# Mathematical Research Methodology

> Frame and refine a math research question, choose tactics (prove vs compute vs simulate), keep a tight research diary.

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

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# Mathematical research methodology

- **State the question precisely** before anything else: domain, hypotheses, unknown, success criterion.
- Catalogue **what is known** (cite theorems, papers) and **what is unknown** explicitly.
- Pick a tactic: a proof attempt, a computer-algebra reduction, or a numerical experiment — and say *why* that tactic.
- Keep a running **research diary** under `/agent-filesystem/research/<slug>/diary.md` with one entry per session: question, attempts, dead ends, next step.
- Re-evaluate after every dead end: is the question wrong, the tactic wrong, or the regime wrong?