How do I cite a theorem from another paper?

Reference the source as usual with your citation number, then specify the theorem: “By Theorem 3.2 in [5]...” or “...follows from [5, Theorem 3.2].” The bracketed format with comma is common in mathematical writing for citing specific results within a source.

How do I cite papers written in other languages?

Include the title in the original language, followed by an English translation in brackets if helpful. Note the language at the end of the citation: “...(French)” or “(in Russian).” MathSciNet often provides translated titles you can reference.

How do I handle self-citations in AMS style?

Format self-citations exactly like any other reference. In your reference list entry, use your name as it appears on the cited paper. Don't use special notation like “—” for repeated author names in AMS style; write out full author names for each entry.

What if a paper has no MR number?

Not all papers appear in MathSciNet—very recent papers, papers in non-indexed journals, or preprints won't have MR numbers. Simply omit the MR number and include other identifiers like DOI or arXiv number when available. You can check MR Lookup periodically to add the number once it's assigned.

Should I cite arXiv preprints or wait for publication?

If a paper has been published, cite the published version rather than the preprint. If you initially cited the preprint, update your reference before submission. For unpublished work that's only available as a preprint, citing the arXiv version is acceptable and standard practice.

How to Cite in AMS Style: Mathematics Citation Guide

This guide will help you understand how to properly cite sources in AMS format, ensuring your academic work meets the necessary standards for mathematics papers.

What is the AMS Format?

The American Mathematical Society (AMS) style is the standard citation format for mathematics journals, including Journal of the American Mathematical Society, Transactions of the AMS, Communications in Algebra, and American Mathematical Monthly. The AMS Style Guide provides comprehensive guidance for mathematical writing and references.

Mathematics papers have unique citation needs—proofs reference specific theorems, notation matters, and precision is paramount. AMS style accommodates these requirements while maintaining clarity.

Quick Overview: AMS Citation Format

AMS offers three in-text citation systems:

Numerical citations: References appear as bracketed numbers [1], [2], [3] corresponding to a numbered reference list.
Author-year citations: References use author surname and year in parentheses (Smith 2024).
Alphanumeric abbreviations: References use abbreviated codes combining author names and year [DL99], [Smi24].

Most mathematics journals use numerical citations, though author-year appears in some publications. The key principle: be consistent throughout your paper.

In-Text Citations in AMS

Numerical System (Most Common)

References are numbered sequentially, and numbers are reused for repeat citations:

Mathematicians help improve efficiency of data centers using Markov chains [1]. This builds on earlier work [2], [3]. As shown in [1], the approach generalizes to other domains.

For multiple citations: [1], [2] or [1, 3, 5] or [4–7] for consecutive references.

Author-Year System

Recent advances in algebraic topology (Morrison 2023) have expanded our understanding of...

Alphanumeric System

Codes combine author initials and year:

The conjecture was first proposed in [DL99] and later proved in [Fab09].

Where [DL99] refers to Denef and Loeser, 1999.

Reference List Format

AMS emphasizes precision and completeness. Always include MathSciNet review numbers (MR numbers) when available, as these provide permanent identifiers for mathematical literature.

Journal Articles

Numerical format: [1]

Alphanumeric format: [DL99]

Key elements:

Author names as they appear (not inverted)
Article title in sentence case
Abbreviated journal title in italics
Volume in bold, followed by year in parentheses
Issue number preceded by "no."
Page range
DOI (formatted with space after "DOI")
MathSciNet review number

Books

[2] [3]

For books in a series, include series name and volume number.

Book Chapters

[4]

Conference Proceedings

[5]

Preprints

[6]

Dissertations

[7]

AMS Formatting Guidelines

"Less is more": The AMS Style Guide emphasizes clarity and conciseness. Avoid unnecessary words and keep mathematical notation consistent.

Journal abbreviations: Use standard mathematical abbreviations. Common examples:

Inventiones Mathematicae → Invent. Math.
Annals of Mathematics → Ann. of Math.
Journal of the American Mathematical Society → J. Amer. Math. Soc.
Transactions of the American Mathematical Society → Trans. Amer. Math. Soc.

MathSciNet: Use the MR Lookup tool to find correct citation information and MR numbers.

Common AMS Mistakes to Avoid

Missing MR numbers: Include MathSciNet review numbers whenever available—they're the standard identifier for mathematical literature.
Incorrect journal abbreviations: Verify abbreviations against MathSciNet or the AMS's standard list.
Inconsistent author name formatting: In AMS style, use author names as they appear on the publication, not inverted (J. Smith, not Smith, J.).
Omitting DOIs: Modern AMS style encourages including DOIs for all references that have them.
Mixing citation systems: Choose numerical, author-year, or alphanumeric and stick with it throughout.

AMS Citation Tools

For mathematics, LaTeX with amsrefs is the standard approach. The amsrefs package formats citations according to AMS conventions automatically.

To get proper amsrefs formatting:

Search for your source in MathSciNet
Select "AMSRefs" from the dropdown menu
Copy the formatted code directly into your LaTeX document

Reference managers like Zotero include AMS style templates, though verifying output against MathSciNet is recommended.

References

American Mathematical Society. AMS Style Guide: Journals [Internet]. Providence (RI): AMS; [cited 2025 Jan 2]. Available from: https://www.ams.org/arc/styleguide/index.html
University of Southern California Libraries. American Mathematical Society (AMS) Citation Style [Internet]. Los Angeles: USC; [cited 2025 Jan 2]. Available from: https://libguides.usc.edu/c.php?g=974981&p=7048536
California State University Channel Islands Writing Center. AMS Style Guide [Internet]. Camarillo (CA): CSUCI; [cited 2025 Jan 2]. Available from: https://www.csuci.edu/wmc/pdf/citations/ams-style-guide-revised2020.pdf

Wonders helps researchers discover mathematical papers and organize citations — with MR numbers and arXiv identifiers, ready for LaTeX.