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.