| 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
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>
