How do I cite a theorem from another paper?

Point at the numbered result inside the bracketed citation: “By [5, Theorem 3.2]…”. CSUCI's AMS guide shows the same pattern with a section — its examples are “[8], [11, Section 4.8], [3, 6, 7]” — and adds that “No page references are included in internal citations.”

How do I cite papers written in other languages?

Give the title in the original language and note the language at the end of the entry — “(French)” or “(Russian)”. MathSciNet records often carry a translated title you can add in brackets.

How do I handle self-citations in AMS style?

Format them like any other reference, using your name as it appears on the cited paper. Write out author names in full for each entry rather than replacing a repeated name with a dash.

What if a paper has no MR number?

Leave it out. Very recent papers, papers in journals MathSciNet does not index, and preprints will not have one. Give the DOI or arXiv identifier instead, and add the MR number later if one is assigned.

Should I cite arXiv preprints or wait for publication?

Cite the published version once it exists, and update a preprint reference before you submit. For work that only exists as a preprint, citing the arXiv version is normal practice.

How to Cite in AMS Style: Mathematics Citation Guide

This guide covers how to cite sources in AMS format, the citation conventions of the American Mathematical Society.

The Official Source and What This Page Rests On

The AMS publishes author resources at ams.org, but its server returns HTTP 403 to automated requests, so this page does not quote the AMS Style Guide directly. The rules below follow two university guides that reproduce AMS's conventions, and both are named where their wording matters:

USC Libraries, "American Mathematical Society (AMS) Citation Style" — the three in-text systems, the numbering rule, and the worked journal entry with its MR number.
CSU Channel Islands Writing & Multiliteracy Center, "AMS Style Guide" — the element order for books and journals, and the note that internal citations carry no page numbers.

Every worked example below is a real, published source, checked today against Crossref, Open Library, DataCite or the arXiv API. The one element this page cannot verify independently is the MR number, because MathSciNet is a subscription database; the MR number shown is the one USC's guide prints alongside that same reference, and it is attributed as such.

Quick Overview: AMS Citation Format

USC's guide sets out three in-text systems:

Numbers in brackets: [1], [2], [3], keyed to a numbered reference list.
Name and year: a bracketed author-year key — USC's guide writes this one as [Smith2019], a key rather than a real reference.
Alphanumeric abbreviation: a short code built, in USC's words, by taking "the first letter of the last name, while also shortening the year" — its example is [S19]. With two authors the code takes both initials, as in the [DL99] entry USC prints for Denef and Loeser below.

Most mathematics journals use bracketed numbers. The ordering of the list follows from your choice: with numerical citations, USC's guide says "references should be numbered sequentially. If a reference is repeated, do not give it another number; rather, use the original reference number." With the name-year or alphanumeric systems you "order the references alphabetically" instead.

In-Text Citations in AMS

Numerical System (Most Common)

The asymptotic approach to the capacity-achieving covariance matrix was developed in [1]. This builds on earlier work [2], [3]. As shown in [1], the argument generalizes.

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

To point at a specific result rather than a page:

By [1, Theorem 3.2], the set is closed. See also [2, Section 4.8].

Alphanumeric System

Codes combine author initials and year. Here [DL99] is the Denef and Loeser entry listed below:

The construction was introduced in [DL99].

Reference List Format

The list follows the paper under the heading "References". Key elements, per CSUCI's guide:

Author names as they appear, initials first (not inverted)
Article title in italics, sentence case
Abbreviated journal title, not italicized
Volume in bold, followed by the year in parentheses
Issue number preceded by "no."
Page range
DOI, written after "DOI" with a space and no colon
MathSciNet review number, where the paper has one

Journal Articles

Alphanumeric key, reproduced from USC's AMS guide — including the MR number, which comes from that guide rather than from a source this page could open:

[DL99] J. Denef and F. Loeser, Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math. 135 (1999), no. 1, 201–232, DOI 10.1007/s002220050284. MR1664700

Numbered, with several authors:

[1] J. Dumont, W. Hachem, S. Lasaulce, P. Loubaton, and J. Najim, On the capacity achieving covariance matrix for Rician MIMO channels: an asymptotic approach, IEEE Trans. Inform. Theory 56 (2010), no. 3, 1048–1069, DOI 10.1109/TIT.2009.2039063.

Single author, older paper with no issue number:

[2] C. J. Earle, Some remarks on the Beltrami equation, Math. Scand. 36 (1975), 44–48, DOI 10.7146/math.scand.a-11561.

Books

[3] O. Ganyushkin and V. Mazorchuk, Classical finite transformation semigroups: an introduction, Springer, London, 2009.

[4] P. M. Higgins, Techniques of semigroup theory, Oxford University Press, Oxford, 1992.

For books in a series, add the series name and volume number after the title.

Book Chapters

A contribution to an edited collection names the collection and its editors:

[5] S. Alsulami, H. Colman, and F. Neumann, The Lusternik-Schnirelmann category for a differentiable stack, Mathematics across contemporary sciences (T. Abualrub, A. S. Jarrah, S. Kallel, and H. Sulieman, eds.), Springer, Cham, 2017, pp. 1–15, DOI 10.1007/978-3-319-46310-0_1.

Conference Proceedings

A proceedings volume is cited like an edited collection, with the meeting identified. The volume in [5] above is in fact the proceedings of AUS-ICMS, Sharjah, UAE, April 2015, and would be cited:

[6] S. Alsulami, H. Colman, and F. Neumann, The Lusternik-Schnirelmann category for a differentiable stack, Mathematics across contemporary sciences, AUS-ICMS, Sharjah, UAE, April 2015 (T. Abualrub, A. S. Jarrah, S. Kallel, and H. Sulieman, eds.), Springer, Cham, 2017, pp. 1–15.

Preprints

Give the arXiv identifier, and replace it with the published reference once the paper appears.

[7] G. Perelman, The entropy formula for the Ricci flow and its geometric applications, preprint, 2002, arXiv:math/0211159.

Dissertations

[8] N. K. Chidambaram, Aspects of enumerative and categorical algebraic geometry, Ph.D. thesis, University of Alberta, 2020, DOI 10.7939/r3-s5ky-km66.

AMS Formatting Guidelines

Journal abbreviations. Mathematics uses standard abbreviated titles, and guides differ on the details — CSUCI writes the IEEE transactions as "IEEE Trans. Info. Theory." where AMS's own reference lists use "IEEE Trans. Inform. Theory". The forms below are the ones used on this page:

Inventiones Mathematicae → Invent. Math.
Mathematica Scandinavica → Math. Scand.
IEEE Transactions on Information Theory → IEEE Trans. Inform. Theory

Check an abbreviation against a recent article in the journal, or against the MathSciNet record if you have access.

MathSciNet. MR numbers are assigned by Mathematical Reviews and shown in MathSciNet records. MathSciNet requires a subscription, which most university libraries hold; MR Lookup is the tool for finding the number for a paper you already have. Do not guess an MR number — omit it instead.

Common AMS Mistakes to Avoid

Inventing or guessing MR numbers. If you cannot see the MathSciNet record, leave the MR number out.
Incorrect journal abbreviations. Check them against the journal's own articles or the MathSciNet record.
Inverting author names. AMS gives names as they appear, initials first: J. Denef, not Denef, J.
Omitting DOIs. Include the DOI for any reference that has one.
Mixing citation systems. Choose numerical, name-year or alphanumeric and keep to it — and remember that the choice also decides whether the list is numbered by appearance or alphabetized.

AMS Citation Tools

For mathematics, LaTeX with the amsrefs package is the standard route: amsrefs formats entries to AMS conventions automatically. If you have MathSciNet access, you can search for a paper, choose the AMSRefs output from the export menu, and paste the result into your document. Reference managers including Zotero ship AMS styles; check their output against a MathSciNet or Crossref record.

Sources for This Page

USC Libraries. "Citation Styles: American Mathematical Society (AMS)." https://libguides.usc.edu/c.php?g=974981&p=7048536 — the three in-text systems, the alphanumeric code rule, the numbering and ordering rules, and the Denef–Loeser entry with its MR number.
CSU Channel Islands Writing & Multiliteracy Center. "AMS Style Guide" (revised 2020). https://www.csuci.edu/wmc/pdf/citations/ams-style-guide-revised2020.pdf — element order for books and journals, the internal-citation examples, and the rule that internal citations carry no page references.
Crossref records for the Denef–Loeser, Dumont et al. and Earle papers and the Alsulami et al. chapter (with the parent volume's editors); Open Library for Ganyushkin–Mazorchuk and Higgins; the arXiv API for math/0211159; DataCite DOI 10.7939/r3-s5ky-km66 for the Alberta thesis.

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