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.

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/)

math-reasoning