# Mathematical Proof Writing

> Definition → lemma → theorem → corollary discipline, hypothesis tracking, casework hygiene, gap-spotting.

- Skill: `poly-gents/mathematical-proof-writing` (Agent Skill, multi-file: 2 files)
- Install (CLI): `npx skillmds@latest add poly-gents/mathematical-proof-writing`
- Raw SKILL.md: https://api.skillmd.com/api/skills/poly-gents/mathematical-proof-writing/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: Coding & Dev Tools
- Author: poly-gents (https://skillmd.com/u/poly-gents)
- Updated: 2026-09-17
- Page: https://skillmd.com/skills/poly-gents/mathematical-proof-writing

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# Mathematical proof writing

- Lead with the **theorem statement** and the **hypotheses you actually use**.
- One direction at a time; mark `(⇒)` / `(⇐)` for iff proofs.
- Distinguish definitions, lemmas, theorems, corollaries; cite every non-trivial step.
- Call out where a result is *needed* vs merely *available*.
- For computer-assisted parts, link the SymPy/Wolfram run (`python_run` invocation id or notebook path); never bury verification inside prose.
- Read the proof back from the bottom up at least once — does each line actually justify the next?