Latex Math Writeup

Document Structure

A typical mathematical writeup follows this structure:

Default Preamble

If no existing preamble is available, use this as a starting point:

\documentclass[11pt]{article}
\usepackage{amsmath, amssymb, amsthm}
\usepackage{hyperref}
\usepackage{booktabs}
\usepackage{geometry}
\geometry{margin=1in}

This is intentionally minimal — customize for your needs (see Customization below).

LaTeX Conventions

Theorem Environments

\newtheorem{theorem}{Theorem}[section]
\newtheorem{lemma}[theorem]{Lemma}
\newtheorem{proposition}[theorem]{Proposition}
\newtheorem{corollary}[theorem]{Corollary}
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}
\theoremstyle{remark}
\newtheorem{remark}[theorem]{Remark}

Verification Tables

When documenting computationally verified results, include verification tables:

\begin{table}[h]
\centering
\begin{tabular}{c|c|c|c}
Parameter & Computed & Expected & Match \\
\hline
$n=1$ & 0.5000 & 1/2 & \checkmark \\
$n=2$ & 0.3333 & 1/3 & \checkmark \\
\end{tabular}
\caption{Numerical verification of [result name]}
\end{table}

Compilation

# Create output directory
mkdir -p output/

# Compile (handles cross-references automatically)
cd output/ && latexmk -pdf document.tex

# Check for errors — always review the log
grep -E "^!" document.log || echo "No errors"
grep -c "Warning" document.log

# Clean build artifacts (keeps .tex and .pdf)
latexmk -c

latexmk -pdf runs pdflatex as many times as needed for TOC and cross-references. latexmk -c removes .aux, .log, .out, .toc, .fls, .fdb_latexmk.

Always verify compilation is clean — no undefined references, no missing packages, no overfull hboxes that break layout. Fix issues before delivering the PDF.

Customization

This skill is designed to be easily modified for your own workflow. Common things to customize:

• Preamble — replace the default preamble with your own (custom packages, macros, fonts)
• Output directory — change output/ to wherever you keep your PDFs
• Document class — swap article for amsart, memoir, beamer, etc.
• Theorem numbering — adjust the \newtheorem definitions to match your convention

Draft Mode

When iterating on a document, compile in draft mode with visible labels so the user can easily reference specific equations, theorems, and sections:

\usepackage{showkeys}  % displays \label names in the margin
\documentclass[draft]{article}  % marks overfull boxes, skips images for speed

This makes it much easier for the user to say "equation eq:main-bound has a typo" instead of "the third equation on page 2."

Label everything — every equation, theorem, lemma, section, and table should have a \label{}. Use descriptive names: eq:spectral-gap, thm:main-result, sec:prelim.

Remove showkeys and draft option for the final version.

Delivering the Draft

If there's no prior setup for how the user views PDFs, ask:

"How should I share the draft? Options: (1) compile and you open the PDF directly, (2) send to Discord, (3) just share the .tex source. How do you usually view PDFs from the terminal?"

Establish this once and reuse for the rest of the session.

Tips

• No abstract for short notes — the Introduction covers the description
• Keep verification tables large enough to be convincing (10+ data points)
• Use \intertext{} inside align environments for inline commentary
• Prefer align over equation for multi-line displays