math-reasoning
lingzhi227/agent-research-skills
Formal mathematical reasoning for research papers—derive equations, write proofs, and generate publication-quality LaTeX.
What is math-reasoning?
Performs rigorous mathematical reasoning including equation derivation, theorem proofs, problem formalization, statistical test selection, and LaTeX notation generation. Use when you need to develop mathematical foundations, verify correctness, or produce formal notation for research papers.
- Derive equations step-by-step with justified intermediate steps and boxed final results
- Write formal proofs using direct, contradiction, induction, construction, or case-based techniques
- Formalize problem settings with variable definitions, domains, assumptions, and objective functions
- Select appropriate statistical tests with p-values, effect sizes, and confidence intervals
- Generate notation tables with consistent ML and statistical symbols
- Verify mathematical correctness including dimensional consistency and boundary cases
How to install math-reasoning
npx skills add https://github.com/lingzhi227/agent-research-skills --skill math-reasoning- LaTeX knowledge helpful but not required
- Familiarity with the mathematical domain being reasoned about
How to use math-reasoning
- 1.Specify the task type: derive, prove, formalize, stats, notation, or verify
- 2.Provide context: equation, theorem statement, problem description, or data description
- 3.Review the generated LaTeX output for consistency with your paper's notation
- 4.Use proof templates from references/proof-templates.md for formal proofs
- 5.Reference the notation guide at references/notation-guide.md for standard symbols
Use cases
- Developing mathematical foundations for a research paper with step-by-step derivations
- Proving theorems or lemmas using formal proof techniques and LaTeX templates
- Converting informal problem descriptions into rigorous mathematical frameworks
- Selecting and justifying statistical tests for empirical analysis
- Creating comprehensive notation tables for multi-section papers
- Researchers writing papers with mathematical content
- PhD students formalizing problem settings and proofs
- Data scientists selecting and justifying statistical methods
- Anyone producing publication-quality mathematical notation and derivations
math-reasoning FAQ
Direct proof, proof by contradiction, mathematical induction, construction, and proof by cases. Templates for each are available in references/proof-templates.md.
Yes. The 'stats' task uses a decision tree to select appropriate statistical tests and reports p-values, effect sizes, and confidence intervals.
Yes. All output is publication-quality LaTeX with proper equation numbering, symbol definitions, and notation consistency.
It requires defining all symbols before first use and maintains a notation table. The 'verify' task checks consistency across sections.
Use the 'verify' task to check dimensional consistency, boundary cases, gradient computations, and notation consistency across your paper.
Full instructions (SKILL.md)
Source of truth, from lingzhi227/agent-research-skills.
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
- Downstream: algorithm-design, paper-writing-section
- See also: symbolic-equation, data-analysis
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