# Revise Math Paper

> Revises a paragraph or section of a mathematical paper. Fixes English errors, improves flow, splits long sentences, and reorders for clarity. Keeps all math content unchanged. Notation changes need user approval. Use when the user asks to revise a paragraph, section, or passage of a math paper.

- Skill: `jiajunma/revise-math-paper` (Agent Skill)
- Install (CLI): `npx skillmds@latest add jiajunma/revise-math-paper`
- Raw SKILL.md: https://api.skillmd.com/api/skills/jiajunma/revise-math-paper/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: jiajunma (https://skillmd.com/u/jiajunma)
- Updated: 2026-09-22
- Page: https://skillmd.com/skills/jiajunma/revise-math-paper

---


# Revise Mathematical Paper (Paragraph/Section)

## Scope

Revise a **paragraph or section** of a mathematical paper. Goals:

- Fix English errors (grammar, punctuation, word choice)
- Improve flow (clarity, sentence structure, transitions)
- Use simple, clear English; prefer short sentences over long ones
- Split long sentences into shorter ones when needed
- Reorder sentences when it improves flow; preserve meaning and keep logic smooth
- Make language vivid and engaging where appropriate
- Vary sentence structures; avoid repeating the same patterns
- Check notation consistency within the passage
- **Critical:** Do NOT change any mathematical content (definitions, statements, proofs, equations)

## Notation handling

- **Consistency check:** Check that each symbol, variable, and notation is used the same way throughout the passage.
- **If notation must change** (e.g., to fix inconsistency): do **not** apply changes automatically. Instead:
  - Present the inconsistencies to the user
  - Propose one or more notation options for the user to choose
  - Wait for user approval before modifying notation
- **If multiple places need modification:** ask the user whether to fix **one place at a time** or **all places at once** before applying any changes.

## Workflow

### 1. Generate the revision

Produce a revised version of the target paragraph or section. Improve English and flow. Use simple, clear language. Prefer short sentences; split long ones when needed. Reorder sentences for better flow when useful, but preserve meaning and logic. Make the prose vivid. Vary sentence structures. Do not:

- Change, add, or remove mathematical definitions
- Alter notation, variable names, or symbols (see Notation handling; user approval required)
- Modify logical statements, theorem statements, or proof steps
- Change the meaning of any mathematical content


### 2. Compare original vs revised

Create a side-by-side or diff-style comparison showing what changed between the original and the revision.

### 3. Check notation consistency

- Scan the passage for inconsistent notation. Examples: same concept with different symbols, or same symbol with different meanings.
- If you find inconsistencies: report them and follow **Notation handling**. Do not auto-fix.

### 4. Verify mathematical content preservation

Systematically check that:

- [ ] Every mathematical symbol, notation, and variable is unchanged in meaning
- [ ] No definitions, hypotheses, or conclusions were added, removed, or altered
- [ ] All equations, formulas, and mathematical statements are identical in content
- [ ] Proof structure and logical steps are preserved

### 5. Produce revision report

Write a report **on the revision itself**. Do not write instructions for fixing it. Format:

```markdown
# Revision Report

## Verdict
- **Pass**: Mathematical content is preserved. Revision is acceptable.
- **Fail**: Mathematical content was altered. Revision must be redone.

## Comparison Summary
[Brief description of what changed. E.g.: English fixes, flow improvements.]

## Notation Consistency
[List any notation inconsistencies found. If found, list proposed options and await user choice per Notation handling.]

## Math-Content Verification
- [Item-by-item verification result for each mathematical element]
- [List any changes that affect math content, if any]

## Conclusion
[One sentence: Pass or Fail. If Fail, include the reason.]
```

### 6. Redo if failed

If the report verdict is **Fail**:

1. Use the revision report as an **additional prompt**. Pay special attention to "Math-Content Verification" and "Conclusion".
2. Redo the revision **starting from the current revised version** (not the original). Fix the points where math content was altered.
3. Return to step 2. Compare the new revision against the original. Verify it. Produce a new report.
4. Repeat until the report verdict is **Pass**.

### 7. Apply the revision

Apply the revised text to the LaTeX file only when:
- The report verdict is **Pass**
- Any notation changes have user approval

Do not apply revisions that failed verification. Do not apply notation changes without explicit user consent.

## Output Expectations

- The report assesses the revision (pass/fail). It does not explain how to correct future revisions.
- Be explicit about what changed. State whether it affects mathematical content.
- If math content was altered: state exactly what was changed and why it fails.
- Do not skip the verification step. Do not apply a revision that failed.
- For notation changes: always seek user approval. When multiple fixes exist, ask whether to fix one place at a time or all at once.