Advances In Mathematics

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.