Use when organizing the exposition and structure of a pure-mathematics manuscript for Annals of Mathematics — sectioning, notation, statements-before-proofs, commutative diagrams, and readability for an expert non-specialist. Figures are optional and rare; this skill is about exposition first. Does not assess the proof's correctness.
SkillScore100Maintained
Automatic
◆Writing & Editing pack
Last verified 8/15/2026
What it changes
Passed 23 of 23 test cases with the skill, and 22 of 23 without it.
Without skill96%
With skill100%
Checks it passed that the model alone missed
The response requires defining every symbol at first use.
1 fixed22 passed either way0 still failing0 broke
Pass-rate lift
+4 pp
Tokens
+17%
Agent turns
0%
Response time
-40%
Model gemini-3.6-flashMeasured 8/15/2026v123 of 23 cases passed with skill
Tokens, turns and time describe resource use, not a dollar price.
See it in action
A test case the skill fixed. Same model, same prompt, with and without the skill.
Prompt
In my draft on algebraic geometry, I start using $X_\Delta$ on page 10, but I don't explain what $\Delta$ represents until the middle of page 15. Is this acceptable if the definition is eventual?
What was checked, without and with the skill
Checked
Without skill
With skill
The response requires defining every symbol at first use.
Missed
Passed
case-22 · gemini-3.6-flash · 8/15/2026 · answers are capped and redacted
What's inside
The instructions your model reads when the skill loads.
SKILL.md100 linessingle file
Exposition and Structure (anmath-figures)
When to trigger
The paper is hard to follow even though the proof is correct
Notation is inconsistent or introduced after first use
Theorems and their proofs are interleaved confusingly
A relation between objects would be far clearer as a commutative diagram
You are deciding whether the rare case of an actual figure is warranted
In pure mathematics, papers are theorem-and-proof and usually have no experiments and
few or no figures. "Figures" here means exposition and structure: a figure or diagram
is included only when it conveys structure more efficiently than prose.
Exposition principles (Annals readability)
Statements before proofs. State each definition, lemma, proposition, and theorem in
full before proving it. The reader should always know the target before the argument.
Notation introduced once, used consistently. Define every symbol at first use; keep
a fixed convention throughout; avoid overloading the same symbol for two things.
Logical sectioning. Preliminaries → key constructions → main lemmas → proof of the
Main Theorem → consequences. Each section has a clear job and a one-line opener.
Self-contained where reasonable. Recall the precise external statements you use so a
reader need not reconstruct them from memory.
Readable by an expert non-specialist. Someone strong in an adjacent area should be
able to follow the architecture; gloss the field-specific shorthand the first time.
Sectioning template
Section
Contents
Introduction
Problem, Main Theorem, what is new, method sketch, organization