Annals of Mathematics Workflow (anmath-workflow)

Overview

This is the router. It does not replace any specialized skill; it tells you which anmath- skill to use at your current stage of a theorem-and-proof manuscript.

Default assumption: unless you say otherwise, the target is Annals of Mathematics, where the bar is significance + originality + a complete, correct, rigorously verified proof with clear exposition. The importance threshold is very high and acceptance is highly competitive.

When to trigger

• You ask "what should I do next?" with a math paper in progress
• You have a draft and need to find the current bottleneck (significance? a gap? exposition?)
• You are cycling between proof, writing, and referee response and have lost the thread
• You received a referee report from Annals and need to switch into revision mode

Routing table

| Current symptom | Next skill | |------------------------------------------------------------------|---------------------------| | Unsure the result clears the Annals importance bar / is in scope | anmath-scope-fit | | Main theorem stated vaguely; significance/positioning unclear | anmath-results-framing | | Proof works but the argument's architecture is not laid out | anmath-methods | | Exposition is hard to follow; sectioning/notation/diagrams weak | anmath-figures | | Long computations / auxiliary lemmas clutter the main line | anmath-supplementary | | Prose is sloppy; "clearly"/"it is easy to see" hide steps | anmath-writing-style | | Paper feels bloated or padded; every section not yet justified | anmath-length-management| | Preparing the cover note to the editors | anmath-cover-letter | | Ready to submit; need the final preflight | anmath-submission | | Want to anticipate how an expert referee will probe the proof | anmath-referee-strategy | | Received a report; need to revise and reply | anmath-revision |

Default order

1. anmath-scope-fit — confirm the result is important and original enough for Annals
2. anmath-results-framing — state the main theorem(s) precisely and position them
3. anmath-methods — lay out the proof strategy, key lemmas, and where the difficulty lies
4. anmath-figures — exposition and structure: sectioning, notation, statements-before-proofs
5. anmath-supplementary — move auxiliary results / long computations to appendices
6. anmath-writing-style — eliminate gaps and "clearly"; tighten every claim
7. anmath-length-management — confirm every section is necessary; cut bloat
8. anmath-cover-letter — concise letter framing significance for the editors
9. anmath-submission — final preflight (format, TeX, MSC, references, arXiv)
10. anmath-referee-strategy — stress-test the proof against expert scrutiny before sending
11. anmath-revision — after the report arrives

> anmath-writing-style and anmath-length-management are late-stage polish; do not > run them before the proof is actually complete and the architecture is fixed.

Decision heuristics

• "I am not sure this is big enough for Annals" → anmath-scope-fit
• "My main theorem is a paragraph, not a precise statement" → anmath-results-framing
• "The proof is right but readers can't see the plan" → anmath-methods
• "A referee would get lost in Section 3" → anmath-figures
• "I have a 6-page computation in the middle of the proof" → anmath-supplementary
• "I wrote 'it is easy to see' and it is not" → anmath-writing-style
• "The paper is 90 pages and I can't justify all of them" → anmath-length-management
• "I'm clicking submit tomorrow" → anmath-submission
• "I got a referee report" → anmath-revision

Difference vs. a generic math-writing toolbox

A generic LaTeX/writing helper optimizes for readability alone. This stack is tuned to the Annals standard: the importance bar is unusually high, and a single hidden gap is fatal. Significance and complete rigor dominate every routing decision here.

Submission bundle layout

The final preflight (anmath-submission) checks a concrete file tree. A single hidden gap is fatal at Annals, so the arXiv/journal package must let a referee verify the proof end-to-end with nothing missing. Target layout:

text
paper-submission/
├── main.tex              % single self-contained source; amsart or Annals class
├── main.pdf              % compiled, matches .tex exactly
├── refs.bib              % all cited works; MathSciNet-verified keys
├── figures/              % vector (.pdf/.eps); each referenced in text
│   └── fig-1.pdf
└── README.txt            % MSC 2020 primary+secondary, arXiv id, prior-submission note
CHECK before upload:
  [ ] main theorem stated precisely in the introduction, with hypotheses explicit
  [ ] every lemma either proved here or cited to a verifiable source
  [ ] no "clearly" / "it is easy to see" standing in for an unwritten step
  [ ] appendices hold long computations; the main line stays readable
  [ ] cover letter frames significance for the editors (anmath-cover-letter)

Anti-patterns

• Do not skip anmath-scope-fit — Annals desk-screens on importance first
• Do not let anmath-figures polish exposition while a proof gap remains open
• Do not let anmath-revision draft a reply before you have actually fixed the text
• Do not treat anmath-supplementary as a dumping ground — essentials stay in main text