math-reasoning

Original：🇺🇸 English
Translated

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.

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Sourcelingzhi227/agent-research-skills
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npx skill4agent add lingzhi227/agent-research-skills math-reasoning

Tags

Translated version includes tags in frontmatter
mathematical-reasoninglatex-generationacademic-paperstatistical-analysistheorem-proof

SKILL.md Content

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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