Write Math

Write Math

Apply the mathematical writing conventions from the reference files below when drafting or editing mathematical content in any format.

Core Principles

1. Clarity over cleverness -- write so a graduate student beginning studies in the field can follow your argument
2. Reader-centered exposition -- minimize the reader's effort at every turn; signal where you are going and why
3. Consistent notation -- define symbols before use, reuse the same letter for the same concept, and never overload
4. Structured proofs -- state the theorem first, summarize the proof strategy, then present the formal argument in linear forward flow
5. Communication over impression -- plain language beats jargon; repetition beats synonym-hunting

Workflow

1. Review against the essential checklist: ./references/essential/checklist.md
2. For specific questions, consult the comprehensive references below

Reference Navigation

Quick reviews (default):

• references/essential/checklist.md -- condensed, actionable rules

Deep dives by topic:

• references/comprehensive/notation.md -- notation principles, implicit conventions, TeX macros, disambiguation
• references/comprehensive/theorems-and-proofs.md -- theorem/lemma hierarchy, proof structure, statement design
• references/comprehensive/paper-structure.md -- title, abstract, introduction, body, conclusions, appendices
• references/comprehensive/english-usage.md -- sentence structure, word choice, logical connectives, common errors
• references/comprehensive/reader-centered-writing.md -- audience awareness, examples, signposting, assertion status
• references/comprehensive/citations-and-references.md -- signposting citations, specific references, journal selection
• references/comprehensive/revision-and-process.md -- drafting workflow, revision strategy, collaboration, reading math

Sources

• Tao, T. "Advice on Writing Papers" (6 posts). terrytao.wordpress.com.
• Knuth, D., Larrabee, T., and Roberts, P. Mathematical Writing. 1989.
• Cohn, H. "Advice." cohn.mit.edu.
• Poonen, B. "Practical Suggestions for Mathematical Writing." MIT.
• Conrad, K. "Advice on Mathematical Writing." UConn.
• Su, F. E. "Guidelines for Good Mathematical Writing."
• Tsitsiklis, J. N. "A Few Tips on Writing Papers with Mathematical Content."
• Lagarias, J. C. "How to Write a Math Paper."
• Goldreich, O. "How to Write a Paper."
• Pak, I. "How to Write a Clear Math Paper: Some 21st Century Tips."
• Trzeciak, J. Writing Mathematical Papers in English. EMS, 1995.
• Berndt, B. C. "How to Write Mathematical Papers." UIUC.
• Krantz, S. G. "How to Write Your First Paper." AMS, 2007.
• Wang, R. "Suggestions for Writing Mathematics in Scientific Papers." 2024.
• Lee, K. P. "A Guide to Writing Mathematics." MIT.
• MIT 18.821. "Notes on Writing Mathematics."
• Cambridge. "A Brief Guide to Mathematical Writing."