Authoring Numbered Equations with Cross-References in LaTeX Using amsmath

Desired Outcome

Produce a LaTeX document where multi-line derivations are numbered automatically, and references to those equations in the surrounding text resolve to the correct numbers after compilation. The workflow should work with pdfLaTeX, XeLaTeX, or LuaLaTeX and require only standard packages.

Prerequisites

• A working TeX distribution (TeX Live 2023+, MikTeX current, or equivalent).
• An editor or command-line access to run latexmk or the engine directly (pdflatex, xelatex, lualatex).
• Basic familiarity with LaTeX document structure (preamble, \begin{document}/\end{document}).

Minimal Preamble

Load amsmath early, before any package that patches math behavior. If you need the extensions from mathtools (e.g., \coloneqq, \mathclap), load it instead; it pulls in amsmath automatically.

\documentclass{article}
\usepackage{amsmath}        % or \usepackage{mathtools}
\usepackage{hyperref}        % optional: makes \eqref links clickable
\begin{document}

Engine note: With XeLaTeX or LuaLaTeX, add \usepackage{unicode-math} after amsmath if you want OpenType math fonts. Do not load legacy math font packages (e.g., mathptmx) together with unicode-math.

Writing a Numbered Multi-Line Derivation

Use the align environment for equations that share alignment points (typically at &= or &\approx). Each line receives a single equation number unless you suppress it with \nonumber.

\begin{align}
  E &= mc^2 \label{eq:einstein} \\
  p &= \gamma m v \label{eq:momentum}
\end{align}

• & marks the alignment column.
• \\ ends a line (not a paragraph break).
• \label{...} must appear inside the environment, on the line you want to reference.

For a derivation that should share one number across several lines, wrap the inner lines in split inside an equation environment:

\begin{equation}
  \begin{split}
    a &= b + c \\
      &= d + e + f
  \end{split}
  \label{eq:split-demo}
\end{equation}

Referencing in Text

Use \eqref{...} (from amsmath) for parenthesized references, or \ref{...} for the raw number. \eqref automatically adds parentheses and, with hyperref, creates a link.

Equation \eqref{eq:einstein} relates energy and mass,
while \eqref{eq:momentum} gives relativistic momentum.

Compilation Procedure

1. Save the file as equations.tex.
2. Run the engine twice (or use latexmk which handles passes automatically):

   # pdfLaTeX
   latexmk -pdf equations.tex
   
   # XeLaTeX
   latexmk -xelatex equations.tex
   
   # LuaLaTeX
   latexmk -lualatex equations.tex
   

3. Open the resulting PDF. Equation numbers should appear at the right margin (or left if leqno class option is used), and references should show numbers, not ??.

Expected Checks

• PDF output: Each align line has a sequential number (1), (2), …; split block shares one number.
• References: \eqref{eq:einstein} renders as “(1)”, not “(??)”.
• Log file: No “LaTeX Warning: Reference `eq:einstein' on page 1 undefined” after the final pass. No “multiply defined” warnings.

Common Failures and Recovery

Symptom	Cause	Fix
Reference shows ??	Only one compile pass; label not yet written to .aux.	Rerun the engine (or latexmk) until references stabilize.
“Label `eq:foo' multiply defined”	Same \label used twice.	Give each label a unique key; adopt a prefix convention like eq:, fig:, sec:.
Equation number missing on a line	\nonumber or \notag present, or line inside align*.	Remove \nonumber or switch from align* to align.
Misaligned columns in align	Missing or extra & markers.	Each line must have the same number of &; use &={} for empty left side if needed.
Unicode glyphs missing with XeLaTeX/LuaLaTeX	unicode-math loaded but no math font set.	Add \setmathfont{Latin Modern Math} (or another OpenType math font) after loading unicode-math.

Verification Checklist

1. Compile the minimal example above with your target engine.
2. Confirm equation numbers appear and increment correctly.
3. Add a new \label and \eqref pair, recompile twice, verify the reference updates.
4. Inspect equations.log for “undefined references” or “multiply defined” warnings.
5. If using XeLaTeX/LuaLaTeX with unicode-math, check that symbols (∑, ∫, Greek letters) render with the chosen math font and spacing looks consistent.

Limitations

• amsmath does not support automatic line-breaking of long equations; use multline or manual breaks with \\ and alignment tweaks.
• Cross-references across \include files work, but labels must be unique project-wide.
• Manual spacing commands (\!, \:, \;, \quad) are sometimes necessary but reduce portability; prefer amsmath’s built-in spacing where possible.

Next Steps

For larger documents, consider cleveref (load after hyperref) to get “Eq. (1)” automatically via \cref{eq:einstein}. For numbered groups of related equations, use the subequations environment to produce (1a), (1b), … while keeping a single parent number.