Greek letters

Type \Alpha for a capital alpha in LaTeX and you get ! Undefined control sequence. — the most common accident at the doorway to Greek letters. The reason is almost disappointingly simple: a capital alpha is shaped exactly like A, so LaTeX assumes you will type the Latin A and never defines a command at all. Every Greek letter in math mode follows that single policy — a name is given only to shapes the Latin alphabet does not already supply. This page works outward from there: the full lowercase and uppercase command sets, variant shapes such as \epsilon versus \varepsilon, how to get bold and upright Greek, and how to put a Greek letter into running text.

Why \Alpha does not exist, and what to type instead

Commands exist for exactly eleven uppercase Greek letters: \Gamma, \Delta, \Theta, \Lambda, \Xi, \Pi, \Sigma, \Upsilon, \Phi, \Psi, \Omega. For the other thirteen you type the matching Latin capital — A B E Z H I K M N O P T X. Open fontmath.ltx in the LaTeX kernel and those eleven declarations really are all there is; \Alpha, \Beta and \Epsilon were never defined in the first place. Α and A, Β and B, Ε and E are the same shape in type, so there was no reason to give them a second name.

It is a clean design and a hostile one to search. Looking up \Alpha turns up nothing because the command is not missing — it was never there. The error only says ! Undefined control sequence.; it does not tell you to type A instead. What makes the rule vivid is the contrast with text mode: the textgreek package does define \textAlpha, \textBeta and \textEpsilon. In running text you are setting real Greek letters rather than mathematical variables, so all twenty-four need names. The eleven of math mode, in other words, is not a fact about Greek at all — it is the number of shapes that Latin does not already cover.

% the eleven uppercase Greek letters that do have commands
\[ \Gamma(n) = (n-1)!, \qquad \Delta x, \qquad \Omega \]
% the other thirteen: type the Latin capital directly
\[ A, B, E, Z, H, I, K, M, N, O, P, T, X \]
% \Alpha, \Beta, \Epsilon ... -> ! Undefined control sequence.

The lowercase Greek letters, \alpha through \omega

Every lowercase letter has a command except omicron — twenty-three of the twenty-four. Omicron is missing for exactly the reason the capitals are: ο is indistinguishable from a Latin lowercase o, so you simply type o in math mode. Thirteen gaps among the capitals and one among the lowercase are not two separate exceptions; they are one rule surfacing in two places. The command names are just the English spellings of the letters — \alpha, \beta, \gamma — so they are closer to being recalled than memorised.

A few pairs are easy to mix up: \xi (ξ) and \zeta (ζ), \nu (ν) and \upsilon (υ), and — most dangerous — \nu (ν) and a Latin lowercase v. Type v when you meant ν and the document still compiles; nothing errors, only the printed page is wrong. In the source, check the command name rather than the shape. One more thing to carry forward: fontmath.ltx takes the lowercase letters from the letters font (in Computer Modern that is cmmi, math italic), so they come out slanted like any variable. The eleven capitals, as the next section shows, come from a completely different font.

The eleven uppercase commands, and why they come out upright

Write \Gamma or \Omega in a formula and, unlike the lowercase letters, it comes out upright (roman). That is not an accident. In fontmath.ltx the lowercase letters are taken from the letters font, but the eleven capitals are taken from the operators font — in Computer Modern that is cmr, the same upright face as the body text. Put \Gamma and \gamma in one formula and one stands straight while the other leans. It is a famous asymmetry, and LaTeX has left it untouched for decades.

Two practical annoyances hide here. The first is a mismatch of shape: the thirteen letters without commands are typed as Latin capitals, so they are set as variables in italic. Put \Gamma (upright) and A (italic) on the same line and they do not match. The second is confusing \Sigma/\Pi with \sum/\prod. The former are letters, the latter are large operators — a different size, and different behaviour for limits, which sit above and below in display style. For a sum or a product always write \sum_{i=1}^{n} or \prod_{i=1}^{n}, and keep \Sigma and \Pi for when you genuinely mean the Greek capital itself.

\epsilon vs \varepsilon, \phi vs \varphi

\epsilon gives the rounded ϵ and \varepsilon gives the lunate ε; likewise \phi gives the closed ϕ and \varphi the open φ. By name, \epsilon looks like the standard one — but mathematical practice mostly wants ε. The ε of the ε–δ definition, and the ε in "for every ε > 0", are conventionally printed in the lunate shape. In other words, to get the letter that comes to mind when someone says "epsilon", you have to type the var form. The names and the usage point in opposite directions, which is exactly why beginners stumble here.

There is a second, older confusion around ϵ. The membership sign ∈ began life as a Greek epsilon: Giuseppe Peano used ε for membership in his 1889 Arithmetices principia, nova methodo exposita, noting that it abbreviated the Latin est, "is". The two shapes later parted ways, but the resemblance still trips people up, and writing x \epsilon A raises no error at all. \in is declared a relation (\mathrel) and therefore carries space on both sides, while \epsilon is an ordinary symbol (\mathord) — so the mistake prints silently as a formula with the spacing squeezed out of it.

% the epsilon-delta definition conventionally uses the lunate \varepsilon
\[ |x - a| < \delta \implies |f(x) - f(a)| < \varepsilon \]
% \epsilon is a letter, \in is a relation -- different commands, different spacing
\[ x \in A, \qquad \epsilon > 0 \]

The practical rule is simple: pick one shape and hold to it throughout the document. Mathematical writing usually means \varepsilon and \varphi; if you are matching an existing house style, follow that instead. Of the table above, only \varkappa (ϰ) and \digamma (ϝ) are undefined in standard LaTeX and need \usepackage{amssymb} in the preamble — forget it and you get, once again, ! Undefined control sequence. Note also that var variants exist only for lowercase letters. Making a capital slanted is not a variant at all but a question of font style, which is where the next sections go.

Bold Greek letters, and why \mathbf{\alpha} does nothing

To set Greek in bold, use \boldsymbol{\alpha} (from amsbsy, which amsmath loads) or \bm{\alpha} (from the bm package). \mathbf{\alpha} does nothing at all — no error, no warning. Measure the boxes and, in Computer Modern at 10pt, \alpha and \mathbf{\alpha} are both exactly 6.43404pt wide. The reason lies in the symbol's class: math alphabet commands such as \mathbf act only on symbols of class \mathalpha, and fontmath.ltx declares the lowercase Greek letters as \mathord, which puts them out of reach.

What makes this genuinely confusing is that uppercase Greek is \mathalpha, so \mathbf{\Gamma} does work — under the same conditions its width changes from 6.25002pt to 6.91663pt. Hence the baffling symptom: the capitals go bold and the lowercase letters refuse. If you are writing vectors or tensors with Greek letters, settle on \boldsymbol or \bm from the outset. \bm is the more flexible of the two: it applies to a whole subformula, as in \bm{\nabla \times E}, and will synthesise a bold face when none is available.

\usepackage{amsmath}  % provides \boldsymbol (via amsbsy)
\usepackage{bm}       % provides \bm
% ...
\[ \boldsymbol{\alpha} \cdot \bm{\omega}, \qquad \bm{\nabla \times E} \]
% \mathbf{\alpha} silently produces the same box as \alpha

Upright Greek and the ISO rules: upgreek and unicode-math

Greek letters used for constants and units should be set upright — that is the ISO 80000-2 convention — and in pdfLaTeX the answer is the upgreek package. Load \usepackage{upgreek} and you get \upalpha, \upmu, \uppi for lowercase and \Upgamma, \Updelta, … for uppercase (eleven of them again, because the rule from the top of this page is still doing its work). ISO 80000-2 prescribes italic for variables and upright for units and for mathematical constants whose value never changes. So the circle constant π properly wants \uppi and the unit prefix micro wants \upmu, while a π used as a variable stays plain \pi.

The same rule cuts the other way. ISO calls for all variables to be italic, so an uppercase Greek letter used as a variable ought to be slanted — yet standard LaTeX sets \Gamma upright, as the previous section showed. Under pdfLaTeX the fix is Walter Schmidt's fixmath, which re-takes the uppercase Greek letters from letters instead of operators (isomath builds on it and adds coordinated faces for vectors, matrices and tensors). Under XeLaTeX or LuaLaTeX, the math-style key of unicode-math settles it in one line: the default math-style=TeX reproduces LaTeX's inherited asymmetry exactly — upright capitals, italic lowercase — while math-style=ISO makes both italic. french and upright are also available. One caution: Γ as a function name (the gamma function) is upright under ISO too, so do not apply the rule mechanically.

\usepackage{upgreek}
% ...
% constants and units are upright
\[ C = 2 \uppi r, \qquad \lambda = 5\,\upmu\mathrm{m} \]
% variables stay italic
\[ \pi_1(X), \qquad \gamma \]

% XeLaTeX / LuaLaTeX: one line switches the whole convention
% \usepackage[math-style=ISO]{unicode-math}

Greek letters in running text: avoiding ! Missing $ inserted

Write \alpha in the body of your text and the run stops with ! Missing $ inserted. The Greek commands are declared as math characters, usable only in math mode, so when TeX meets one in horizontal mode it tries to supply a $ and fails. The quick escape is $\alpha$, but that sets the letter as a slanted variable, which is not really right for Greek that is part of the prose — a unit such as μm, or a species name. The tool you want depends on whether you are writing a formula or writing a sentence.

For prose there is the textgreek package: \textalpha, \textbeta, \textmu and, alongside them, \textAlpha through \textOmega — all twenty-four in both cases. The capitals that numbered only eleven in math mode are complete here. To typeset Greek-language text itself, the standard route is babel with the greek option (in practice greek.ldf from babel-greek), writing inside \textgreek{…}, where LGR transliteration input is converted to Greek letters. If all you need is the micro prefix, siunitx offers \micro. Whichever route you take, treat writing $\mu$m as the last resort rather than the first.

\usepackage{textgreek}
% ...
A wavelength of 5\,\textmu m, and a coefficient \textalpha.
% writing \alpha here instead -> ! Missing $ inserted.