Essential Tools for Writing Mathematics Papers

The Mathematics Writing Toolkit

Writing a mathematics paper requires more than mathematical knowledge. You need a set of tools for typesetting, managing references, drawing diagrams, collaborating with coauthors, and organizing your work. This guide covers the essential tools that mathematicians use, from students writing their first homework to researchers preparing journal submissions.

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LaTeX: The Foundation

Every mathematics paper is written in LaTeX. There is no practical alternative for professional mathematical writing. If you are not yet comfortable with LaTeX, see our guide to Overleaf and LaTeX.

Overleaf

Overleaf is the most popular choice for writing mathematics, especially for:

• Beginners who do not want to install a LaTeX distribution
• Collaborative papers where multiple authors edit simultaneously
• Students submitting homework and theses

The free plan includes basic collaboration and compilation. The paid plans add track changes, longer compile times, and GitHub sync.

Local LaTeX Editors

For longer projects or when you need more control, a local installation may be preferable:

• TeXstudio (texstudio.org) — Full-featured IDE with autocomplete, integrated PDF viewer, and error highlighting
• VS Code + LaTeX Workshop (marketplace.visualstudio.com) — Modern, extensible editor with excellent LaTeX support
• Vim/Neovim + VimTeX (github.com/lervag/vimtex) — For Vim users, extremely fast editing with snippet support
• Emacs + AUCTeX — The traditional choice of many senior mathematicians

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Reference Management

BibTeX and BibLaTeX

LaTeX uses BibTeX (or its modern successor BibLaTeX) for managing references. You create a .bib file containing entries like:

@article{atiyah1963,
  author  = {Atiyah, Michael F. and Singer, Isadore M.},
  title   = {The Index of Elliptic Operators on Compact Manifolds},
  journal = {Bulletin of the American Mathematical Society},
  volume  = {69},
  number  = {3},
  pages   = {422--433},
  year    = {1963}
}

Then cite with \cite{atiyah1963} in your LaTeX document.

Where to Find BibTeX Entries

You rarely need to type BibTeX entries manually:

• MathSciNet (mathscinet.ams.org) — The standard reference database for mathematics. Every reviewed paper has a ready-made BibTeX entry. Requires institutional access.
• zbMATH Open (zbmath.org) — An open-access alternative to MathSciNet with BibTeX export.
• Google Scholar (scholar.google.com) — Click "Cite" below any search result, then "BibTeX" for an entry. Not always perfectly formatted but convenient.
• arXiv — Each paper's abstract page includes a link to export citation data.

Reference Managers

For organizing large collections of papers:

• Zotero (zotero.org) — Free, open-source, with browser extensions for automatically saving papers, BibTeX export, and shared libraries. The best general-purpose choice.
• Mendeley (mendeley.com) — Similar to Zotero with built-in PDF annotation.
• JabRef (jabref.org) — A free, open-source BibTeX-specific manager that works directly with .bib files.

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Diagram and Figure Tools

Mathematics papers often need diagrams: commutative diagrams, graph theory figures, geometric illustrations, and plots.

TikZ and PGF

TikZ is a LaTeX package for creating figures directly in your document:

\begin{tikzpicture}
  \draw (0,0) circle (1);
  \draw (-1,0) -- (1,0);
  \draw (0,-1) -- (0,1);
  \node at (0.5, 0.5) {$I$};
\end{tikzpicture}

TikZ produces beautiful, publication-quality diagrams that match your document's fonts perfectly. It has a steep learning curve but is extremely powerful.

tikz-cd: Commutative Diagrams

The tikz-cd package simplifies commutative diagrams:

\begin{tikzcd}
  A \arrow[r, "f"] \arrow[d, "g"'] & B \arrow[d, "h"] \\
  C \arrow[r, "k"'] & D
\end{tikzcd}

This renders a clean commutative square with labeled arrows — essential for algebra, topology, and category theory papers.

quiver: Visual Commutative Diagram Editor

quiver is a free, web-based visual editor for commutative diagrams. You draw the diagram with your mouse, and it exports tikz-cd code. This is invaluable for complex diagrams.

Inkscape

Inkscape is a free vector graphics editor useful for creating figures that are too complex for TikZ. You can create SVG or PDF figures and include them in your LaTeX document.

Ipe

Ipe is a drawing editor specifically designed for creating figures for LaTeX documents. It uses LaTeX for text rendering, so labels in your figures match your document's fonts exactly.

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Computation and Verification

SageMath and Mathematica

Use computational tools to verify calculations, generate examples, and produce data. See our guides to SageMath and Python and Wolfram Alpha and Mathematica.

Lean and Other Proof Assistants

Proof assistants like Lean are increasingly used to formally verify mathematical proofs. The Mathlib library contains a growing collection of formalized mathematics.

While formal verification is not yet standard practice, familiarity with proof assistants is becoming valuable, especially in areas like combinatorics, algebra, and analysis where computer verification can catch subtle errors.

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Collaboration Tools

Overleaf (Real-Time Collaboration)

Overleaf's collaboration features make it the default tool for multi-author papers. Share a link and multiple people can edit simultaneously.

Git and GitHub

For more serious version control, use Git with GitHub or GitLab:

• Track every change to your paper
• Work offline and sync later
• Branch for experimental sections
• Review coauthors' changes through pull requests

See our guide to using GitHub for mathematics.

Email and arXiv

The traditional workflow is simple: write in LaTeX, email drafts to coauthors, and post the final version on arXiv. This still works perfectly well for many collaborations.

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Writing Tools

Grammarly and LanguageTool

For checking prose in your paper's introduction and exposition, Grammarly and LanguageTool can catch grammatical errors and awkward phrasing. They do not understand mathematical notation, but they are useful for the non-mathematical text.

Detexify

Detexify lets you draw a symbol and find the corresponding LaTeX command. Invaluable when you know what a symbol looks like but not its name.

Mathpix Snip

Mathpix converts screenshots of mathematical equations into LaTeX code. This is useful for digitizing handwritten mathematics or equations from PDFs.

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Organizing Your Paper

AMS Article Templates

The American Mathematical Society provides LaTeX document classes and templates for AMS journals. Even if you are not submitting to an AMS journal, the amsart document class is a clean, professional starting point for any mathematics paper.

Standard Paper Structure

Most mathematics papers follow this structure:

1. Title, authors, abstract
2. Introduction — State the main results, provide context, outline the paper
3. Preliminaries — Definitions and known results you will need
4. Main sections — Proofs of the main results
5. Applications or examples (if applicable)
6. Acknowledgments
7. References

Writing Tips

• State your main theorem early. Readers should know the main result by the end of the introduction.
• Define all notation. Never use a symbol without defining it.
• Number all equations that you reference later; leave unnumbered the ones you do not reference.
• Use \label and \ref consistently. Never hardcode theorem or equation numbers.
• Write in the present tense for mathematical statements: "Theorem 3 shows that..." not "Theorem 3 showed that..."

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A Complete Workflow

Here is a realistic workflow for writing a mathematics paper:

1. Draft on paper. Write proofs by hand first. Only move to LaTeX when you are confident in the mathematics.
2. Set up the project. Create a folder with your .tex file, .bib file, and figure files. Initialize a Git repository.
3. Write the introduction last. Draft the main sections first, then write an introduction that accurately reflects the final content.
4. Compile frequently. Do not write 20 pages before compiling. Fix errors as they appear.
5. Get feedback. Share drafts with your advisor, colleagues, and friends. Fresh eyes catch errors you will not see.
6. Polish. Check every reference, verify every cross-reference, proofread every sentence.
7. Post on arXiv. Then submit to a journal.

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Summary Table

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Final Thoughts

The right tools make mathematical writing more efficient and more enjoyable. But remember that tools are in service of the mathematics. A well-written paper with a beautiful proof, typed with care and checked thoroughly, will always be more valuable than a flashy document produced with every tool imaginable but containing a flawed argument.

Master the tools, then focus on the mathematics.

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References

• Overleaf — Online LaTeX Editor
• TeXstudio
• LaTeX Workshop for VS Code
• Zotero
• JabRef
• MathSciNet
• zbMATH Open
• TikZ/PGF on CTAN
• tikz-cd on CTAN
• quiver — Commutative Diagram Editor
• Inkscape
• Ipe Drawing Editor
• Detexify
• Mathpix
• AMS LaTeX Resources
• Lean Theorem Prover
• Git
• GitHub