a circle constant equal to $2\pi$ , although $\pi$ remains the overwhelmingly familiar convention.

\boxed{\hspace{6em}\mathclap{\Huge Υ\qquad υ}\hspace{6em}\vphantom{\Huge \int}}

NAME Upsilon

SAY

UK YOOP-si-luhn · yoop-SIGH-luhn

US UP-suh-lahn

PRONUNCIATION NOTE Upsilon is another Greek-letter name whose established English pronunciation varies substantially. [9]

READ ALOUD

\Upsilon(x)

“Capital upsilon of x.”

PLAIN TEXT \upsilon\

LATEX \\\upsilon\ Capital: \\\Upsilon\

COMMONLY USED FOR Specialised variables and functions, particularly in advanced mathematics and physics.

\boxed{\hspace{6em}\mathclap{\Huge Φ\qquad φ\qquad ϕ}\hspace{6em}\vphantom{\Huge \int}}

NAME Phi

SAY

UK FIE

US FIE · FEE

PRONUNCIATION NOTE FIE is widely understood throughout English-speaking mathematics. FEE is also established, especially in American usage.

READ ALOUD

\phi(x)

“Phi of x.”

PLAIN TEXT \phi\

LATEX \\\phi\ Variant: \\\varphi\

COMMONLY USED FOR Angles, functions, mappings, potentials and the golden ratio.

The two lowercase shapes

\phi \qquad \varphi

are conventional forms of phi. An author may choose to use both for different objects, but if so that distinction comes from the author's notation.

\boxed{\hspace{6em}\mathclap{\Huge Χ\qquad χ}\hspace{6em}\vphantom{\Huge \int}}

NAME Chi

SAY

UK / US K-EYE

READ ALOUD

\chi^2

“Chi squared.”

PLAIN TEXT \chi\

LATEX \\\chi\

COMMONLY USED FOR Functions, variables, characteristic objects and statistical notation.

DON'T CONFUSE

Lowercase chi can resemble an italic Latin $x$ .

\boxed{\hspace{6em}\mathclap{\Huge Ψ\qquad ψ}\hspace{6em}\vphantom{\Huge \int}}

NAME Psi

SAY

UK PS-EYE · SIGH

US SIGH

READ ALOUD

\psi(x)

“Psi of x.”

PLAIN TEXT \psi\

LATEX \\\psi\ Capital: \\\Psi\

COMMONLY USED FOR Functions and variables, especially wavefunctions in physics.

\boxed{\hspace{6em}\mathclap{\Huge Ω\qquad ω}\hspace{6em}\vphantom{\Huge \int}}

NAME Omega

SAY

UK OH-mi-guh

US oh-MAY-guh · oh-MEG-uh

READ ALOUD

\omega=2\pi f

“Omega equals two pi f.”

PLAIN TEXT \omega\

LATEX \\\omega\ Capital: \\\Omega\

COMMONLY USED FOR Sets, probability spaces, angular frequency and parameters.

Capital omega, $\Omega$ , is also the SI symbol for the ohm in electrical contexts.

Now try reading some mathematics

Knowing the names of the letters is only the beginning.

Consider

\sum_{n=1}^{\infty}\frac{1}{n^2}.

You could describe its typography:

“Capital sigma, n equals one underneath, infinity above, one over n superscript two.”

But that is not how a mathematician would normally say it.

A natural reading is:

“The sum from n equals one to infinity of one over n squared.”

Likewise,

x\in\mathbb R

is not normally:

“x, element symbol, blackboard-bold R.”

It is:

“x is in the real numbers.”

Or simply:

“x is real.”

Mathematical speech is not dictation.

The symbols encode grammar.

Reading mathematics aloud means recovering it.

Arithmetic

\boxed{\hspace{6em}\mathclap{\Huge +}\hspace{6em}\vphantom{\Huge \int}}

NAME Plus sign

SAY

UK / US PLUS

READ ALOUD

2+3

“Two plus three.”

PLAIN TEXT \+\

LATEX \+\

MEANING Addition.

\boxed{\hspace{6em}\mathclap{\Huge -}\hspace{6em}\vphantom{\Huge \int}}

NAME Minus sign

SAY

UK / US MY-nus

READ ALOUD

5-2

“Five minus two.”

But

-3

is normally:

“Negative three.”

PLAIN TEXT \-\

LATEX \-\

MEANING Subtraction, negation or a negative quantity, depending on position.

The mathematical minus sign and the ordinary keyboard hyphen are not quite the same typographic character, although plain text commonly uses the hyphen as a substitute.

\boxed{\hspace{6em}\mathclap{\Huge \pm}\hspace{6em}\vphantom{\Huge \int}}

NAME Plus-or-minus sign

SAY

UK / US plus or MY-nus

READ ALOUD

x=3\pm0.1

“x equals three plus or minus zero point one.”

PLAIN TEXT \+/-\

LATEX \\\pm\

MEANING Both the positive and negative alternatives are being considered.

\boxed{\hspace{6em}\mathclap{\Huge \mp}\hspace{6em}\vphantom{\Huge \int}}

NAME Minus-or-plus sign

SAY

UK / US minus or plus

READ ALOUD

a\pm b,\qquad c\mp d

“a plus or minus b, and correspondingly c minus or plus d.”

PLAIN TEXT \-/+\

LATEX \\\mp\

MEANING Usually paired with $\pm$ to keep two linked choices coordinated.

\boxed{\hspace{6em}\mathclap{\Huge \times}\hspace{6em}\vphantom{\Huge \int}}

NAME Multiplication sign

SAY

UK / US times

READ ALOUD

3\times4

“Three times four.”

For dimensions,

\1920 × 1080\

is naturally read:

“Nineteen twenty by ten eighty.”

For a vector cross product, the same glyph may be read “cross”.

PLAIN TEXT \x\ or \\*\, depending on context

LATEX \\\times\

MEANING Multiplication, dimensions, Cartesian product, cross product or another context-defined operation.

\boxed{\hspace{6em}\mathclap{\Huge \cdot}\hspace{6em}\vphantom{\Huge \int}}

NAME Centred dot

SAY

UK / US dot

READ ALOUD

a\cdot b

Depending on context:

“a times b.”

“a dot b.”

or:

“the dot product of a and b.”

PLAIN TEXT \\*\

LATEX \\\cdot\

MEANING Context-dependent multiplication or product notation.

\boxed{\hspace{6em}\mathclap{\Huge *}\hspace{6em}\vphantom{\Huge \int}}

NAME Asterisk · star

SAY

UK / US AS-tuh-risk · star

READ ALOUD

In plain-text arithmetic,

\3 \* 4\

is usually:

“Three times four.”

But in higher mathematics the same mark may be read as “star” and can denote convolution, an adjoint or another author-defined operation.

PLAIN TEXT \\*\

LATEX \\*\ or a context-specific command

MEANING Highly context-dependent.

\boxed{\hspace{6em}\mathclap{\Huge \div}\hspace{6em}\vphantom{\Huge \int}}

NAME Division sign

SAY

UK / US di-VY-did by when read as an operation

READ ALOUD

6\div2

“Six divided by two.”

PLAIN TEXT \/\

LATEX \\\div\

MEANING Division.

\boxed{\hspace{6em}\mathclap{\Huge /}\hspace{6em}\vphantom{\Huge \int}}

NAME Slash

SAY

UK / US SLASH

READ ALOUD

a/b

Often:

“a over b.”

Or:

“a divided by b.”

In units, \/\ is often read:

“per.”

PLAIN TEXT \/\

LATEX \/\

MEANING Division, ratio, “per”, or another context-defined separation.

\boxed{\hspace{6em}\mathclap{\Huge \%}\hspace{6em}\vphantom{\Huge \int}}

NAME Percent sign

SAY

UK / US per SENT

READ ALOUD

25\%

“Twenty-five percent.”

PLAIN TEXT \%\

LATEX \\\%\

MEANING Per hundred.

Equality and comparison

\boxed{\hspace{6em}\mathclap{\Huge =}\hspace{6em}\vphantom{\Huge \int}}

NAME Equals sign

SAY

UK / US EE-kwulz

READ ALOUD

x=4

“x equals four.”

Or:

“x is equal to four.”

PLAIN TEXT \=\

LATEX \=\

MEANING The two sides have equal value.

\boxed{\hspace{6em}\mathclap{\Huge \ne}\hspace{6em}\vphantom{\Huge \int}}

NAME Not-equal sign

SAY

UK / US not equal to

READ ALOUD

x\ne0

“x does not equal zero.”

Or:

“x is not equal to zero.”

PLAIN TEXT \\!=\

LATEX \\\ne\ or \\\neq\

\boxed{\hspace{6em}\mathclap{\Huge <\qquad >}\hspace{6em}\vphantom{\Huge \int}}

NAME Less-than sign · Greater-than sign

SAY

UK / US less than · greater than

READ ALOUD

3<5

“Three is less than five.”

x>0

“x is greater than zero.”

PLAIN TEXT \\<\ · \\>\

LATEX \\<\ · \\>\

\boxed{\hspace{6em}\mathclap{\Huge \le\qquad \ge}\hspace{6em}\vphantom{\Huge \int}}

NAME Less-than-or-equal sign · Greater-than-or-equal sign

SAY

UK / US less than or equal to · greater than or equal to

READ ALOUD

x\le5

“x is less than or equal to five.”

y\ge0

“y is greater than or equal to zero.”

PLAIN TEXT \\<=\ · \\>=\

LATEX \\\le\ · \\\ge\

\boxed{\hspace{6em}\mathclap{\Huge \ll\qquad\gg}\hspace{6em}\vphantom{\Huge \int}}

NAME Much-less-than sign · Much-greater-than sign

SAY

UK / US much less than · much greater than

READ ALOUD

a\ll b

“a is much less than b.”

a\gg b

“a is much greater than b.”

PLAIN TEXT \\<\<\ · \\>\>\ where the context is unambiguous

LATEX \\\ll\ · \\\gg\

MEANING Usually a strong size comparison.

CONTEXT NOTE In analytic number theory, $\ll$ also appears as Vinogradov notation, closely related to big-O notation.

\boxed{\hspace{6em}\mathclap{\Huge \approx}\hspace{6em}\vphantom{\Huge \int}}

NAME Approximately-equal sign

SAY

UK / US approximately equal to

READ ALOUD

\pi\approx3.14159

“Pi is approximately equal to three point one four one five nine.”

PLAIN TEXT \\~=\ is sometimes used informally

LATEX \\\approx\

MEANING The values are close enough for the purpose at hand, rather than exactly equal.

\boxed{\hspace{6em}\mathclap{\Huge \sim}\hspace{6em}\vphantom{\Huge \int}}

NAME Tilde

SAY

UK / US TIL-duh

READ ALOUD

This depends strongly on context.

f(x)\sim g(x)

may be read:

“f of x is asymptotic to g of x.”

But

X\sim N(0,1)

is naturally read:

“X is distributed as N zero one.”

PLAIN TEXT \\~\

LATEX \\\sim\

MEANING Context-dependent: asymptotic relation, distribution, similarity, equivalence relation or another author-defined relation.

The word tilde tells you what the glyph is called.

It does not, by itself, tell you what the mathematics means.

\boxed{\hspace{6em}\mathclap{\Huge \equiv}\hspace{6em}\vphantom{\Huge \int}}

NAME Triple bar · equivalence or congruence symbol

SAY

UK / US equivalent, congruent or identically equal, depending on use

READ ALOUD

17\equiv2\pmod 5

“Seventeen is congruent to two modulo five.”

Elsewhere,

f(x)\equiv0

may be read:

“f of x is identically zero.”

PLAIN TEXT No single universal substitute; describe the relation if necessary.

LATEX \\\equiv\

MEANING Context-dependent equivalence, congruence, identity or definition.

See Modular arithmetic and Residue class.

\boxed{\hspace{6em}\mathclap{\Huge \propto}\hspace{6em}\vphantom{\Huge \int}}

NAME Proportional-to sign

SAY

UK / US pro-POR-shuh-nuhl to

READ ALOUD

y\propto x^2

“y is proportional to x squared.”

PLAIN TEXT \proportional to\

LATEX \\\propto\

Powers, roots and little marks

Some of the most important notation is not a whole new symbol.

It is something attached to another one.

x^2

NAME Superscript · exponent

SAY

UK / US SOO-per-script · EK-spoh-nent

READ ALOUD

x^2

“x squared.”

x^3

“x cubed.”

x^n

“x to the power n.”

Or:

“x to the n.”

PLAIN TEXT \x^2\ · \x^n\

LATEX \x^2\ · \x^n\

x_n

NAME Subscript

SAY

UK / US SUB-script

READ ALOUD

x_n

“x sub n.”

In a context where the indexing is obvious, mathematicians may simply say:

“x n.”

PLAIN TEXT \x\_n\

LATEX \x\_n\

\boxed{\hspace{6em}\mathclap{\Huge \sqrt{\phantom{x}}}\hspace{6em}\vphantom{\Huge \int}}

NAME Radical sign · square-root sign

SAY

UK / US RAD-i-kuhl sign · square root sign

READ ALOUD

\sqrt9

“The square root of nine.”

\sqrt[n]{x}

“The nth root of x.”

PLAIN TEXT \sqrt(x)\

LATEX \\\sqrt{x}\

\boxed{\hspace{6em}\mathclap{\Huge !}\hspace{6em}\vphantom{\Huge \int}}

NAME Factorial sign, when used after a number

SAY

UK / US fak-TOR-ee-uhl

READ ALOUD

5!

“Five factorial.”

PLAIN TEXT \\!\

LATEX \\!\

MEANING For a positive integer,

5!=5\times4\times3\times2\times1.

The exclamation mark has very different jobs in ordinary prose and programming.

\boxed{\hspace{6em}\mathclap{\Huge '}\hspace{6em}\vphantom{\Huge \int}}

NAME Prime

SAY

UK / US PRIME

READ ALOUD

f'(x)

“f prime of x.”

f''(x)

“f double prime of x.”

PLAIN TEXT \f'\ · \f''\

LATEX \f'\ · \f''\

\hat{x}

NAME Hat

SAY

UK / US HAT

READ ALOUD

\hat{x}

“x hat.”

PLAIN TEXT \x-hat\

LATEX \\\hat{x}\

COMMONLY USED FOR Estimates and transformed or specially distinguished quantities.

Its exact meaning depends on the subject.

\bar{x}

NAME Bar · overbar

SAY

UK / US BAR · OH-ver-bar

READ ALOUD

\bar{x}

“x bar.”

PLAIN TEXT \x-bar\

LATEX \\\bar{x}\ or \\\overline{x}\

READ ALOUD — COMPLEX ANALYSIS

\bar z

“z bar.”

Or, semantically:

“The complex conjugate of z.”

COMMONLY USED FOR Means, complex conjugates and other context-defined transformations.

In statistics, $\bar{x}$ commonly denotes a sample mean.

In complex analysis, an overbar may denote complex conjugation.

\tilde{x}

NAME Tilde

SAY

UK / US TIL-duh

READ ALOUD

\tilde{x}

“x tilde.”

PLAIN TEXT \x-tilde\

LATEX \\\tilde{x}\

MEANING Entirely context-dependent.

\dot{x}

NAME Dot

SAY

UK / US DOT

READ ALOUD

\dot{x}

“x dot.”

\ddot{x}

“x double dot.”

PLAIN TEXT \x-dot\

LATEX \\\dot{x}\ · \\\ddot{x}\

COMMONLY USED FOR Derivatives with respect to time, especially in mechanics.

The large operators

\boxed{\hspace{6em}\mathclap{\Huge \sum}\hspace{6em}\vphantom{\Huge \int}}

NAME Summation sign

SAY

UK / US suh-MAY-shun sign

It is also commonly referred to simply as:

sigma

READ ALOUD

\sum_{n=1}^{10} n

“The sum from n equals one to ten of n.”

PLAIN TEXT \sum\

LATEX \\\sum\

MEANING Add a sequence of terms.

Its shape comes from capital sigma, $\Sigma$ .

\boxed{\hspace{6em}\mathclap{\Huge \prod}\hspace{6em}\vphantom{\Huge \int}}

NAME Product sign

SAY

UK / US PROD-ukt sign

READ ALOUD

\prod_{k=1}^{n}a_k

“The product from k equals one to n of a sub k.”

PLAIN TEXT \product\ or \prod\

LATEX \\\prod\

MEANING Multiply a sequence of terms.

Its shape comes from capital pi, $\Pi$ .

\boxed{\hspace{6em}\mathclap{\Huge \int}\hspace{6em}\vphantom{\Huge \int}}

NAME Integral sign

SAY

UK / US IN-ti-gruhl

READ ALOUD

\int_a^b f(x)\,dx

“The integral from a to b of f of x d x.”

PLAIN TEXT \integral\

LATEX \\\int\

MEANING Integration.

Leibniz's integral sign was a long s, for Latin summa — sum. [10]

\boxed{\hspace{6em}\mathclap{\Huge \iint}\hspace{6em}\vphantom{\Huge \int}}

NAME Double integral

SAY

UK / US double integral

READ ALOUD

\iint_R f(x,y)\,dA

“The double integral over R of f of x y d A.”

PLAIN TEXT \double integral\

LATEX \\\iint\

\boxed{\hspace{6em}\mathclap{\Huge \oint}\hspace{6em}\vphantom{\Huge \int}}

NAME Contour integral · closed integral

SAY

UK / US CON-tour integral · closed integral

READ ALOUD

\oint_C f(z)\,dz

“The contour integral around C of f of z d z.”

PLAIN TEXT \contour integral\

LATEX \\\oint\

The small circle indicates integration around a closed contour.

Calculus and analysis

\frac{d}{dx}

NAME Derivative operator

SAY

UK / US d by d x

READ ALOUD

\frac{d}{dx}f(x)

“d by d x of f of x.”

Or, more naturally:

“The derivative of f with respect to x.”

PLAIN TEXT \d/dx\

LATEX \\\frac{d}{dx}\

\boxed{\hspace{6em}\mathclap{\Huge \partial}\hspace{6em}\vphantom{\Huge \int}}

NAME Partial-derivative symbol

SAY

UK / US PAR-shuhl

READ ALOUD

\frac{\partial f}{\partial x}

“Partial f over partial x.”

Or:

“The partial derivative of f with respect to x.”

PLAIN TEXT \partial\

LATEX \\\partial\

COMMONLY USED FOR Partial derivatives.

You may hear the glyph described informally as a “curly d”.

But partial is the useful mathematical reading.

\boxed{\hspace{6em}\mathclap{\Huge \nabla}\hspace{6em}\vphantom{\Huge \int}}

NAME Nabla

SAY

UK / US NAB-luh

ALSO CALLED Del

READ ALOUD

\nabla f

Often:

“Grad f.”

Or:

“The gradient of f.”

It may also be read literally as:

“Nabla f.”

PLAIN TEXT \nabla\ or \del\

LATEX \\\nabla\

COMMONLY USED FOR Gradient, divergence and curl in vector calculus.

The name nabla was suggested in the nineteenth century because the inverted triangular form was compared with the shape of an ancient harp. [11]

This triangular symbol is particularly useful because its name and its natural reading inside an expression may be different.

The symbol is called nabla.

But if

\nabla f

means the gradient of $f$ , a mathematician may simply say:

“the gradient of f.”

That distinction will keep returning.

A symbol has a shape, a name, a reading and a meaning — and those are not always the same thing.

\boxed{\hspace{6em}\mathclap{\Huge \infty}\hspace{6em}\vphantom{\Huge \int}}

NAME Infinity sign

SAY

UK / US in-FIN-i-tee

READ ALOUD

n\to\infty

“n tends to infinity.”

PLAIN TEXT \infinity\ or sometimes \inf\

LATEX \\\infty\

Infinity is not simply an ordinary real number hiding at the far end of the number line. Its precise role depends on the mathematical setting.

\lim_{x\to a}

NAME Limit

SAY

UK / US LIM-it

READ ALOUD

\lim_{x\to a}f(x)

“The limit as x tends to a of f of x.”

PLAIN TEXT \lim x-\>a\

LATEX \\\lim\_{x\\to a}\

Big O and little o

O(f(x))

NAME Big O notation

SAY

UK / US big OH

READ ALOUD

g(x)=O(f(x))

“g of x is big O of f of x.”

PLAIN TEXT \O(f(x))\

LATEX \O(f(x))\

MEANING An asymptotic bound: roughly, $g$ does not grow faster than a constant multiple of $f$ in the stated limiting regime.

o(f(x))

NAME Little o notation

SAY

UK / US little OH

READ ALOUD

g(x)=o(f(x))

“g of x is little o of f of x.”

PLAIN TEXT \o(f(x))\

LATEX \o(f(x))\

MEANING A stronger asymptotic statement: $g$ becomes negligible compared with $f$ in the stated limiting regime.

Real part, imaginary part and argument

\operatorname{Re}(z)\qquad \operatorname{Im}(z)\qquad \arg z

NAME Real part · Imaginary part · Argument

SAY

UK / US real part · imaginary part · AR-gyuh-ment

READ ALOUD

\operatorname{Re}(z)

“The real part of z.”

\operatorname{Im}(z)

“The imaginary part of z.”

\arg z

“The argument of z.”

PLAIN TEXT \Re(z)\ · \Im(z)\ · \arg(z)\

LATEX \\\operatorname{Re}(z)\ · \\\operatorname{Im}(z)\ · \\\arg z\

COMMONLY USED FOR Complex numbers and complex analysis.

Arrows

Arrows are deceptively simple.

They are also some of the most grammatical symbols in mathematics.

\boxed{\hspace{6em}\mathclap{\Huge \to}\hspace{6em}\vphantom{\Huge \int}}

NAME Right arrow

SAY

UK / US right arrow

READ ALOUD

x\to0

“x tends to zero.”

But:

f:A\to B

may be read:

“f from A to B.”

Or:

“f maps A to B.”

PLAIN TEXT \-\>\

LATEX \\\to\

MEANING Context-dependent: tendency, mapping, transformation, transition or another directed relation.

The symbol is a right arrow.

That does not mean you should say “right arrow” every time you meet it.

\boxed{\hspace{6em}\mathclap{\Huge \mapsto}\hspace{6em}\vphantom{\Huge \int}}

NAME Maps-to arrow

SAY

UK / US maps to

READ ALOUD

x\mapsto x^2

“x maps to x squared.”

PLAIN TEXT \|-\>\

LATEX \\\mapsto\

\boxed{\hspace{6em}\mathclap{\Huge \circ}\hspace{6em}\vphantom{\Huge \int}}

NAME Composition symbol · small circle

SAY

UK / US composition · circle

READ ALOUD

f\circ g

“f composed with g.”

You may also hear:

“f circle g.”

PLAIN TEXT \compose(f,g)\ when plain text must be explicit

LATEX \f\\circ g\

MEANING Function composition in this context.

\boxed{\hspace{6em}\mathclap{\Huge \Rightarrow}\hspace{6em}\vphantom{\Huge \int}}

NAME Double right arrow · implication arrow

SAY

UK / US implies

READ ALOUD

P\Rightarrow Q

“P implies Q.”

PLAIN TEXT \=\>\

LATEX \\\Rightarrow\

\boxed{\hspace{6em}\mathclap{\Huge \Leftrightarrow}\hspace{6em}\vphantom{\Huge \int}}

NAME Double implication arrow

SAY

UK / US if and only if

READ ALOUD

P\Leftrightarrow Q

“P if and only if Q.”

Mathematicians often abbreviate if and only if in writing as:

iff

PLAIN TEXT \\<=\>\

LATEX \\\Leftrightarrow\

\boxed{\hspace{6em}\mathclap{\Huge \leftarrow}\hspace{6em}\vphantom{\Huge \int}}

NAME Left arrow

SAY

UK / US left arrow

READ ALOUD Its natural reading depends on context. It may indicate a left-directed map, a limiting direction, or — in computing and pseudocode — assignment.

PLAIN TEXT \\<-\

LATEX \\\leftarrow\

\boxed{\hspace{6em}\mathclap{\Huge \leftrightarrow}\hspace{6em}\vphantom{\Huge \int}}

NAME Left-right arrow

SAY

UK / US left-right arrow

READ ALOUD Depending on context: “corresponds to”, “is in correspondence with”, or another explicitly defined bidirectional relation.

PLAIN TEXT \\<-\>\

LATEX \\\leftrightarrow\

\boxed{\hspace{6em}\mathclap{\Huge \Leftarrow}\hspace{6em}\vphantom{\Huge \int}}

NAME Double left arrow · reverse implication arrow

SAY

UK / US is implied by

READ ALOUD

P\Leftarrow Q

“P is implied by Q.”

Or:

“Q implies P.”

PLAIN TEXT Write \is implied by\ when plain text matters.

LATEX \\\Leftarrow\

Geometry

\boxed{\hspace{6em}\mathclap{\Huge \angle}\hspace{6em}\vphantom{\Huge \int}}

NAME Angle sign

SAY

UK / US angle

READ ALOUD

\angle ABC

“Angle A B C.”

PLAIN TEXT \angle ABC\

LATEX \\\angle ABC\

\boxed{\hspace{6em}\mathclap{\Huge ^\circ}\hspace{6em}\vphantom{\Huge \int}}

NAME Degree sign

SAY

UK / US degree

READ ALOUD

90^\circ

“Ninety degrees.”

PLAIN TEXT \90 degrees\

LATEX \90^\\circ\

\boxed{\hspace{6em}\mathclap{\Huge \cong}\hspace{6em}\vphantom{\Huge \int}}

NAME Congruent-to sign

SAY

UK / US congruent to

READ ALOUD

\triangle ABC\cong\triangle DEF

“Triangle A B C is congruent to triangle D E F.”

In other branches of mathematics, the same or a closely related symbol may be read as “isomorphic to”.

PLAIN TEXT \congruent to\

LATEX \\\cong\

MEANING Context-dependent equivalence; in elementary geometry, congruence.

Sets

\boxed{\hspace{6em}\mathclap{\Huge \in}\hspace{6em}\vphantom{\Huge \int}}

NAME Element-of sign

SAY

UK / US element of

READ ALOUD

x\in A

Most naturally:

“x is in A.”

Also:

“x belongs to A.”

Or, more literally:

“x is an element of A.”

PLAIN TEXT \in\

LATEX \\\in\

This is a particularly good example of why the name of a glyph and the natural reading of an expression are not necessarily identical.

\boxed{\hspace{6em}\mathclap{\Huge \notin}\hspace{6em}\vphantom{\Huge \int}}

NAME Not-an-element-of sign

SAY

UK / US not an element of

READ ALOUD

x\notin A

“x is not in A.”

Or:

“x does not belong to A.”

PLAIN TEXT \not in\

LATEX \\\notin\

\boxed{\hspace{6em}\mathclap{\Huge \subset\qquad \subseteq}\hspace{6em}\vphantom{\Huge \int}}

NAME Subset signs

SAY

UK / US subset of · subset of or equal to

READ ALOUD

A\subseteq B

“A is a subset of B.”

Or:

“A is contained in B.”

PLAIN TEXT \subset\ · \subseteq\

LATEX \\\subset\ · \\\subseteq\

PRONUNCIATION / CONVENTION NOTE Authors do not all use $\subset$ in exactly the same way.

Some reserve it for a proper subset.

Others use it where equality may also be possible.

The form $\subseteq$ explicitly allows equality.

When the distinction matters, check the author's convention.

\boxed{\hspace{6em}\mathclap{\Huge \supset\qquad\supseteq}\hspace{6em}\vphantom{\Huge \int}}

NAME Superset signs

SAY

UK / US superset of · superset of or equal to

READ ALOUD

A\supseteq B

“A is a superset of B.”

Or:

“A contains B.”

PLAIN TEXT \superset\ · \superseteq\

LATEX \\\supset\ · \\\supseteq\

As with subset notation, conventions about the strict-looking form are not perfectly uniform. Check the author's convention when the distinction matters.

\boxed{\hspace{6em}\mathclap{\Huge \cup}\hspace{6em}\vphantom{\Huge \int}}

NAME Union

SAY

UK / US YOO-nee-un

READ ALOUD

A\cup B

“A union B.”

PLAIN TEXT \union\

LATEX \\\cup\

MEANING The elements that are in A, B, or both.

\boxed{\hspace{6em}\mathclap{\Huge \cap}\hspace{6em}\vphantom{\Huge \int}}

NAME Intersection

SAY

UK / US in-ter-SEK-shun

READ ALOUD

A\cap B

“A intersection B.”

PLAIN TEXT \intersection\

LATEX \\\cap\

MEANING The elements common to both sets.

\boxed{\hspace{6em}\mathclap{\Huge \setminus}\hspace{6em}\vphantom{\Huge \int}}

NAME Set-difference sign

SAY

UK / US set minus

READ ALOUD

A\setminus B

“A set minus B.”

You may also hear:

“A without B.”

PLAIN TEXT \A \\ B\ where the context is clear

LATEX \A\\setminus B\

MEANING The elements in $A$ that are not in $B$ .

\boxed{\hspace{6em}\mathclap{\Huge \varnothing}\hspace{6em}\vphantom{\Huge \int}}

NAME Empty-set symbol

SAY

UK / US empty set

READ ALOUD

A=\varnothing

“A is the empty set.”

PLAIN TEXT \empty set\ or sometimes \{}\ where the meaning is unambiguous

LATEX \\\varnothing\ or \\\emptyset\

MEANING A set containing no elements.

DON'T CONFUSE

\varnothing \qquad \phi \qquad 0

can look surprisingly similar at a glance.

They are not the same symbol.

\boxed{\hspace{6em}\mathclap{\Huge \{\qquad \}}\hspace{6em}\vphantom{\Huge \int}}

NAME Braces · curly brackets

SAY

UK / US BRAY-siz · curly brackets

READ ALOUD

\{1,2,3\}

“The set one, two, three.”

And:

\{x:x>0\}

“The set of x such that x is greater than zero.”

PLAIN TEXT \{ }\

LATEX \\\{\ · \\\}\

Braces can stretch vertically when they enclose taller mathematics.

Logic

\boxed{\hspace{6em}\mathclap{\Huge \forall}\hspace{6em}\vphantom{\Huge \int}}

NAME Universal quantifier

SAY

UK / US universal quantifier

READ ALOUD

\forall x\in\mathbb R

“For all x in the real numbers.”

Or:

“For every x in the real numbers.”

PLAIN TEXT \for all\

LATEX \\\forall\

\boxed{\hspace{6em}\mathclap{\Huge \exists}\hspace{6em}\vphantom{\Huge \int}}

NAME Existential quantifier

SAY

UK / US existential quantifier

READ ALOUD

\exists x

“There exists an x.”

PLAIN TEXT \there exists\

LATEX \\\exists\

\boxed{\hspace{6em}\mathclap{\Huge \nexists}\hspace{6em}\vphantom{\Huge \int}}

NAME There-does-not-exist sign

SAY

UK / US there does not exist

READ ALOUD

\nexists x

“There does not exist an x.”

PLAIN TEXT \there does not exist\

LATEX \\\nexists\

\boxed{\hspace{6em}\mathclap{\Huge \neg}\hspace{6em}\vphantom{\Huge \int}}

NAME Negation sign

SAY

UK / US nee-GAY-shun sign

READ ALOUD

\neg P

“Not P.”

PLAIN TEXT \not\

LATEX \\\neg\

\boxed{\hspace{6em}\mathclap{\Huge \land}\hspace{6em}\vphantom{\Huge \int}}

NAME Logical conjunction

SAY

UK / US conjunction

READ ALOUD

P\land Q

“P and Q.”

PLAIN TEXT \and\

LATEX \\\land\

\boxed{\hspace{6em}\mathclap{\Huge \lor}\hspace{6em}\vphantom{\Huge \int}}

NAME Logical disjunction

SAY

UK / US disjunction

READ ALOUD

P\lor Q

“P or Q.”

PLAIN TEXT \or\

LATEX \\\lor\

The familiar number systems

These symbols use blackboard-bold lettering.

They are letters, but in mathematical writing they conventionally name familiar sets of numbers.

\boxed{\hspace{6em}\mathclap{\Huge \mathbb N}\hspace{6em}\vphantom{\Huge \int}}

NAME Blackboard-bold N

SAY

UK / US blackboard-bold N

READ ALOUD

n\in\mathbb N

“n is a natural number.”

Or:

“n is in the natural numbers.”

PLAIN TEXT \N\

LATEX \\\mathbb{N}\

MEANING The natural numbers.

A convention warning belongs here.

Some authors include zero in $\mathbb N$ .

Others begin at one.

\boxed{\hspace{6em}\mathclap{\Huge \mathbb Z}\hspace{6em}\vphantom{\Huge \int}}

NAME Blackboard-bold Z

SAY

UK blackboard-bold ZED

US blackboard-bold ZEE

READ ALOUD

n\in\mathbb Z

“n is an integer.”

Or:

“n is in the integers.”

PLAIN TEXT \Z\

LATEX \\\mathbb{Z}\

MEANING The integers.

The choice of Z is historically associated with the German Zahlen — numbers.

\boxed{\hspace{6em}\mathclap{\Huge \mathbb Q}\hspace{6em}\vphantom{\Huge \int}}

NAME Blackboard-bold Q

SAY

UK / US blackboard-bold Q

READ ALOUD

q\in\mathbb Q

“q is rational.”

Or:

“q is in the rational numbers.”

PLAIN TEXT \Q\

LATEX \\\mathbb{Q}\

MEANING The rational numbers.

Q usefully suggests quotient: a ratio of integers.

\boxed{\hspace{6em}\mathclap{\Huge \mathbb R}\hspace{6em}\vphantom{\Huge \int}}

NAME Blackboard-bold R

SAY

UK / US blackboard-bold R

READ ALOUD

x\in\mathbb R

“x is real.”

Or:

“x is in the real numbers.”

PLAIN TEXT \R\

LATEX \\\mathbb{R}\

MEANING The real numbers.

\boxed{\hspace{6em}\mathclap{\Huge \mathbb C}\hspace{6em}\vphantom{\Huge \int}}

NAME Blackboard-bold C

SAY

UK / US blackboard-bold C

READ ALOUD

z\in\mathbb C

“z is a complex number.”

Or:

“z is in the complex numbers.”

PLAIN TEXT \C\

LATEX \\\mathbb{C}\

MEANING The complex numbers.

See Complex number and Complex plane.

One innocent-looking bar

Now we come to one of the best examples in the whole guide.

\boxed{\hspace{6em}\mathclap{\Huge |}\hspace{6em}\vphantom{\Huge \int}}

NAME Vertical bar

SAY

UK / US VER-ti-kuhl bar

READ ALOUD

|x|

“The absolute value of x.”

For a complex number, you may instead hear:

“The modulus of x.”

a\mid b

“a divides b.”

\{x\mid x>0\}

“The set of x such that x is greater than zero.”

P(A\mid B)

“The probability of A given B.”

|A|

For a matrix $A$ :

“The determinant of A.”

|S|

For a finite set $S$ :

“The cardinality of S.”

Or:

“The size of S.”

PLAIN TEXT \|\

LATEX Depends on its role: for example \|x|\ or \\\mid\

MEANING Context-dependent.

One little line.

Several different mathematical readings.

The same basic glyph can take part in absolute value, modulus, divisibility, set-builder notation, conditional probability, determinants and other specialised constructions.

So saying that \|\ is pronounced “vertical bar” is only half an answer.

That tells you what the mark is called.

It does not necessarily tell you what you should say when you encounter it in mathematics.

(A symbol has a shape, a name, a reading and a meaning — and those are not always the same thing.)

\boxed{\hspace{6em}\mathclap{\Huge \nmid}\hspace{6em}\vphantom{\Huge \int}}

NAME Does-not-divide sign

SAY

UK / US does not divide

READ ALOUD

a\nmid b

“a does not divide b.”

PLAIN TEXT \a does not divide b\

LATEX \a\\nmid b\

\boxed{\hspace{6em}\mathclap{\Huge \|}\hspace{6em}\vphantom{\Huge \int}}

NAME Double vertical bar

SAY

UK / US double vertical bar

READ ALOUD

\|x\|

“The norm of x.”

PLAIN TEXT \||x||\

LATEX \\\|x\\|\

COMMONLY USED FOR Norms and other magnitude-like constructions.

Do not confuse this use with the geometrical parallel symbol merely because the glyphs are visually related.

Colons, definitions and punctuation

\boxed{\hspace{6em}\mathclap{\Huge :}\hspace{6em}\vphantom{\Huge \int}}

NAME Colon

SAY

UK / US KOH-lun

READ ALOUD

\{x:x>0\}

“The set of x such that x is greater than zero.”

In other contexts the colon may not need to be spoken explicitly at all.

PLAIN TEXT \:\

LATEX \:\

MEANING Punctuation whose mathematical function depends on context.

\boxed{\hspace{6em}\mathclap{\Huge :=}\hspace{6em}\vphantom{\Huge \int}}

NAME Definition symbol

SAY

UK / US is defined as · is defined to be

READ ALOUD

f(x):=x^2+1

“f of x is defined to be x squared plus one.”

PLAIN TEXT \:=\

LATEX Often \:=\, or a specialised definition-relation command.

MEANING The expression on the left is being defined by the expression on the right.

Other symbols are also used for definitions.

Brackets

\boxed{\hspace{6em}\mathclap{\Huge (\qquad )}\hspace{6em}\vphantom{\Huge \int}}

NAME

UK: round brackets · brackets US: parentheses

SAY

UK round brackets

US par-EN-thuh-seez

READ ALOUD

f(x)

Not normally:

“f open parenthesis x close parenthesis.”

Simply:

“f of x.”

PLAIN TEXT \( )\

LATEX \(\ · \)\

Natural mathematical speech is not dictation.

\boxed{\hspace{6em}\mathclap{\Huge [\qquad ]}\hspace{6em}\vphantom{\Huge \int}}

NAME Square brackets

SAY

UK / US square brackets

READ ALOUD

When the punctuation itself has to be described:

“open square bracket”

and

“close square bracket.”

In an ordinary mathematical expression the grouping may instead be conveyed by the phrasing.

PLAIN TEXT \\[ \]\

LATEX \\[\ · \\]\

\boxed{\hspace{6em}\mathclap{\Huge \langle\qquad\rangle}\hspace{6em}\vphantom{\Huge \int}}

NAME Angle brackets

SAY

UK / US angle brackets

READ ALOUD

\langle u,v\rangle

In an inner-product context:

“The inner product of u and v.”

Elsewhere angle brackets may denote an ordered tuple, pairing or another author-defined construction.

PLAIN TEXT \\<u,v\>\ where context makes the use clear

LATEX \\\langle u,v\\rangle\

\boxed{\hspace{6em}\mathclap{\Huge \lfloor\qquad \rfloor}\hspace{6em}\vphantom{\Huge \int}}

NAME Floor brackets

SAY

UK / US floor

READ ALOUD

\lfloor x\rfloor

“The floor of x.”

PLAIN TEXT \floor(x)\

LATEX \\\lfloor x\\rfloor\

MEANING The greatest integer less than or equal to $x$ .

\boxed{\hspace{6em}\mathclap{\Huge \lceil\qquad \rceil}\hspace{6em}\vphantom{\Huge \int}}

NAME Ceiling brackets

SAY

UK / US SEE-ling

READ ALOUD

\lceil x\rceil

“The ceiling of x.”

PLAIN TEXT \ceil(x)\

LATEX \\\lceil x\\rceil\

MEANING The least integer greater than or equal to $x$ .

Dots

\boxed{\hspace{6em}\mathclap{\Huge \ldots}\hspace{6em}\vphantom{\Huge \int}}

NAME Ellipsis

SAY

UK / US ih-LIP-sis

READ ALOUD

1,2,3,\ldots

“One, two, three, and so on.”

Sometimes the dots are simply conveyed by a pause or by saying “continuing”.

PLAIN TEXT \...\

LATEX \\\ldots\

The dots are not a licence to guess.

In serious mathematics, the intended continuation must be clear from context.

\boxed{\hspace{6em}\mathclap{\Huge \cdots\qquad\vdots\qquad\ddots}\hspace{6em}\vphantom{\Huge \int}}

NAME Centred dots · Vertical dots · Diagonal dots

SAY

UK / US dots · vertical dots · diagonal dots

READ ALOUD Usually these are not dictated glyph by glyph. In a matrix or patterned expression they indicate that the visible pattern continues.

PLAIN TEXT \...\ plus a verbal description where direction matters

LATEX \\\cdots\ · \\\vdots\ · \\\ddots\

COMMONLY USED FOR Matrices, products, sequences and repeated patterns.

A few symbols with names of their own

\boxed{\hspace{6em}\mathclap{\Huge \perp}\hspace{6em}\vphantom{\Huge \int}}

NAME Perpendicular · orthogonality sign

SAY

UK / US per-pen-DIK-yuh-luh · or-THOG-uh-nuhl

READ ALOUD

a\perp b

“a is perpendicular to b.”

Or, in a more general setting:

“a is orthogonal to b.”

PLAIN TEXT \perp\

LATEX \\\perp\

\boxed{\hspace{6em}\mathclap{\Huge \parallel}\hspace{6em}\vphantom{\Huge \int}}

NAME Parallel sign

SAY

UK / US PAR-uh-lel

READ ALOUD

a\parallel b

“a is parallel to b.”

PLAIN TEXT \parallel\

LATEX \\\parallel\

DON'T CONFUSE

A visually similar pair of bars may form a norm:

\|x\|,

which is read:

“the norm of x.”

\boxed{\hspace{6em}\mathclap{\Huge \therefore}\hspace{6em}\vphantom{\Huge \int}}

NAME Therefore sign

SAY

UK / US THAIR-for

READ ALOUD

x=2\therefore x^2=4

“x equals two, therefore x squared equals four.”

PLAIN TEXT \therefore\

LATEX \\\therefore\

\boxed{\hspace{6em}\mathclap{\Huge \because}\hspace{6em}\vphantom{\Huge \int}}

NAME Because sign

SAY

UK / US bi-KOZ

READ ALOUD

The symbol is read:

“because.”

PLAIN TEXT \because\

LATEX \\\because\

It is much less common in modern formal mathematical prose than the therefore sign.

\boxed{\hspace{6em}\mathclap{\Huge \blacksquare}\hspace{6em}\vphantom{\Huge \int}}

NAME End-of-proof symbol

SAY

UK / US end-of-proof symbol

ALSO CALLED Tombstone · Halmos symbol

READ ALOUD

Usually nothing at all.

The symbol visually marks the end of a proof.

Conceptually, it can occupy the place once commonly filled by:

QED

from the Latin quod erat demonstrandum.

PLAIN TEXT \QED\

LATEX Often supplied automatically by a proof environment; \\\blacksquare\ produces the glyph directly.

A few marks that often appear around mathematics

Not every mark on a mathematical page is itself a mathematical operator.

But knowing what to call it can still be useful.

\boxed{\hspace{6em}\mathclap{\Huge \checkmark}\hspace{6em}\vphantom{\Huge \int}}

NAME Check mark · tick

SAY

UK TICK · check mark

US check mark

READ ALOUD

Usually it is not part of an equation to be spoken word by word.

In a table or list it may simply indicate:

“yes”,

“correct”,

“included”,

or another locally defined status.

PLAIN TEXT \check\ or \yes\

LATEX \\\checkmark\ where supported

\boxed{\hspace{6em}\mathclap{\Huge \S}\hspace{6em}\vphantom{\Huge \int}}

NAME Section sign

SAY

UK / US SEK-shun sign

READ ALOUD

\S 3

“Section three.”

PLAIN TEXT \section 3\

LATEX \\\S\

This is primarily a reference and publishing symbol rather than a mathematical operator, but it often appears in technical writing.

Reading whole expressions aloud

Now the symbols can become sentences.

A limit

\lim_{x\to a}f(x)=L.

Read aloud:

“The limit as x tends to a of f of x equals L.”

Not:

“lim sub x right-arrow a f open bracket x close bracket equals capital L.”

An integral

\int_0^\infty e^{-x}\,dx=1.

Read aloud:

“The integral from zero to infinity of e to the minus x d x equals one.”

Membership

z\in\mathbb C.

Read aloud:

“z is a complex number.”

Or:

“z is in the complex numbers.”

Quantifiers

\forall\varepsilon>0\;\exists\delta>0.

Read aloud:

“For every epsilon greater than zero, there exists a delta greater than zero.”

A sum

\sum_{n=1}^{\infty}\frac1{n^2}.

Read aloud:

“The sum from n equals one to infinity of one over n squared.”

A function

f:A\to B.

Read aloud:

“f maps A to B.”

The arrow has become a verb.

Conditional probability

P(A\mid B).

Read aloud:

“The probability of A given B.”

The vertical bar has become a word that is nowhere in its ordinary name.

That is why reading mathematics aloud is not simply a matter of memorising the names of shapes.

When symbols change size

Some mathematical symbols do not have one fixed visual size.

Compare:

(x+1)

with:

\left( \frac{a+b}{c+d} \right).

The parentheses grow because the expression inside them is taller.

Braces, vertical bars and radicals can behave similarly.

Large operators such as summation and integration signs may also take different visual forms in inline and displayed mathematics.

The specimen box in this guide therefore shows an isolated symbol under consistent conditions.

When the symbol changes shape or size in real mathematical use, we show that separately.

We do not distort the specimen itself.

Same shape, different meaning

Perhaps the most important lesson in this whole guide is that a mathematical symbol is rarely a little picture with one permanent translation.

Consider:

\sim.

It might express asymptotic behaviour.

It might say that a random variable follows a probability distribution.

It might denote similarity.

It might denote an equivalence relation defined by the author.

Or consider:

|.

We have already seen it participate in:

absolute value,

divisibility,

set-builder notation,

conditional probability.

Even an ordinary Greek letter can change jobs completely from one paper to another.

So there are several different questions:

What shape am I looking at?

What is it called?

How do I say that name?

How do I read this particular expression aloud?

What does it mean here?

Those questions are related.

They are not identical.

Pronunciation is convention, not mathematics

A British mathematician may say:

BEE-tuh

where an American mathematician says:

BAY-tuh.

One may say:

ZEE-tuh

where another says:

ZAY-tuh.

Epsilon has established alternatives even within British English.

Xi varies more dramatically still.

None of this alters the formula.

The English names used by mathematicians belong to spoken scholarly traditions that developed across countries, institutions and disciplines.

Modern Greek pronunciation is another subject again.

So this guide does not try to crown one accent mathematically correct.

Where one pronunciation strongly dominates, we give it plainly.

Where British and American usage differ, we show both.

Where several established English pronunciations coexist, we keep them visible.

The written mathematics is shared even when the spoken mathematics has an accent.

Typing mathematics when you cannot find the symbol

You do not always have a mathematical keyboard or symbol palette available.

If you are writing an email, searching the web, sending a message or making a rough note, clarity matters more than typography.

Useful plain-text forms include:

\alpha\, \beta\, \theta\, \xi\

\\<=\ for $\le$

\\>=\ for $\ge$

\\!=\ for $\ne$

\-\>\ for $\to$

\=\>\ for $\Rightarrow$

\\<=\>\ for $\Leftrightarrow$

\+/-\ for $\pm$

\sqrt(x)\ for $\sqrt{x}$

\sum\ for $\sum$

\integral\ for $\int$

\partial\ for $\partial$

\infinity\ or sometimes \inf\ for $\infty$

\R\, \C\, \Z\, \Q\, \N\ for the familiar number systems where the context is clear.

Those are communication fallbacks.

They are not replacements for properly typeset mathematics.

For mathematical authoring, LaTeX gives much greater precision.

That is why every entry in this guide includes both forms wherever useful.

A note about accessibility

For somebody reading mathematics visually, an entire expression can sometimes be recognised almost at once.

For somebody using speech output, its structure has to be turned into language.

That is not always trivial.

Consider again:

P(A\mid B).

A useful spoken rendering contains the word:

given

not merely:

“vertical bar”.

Likewise,

x^2

is naturally:

“x squared”

rather than:

“x superscript two”.

Accessible mathematical systems therefore need more than the visible character alone.

They need structure.

This distinction is reflected in modern accessibility work such as W3C MathML and MathCAT, where mathematical structure and context can determine the spoken rendering rather than forcing a one-glyph-one-word transcription. [12, 13]

And that reveals something fundamental about mathematical notation.

The meaning lives partly in the relationships between symbols, not only in the symbols themselves.

Where to go next

This guide tells you what notation is called and how to begin speaking it.

The mathematics behind the symbols goes much further.

Riemann Console's Glossary provides definitions and guided explanations for many of the ideas that appear here.

Useful starting points include:

Complex number

Complex plane

Riemann zeta function

Completed xi function

Modular arithmetic

Residue class

and in the Explain series:

What is the Riemann zeta function?

What is the Riemann xi function?

In the finished guide, individual entries should link directly to the most useful glossary definition or Explain article wherever one genuinely exists.

Sources

Pronunciations in this guide are drawn from established English dictionary evidence, with regional and alternative forms retained where the sources support them. Context-sensitive mathematical readings are treated separately: the way a symbol is spoken inside an expression can depend on its mathematical role rather than on the glyph's ordinary name.

Historical notes are sourced independently from pronunciation claims, and the accessibility discussion draws on current MathML and MathCAT work on structured mathematical speech.

The numbered references generated below provide the sources for claims that need explicit support. The Further reading section above offers broader starting points for exploring mathematical notation, pronunciation and accessibility.

The symbols are not silent

Mathematics is usually introduced as something to calculate, prove or understand.

But mathematics is also something people say to one another.

They stand at blackboards.

They teach.

They discuss proofs.

They ask whether theta tends to zero.

They say that x belongs to a set.

They take the gradient of a function.

They integrate from zero to infinity.

They wonder where the zeros of zeta lie.

The symbols on the page therefore belong to a spoken language as well as a written one.

Once you know their names, an equation that once looked like a page of mysterious squiggles begins to sound like a sentence.

And once it sounds like a sentence, it often becomes easier to think with.

References

The Open University of Japan. “理数系科目の字幕の付け方注意点 — mathematical/scientific captioning guidance.” The Open University of Japan (2026). Source
The Open University of Japan. “ギリシャ文字 (Greek letters).” The Open University of Japan (2026). Source
Cambridge Dictionary. “Beta — English pronunciation.” Cambridge University Press (2026). Source
Cambridge Dictionary. “Epsilon — English pronunciation.” Cambridge University Press (2026). Source
Collins English Dictionary. “Epsilon — definition and pronunciation.” HarperCollins (2026). Source
Cambridge Dictionary. “Xi — English pronunciation.” Cambridge University Press (2026). Source
Collins English Dictionary. “Xi — definition and pronunciation.” HarperCollins (2026). Source
Collins English Dictionary. “Omicron — definition and pronunciation.” HarperCollins (2026). Source
Cambridge Dictionary. “Upsilon — English pronunciation.” Cambridge University Press (2026). Source
Jeff Miller. “Earliest Uses of Symbols of Calculus.” MacTutor History of Mathematics (2026). Source
Jeff Miller. “Earliest Known Uses of Some of the Words of Mathematics — Nabla.” MacTutor History of Mathematics (2026). Source
W3C Math Working Group; David Carlisle (editor). “Mathematical Markup Language (MathML) Version 4.0.” World Wide Web Consortium (2026). Source
DAISY Consortium. “MathCAT — Math Capable Assistive Technology.” GitHub / DAISY Consortium (2026). Source

How do you say that?

Look at the symbols

How to use this guide

A note about language

The Greek alphabet

Now try reading some mathematics

Arithmetic

Equality and comparison

Powers, roots and little marks

The large operators

Calculus and analysis

Big O and little o

Real part, imaginary part and argument

Arrows

Geometry

Sets

Logic

The familiar number systems

One innocent-looking bar

Colons, definitions and punctuation

Brackets

Dots

A few symbols with names of their own

A few marks that often appear around mathematics

Reading whole expressions aloud

A limit

An integral

Membership

Quantifiers

A sum

A function

Conditional probability

When symbols change size

Same shape, different meaning

Pronunciation is convention, not mathematics

Typing mathematics when you cannot find the symbol

A note about accessibility

Where to go next

Further reading

Sources

Historical notes are sourced independently from pronunciation claims, and the accessibility discussion draws on current MathML and MathCAT work on structured mathematical speech.

The numbered references generated below provide the sources for claims that need explicit support. The Further reading section above offers broader starting points for exploring mathematical notation, pronunciation and accessibility.

The symbols are not silent

References

Glossary connections