/math-reasoning

name: math-reasoning
description: 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.
argument-hint: [task-or-context]

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/)