# Math Reasoning

> Formal mathematical reasoning for research papers — derive equations, write proofs, formalize problem settings, select statistical tests, and generate LaTeX math notation. Use when the user needs mathematical derivations, theorem proofs, notation tables, or statistical analysis formalization.

- Skill: `om-scogo/math-reasoning` (Agent Skill, multi-file: 4 files)
- Install (CLI): `npx skillmds add om-scogo/math-reasoning`
- Raw SKILL.md: https://api.skillmd.com/api/skills/om-scogo/math-reasoning/raw
- Safety review: pending
- Works with: Claude Code, Claude.ai, OpenAI Codex
- Category: AI & ML
- Author: om-scogo (https://skillmd.com/u/om-scogo)
- Updated: 2026-09-08
- Page: https://skillmd.com/skills/om-scogo/math-reasoning

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# Mathematical Reasoning

Perform rigorous mathematical reasoning and produce publication-quality LaTeX output.

## Input

- `$0` — Task type: `derive`, `prove`, `formalize`, `stats`, `notation`, `verify`
- `$1` — Context: equation, theorem statement, problem description, or data description

## Tasks

### `derive` — Step-by-step equation derivation
Show every intermediate step. Justify each with the rule applied. Box final result with `\boxed{}`. Number important equations with `\label{eq:name}`.

### `prove` — Formal theorem proof
Use appropriate technique: direct, contradiction, induction, construction, or cases. See `references/proof-templates.md` for LaTeX templates.

### `formalize` — Problem setting formalization
Convert informal description into formal mathematical framework with: variable definitions, domain/range specifications, assumptions, objective function.

### `stats` — Statistical test selection
Use the decision tree in `references/notation-guide.md` to select appropriate tests. Report p-values, effect sizes, confidence intervals.

### `notation` — Generate notation table
Create a `\begin{table}` with all symbols used in the paper. Use standard ML notation from `references/notation-guide.md`.

### `verify` — Check mathematical correctness
Verify: dimensional consistency, boundary cases, gradient computations, notation consistency across sections.

## References

- Standard ML notation + statistical tests: `~/.claude/skills/math-reasoning/references/notation-guide.md`
- Proof templates and theorem environments: `~/.claude/skills/math-reasoning/references/proof-templates.md`

## Rules

- Define ALL symbols before first use: "Let $\mathcal{X}$ denote..."
- Use consistent notation throughout the paper
- Number equations that are referenced later
- Use `\tag{reason}` for key derivation steps
- State assumptions explicitly
- Cite lemmas and prior results used in proofs

## Related Skills
- Upstream: [research-planning](../research-planning/)
- Downstream: [algorithm-design](../algorithm-design/), [paper-writing-section](../paper-writing-section/)
- See also: [symbolic-equation](../symbolic-equation/), [data-analysis](../data-analysis/)