advances-in-mathematics - SKILL.md Agent Skill

name: advances-in-mathematics description: Use when targeting Advances in Mathematics (Adv. Math.) or deciding whether a pure mathematics manuscript fits this broad-scope Elsevier research venue. Encodes the journal's fit, framing, proof standard, house style, official-submission re-check, and desk-reject heuristics.

Advances in Mathematics (advances-in-mathematics)

Journal positioning

Advances in Mathematics, published by Elsevier, is a leading general journal of pure mathematics that publishes high-quality original research across all major areas. Its defining character is breadth at a high standard: it is not restricted to a single field and welcomes strong results from algebra, geometry, topology, number theory, analysis, combinatorics, and beyond, provided the work is significant and of interest beyond a narrow sub-community. Advances sits just below the very top general journals in selectivity — excellent, substantial research that may not reach the field-reshaping bar of Annals is well placed here. The journal rewards new theorems, new structures, and new methods presented with clarity and full rigor.

This skill is a fit / venue-selection / re-framing tool. It does not replace the journal's current official submission guidelines. Before submitting, re-check the live author instructions on the Advances in Mathematics Elsevier site and confirm submission procedures.

When to trigger

The author is considering Advances in Mathematics for a strong, general-interest pure-mathematics paper.
A result is excellent and of broad interest but the author is unsure whether it reaches inventiones-mathematicae or journal-of-the-american-mathematical-society level.
A paper spans or bridges sub-fields and the author wants a high-standard generalist venue rather than a specialized one.
The author needs Advances' significance and rigor bar, plus common rejection reasons, before submission.

Scope & topic fit

Pure mathematics across all major areas: algebra, representation theory, algebraic and differential geometry, topology, number theory, analysis, probability, combinatorics, logic, category theory.
New theorems of substantial interest, new mathematical structures or invariants, and new methods with potential to influence work beyond the immediate problem.
Results that bridge sub-fields or import techniques from one area into another are well suited to a generalist venue.
Strong, complete advances that are significant but perhaps more specialized than the very top general journals require.
Survey or purely expository work is generally not the focus; contributions must be primary research with new, fully proved results.

Method & evidence bar

The primary standard is mathematical correctness: every claim must be fully proved; no proof sketches, unresolved cases, or conditional results in place of complete arguments (unless conditionality is the explicit contribution).
Significance is judged on interest and substance to a broad mathematical readership, not on citation counts or problem fame alone.
Novelty matters: new technique or genuinely new results are expected; routine extensions of known arguments are unlikely to clear the bar.
Exposition must let expert referees verify correctness: precise statements, complete proofs, and clear separation of new from standard material.
MSC (Mathematics Subject Classification) codes must be assigned correctly to signal scope and assist referee assignment.
arXiv posting is standard practice; most submissions appear on arXiv before or contemporaneously with submission.

Structure & house style

No imposed structural template beyond mathematical convention: introduction (context, precise statement of results, proof strategy), preliminaries, core proof sections, optional appendices.
The introduction should state main results precisely, explain significance to a broad mathematical audience, and outline key ideas — generalist referees and a broad editorial board read it first.
LaTeX is standard; Elsevier formatting conventions apply — re-check the current style requirements and reference style on the submission site.
References must be complete and correctly formatted; preprint citations should carry stable arXiv identifiers.
Length is set by mathematical necessity; there is no fixed page limit, but unnecessary length attracts scrutiny — concise, complete arguments are valued.

Official-submission checklist

Before giving submission-ready advice, read ../../resources/source-basis.md and ../../resources/official-source-map.md; start from the official source anchors for this journal family, then cite the current journal-specific page you checked.
Check the current Advances in Mathematics submission instructions on the Elsevier site and re-verify the submission system and procedure.
Assign MSC primary and secondary classification codes.
Post to arXiv (or confirm prior posting) with the identifier ready for correspondence.
Prepare a cover letter stating the main result, its significance to a broad readership, and suggested/excluded referees with conflicts noted.
Confirm all co-authors have approved the submission and re-check current open-access/APC options under Elsevier.
If the live official instructions conflict with this skill, the official instructions win.

Pre-submission self-check

One sentence stating the main theorem and why it is of broad mathematical interest.
Every claim is fully proved; no gaps, sketches, or unresolved cases.
The result is genuinely new and substantial, not a routine extension of known arguments.
The introduction states results precisely, explains significance, and outlines proof ideas for a generalist audience.
The paper is posted or ready to post on arXiv with correct MSC codes.
An honest assessment: is this best at Advances, or does its significance warrant a try at inventiones-mathematicae or journal-of-the-american-mathematical-society first?

Common desk-reject triggers

A correct but incremental result that extends known techniques without a substantially new idea.
A narrowly specialized paper of interest only to a small sub-community, better suited to a field journal.
An incomplete proof: any identifiable gap, unresolved case, or unjustified claim.
An introduction that fails to convey significance or broad interest to a generalist editorial board.
Expository or survey material submitted as primary research without new theorems.

Re-routing decision

Result of exceptional, field-reshaping significance → annals-of-mathematics. Top-tier general-interest advance just above the Advances bar → inventiones-mathematicae or journal-of-the-american-mathematical-society. Deep analysis / PDE / applied-analysis with substantial theorem content → communications-on-pure-and-applied-mathematics. Narrowly specialized result → a field-specific journal (Duke Mathematical Journal for broad-but-deep work, or area-specific society journals).

Output format

[Fit] High / Medium / Low (one-line reason)
[Target] Advances in Mathematics
[Topic tags] <2–3 MSC areas>
[Method/evidence] <is the main result fully proved, genuinely new, and of broad mathematical interest?>
[Top risk] <the single most likely reason for rejection — usually significance or breadth>
[Official items to re-check] <submission procedure / MSC codes / arXiv posting / cover letter / style file>
[Re-route suggestion] <if not a fit, a better-matched venue>