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/)