math-reasoning

math-reasoning is a skill for performing rigorous formal mathematical reasoning and producing publication-quality LaTeX output for research papers. It addresses the common need in ML/AI research writing to derive equations carefully, write formal proofs, formalize problem settings, choose appropriate statistical tests, and generate consistent notation — all while keeping notation and assumptions explicit and reproducible.

The skill is organized around task types passed as arguments: `derive` (step-by-step equation derivation with justified intermediate steps and boxed results), `prove` (formal theorem proofs using direct, contradiction, induction, construction, or cases techniques), `formalize` (converting informal descriptions into formal frameworks with variables, domains, assumptions, and objectives), `stats` (statistical test selection via a decision tree, reporting p-values, effect sizes, and confidence intervals), `notation` (generating a symbol table), and `verify` (checking dimensional consistency, boundary cases, gradients, and notation consistency). It bundles two reference files: a standard ML/AI notation guide with LaTeX for sets, probability, optimization, linear algebra, and common operations plus a statistical-tests decision tree, and a set of proof templates covering theorem environments, proof techniques, convergence and generalization bounds, and complexity analysis.

It targets ML/AI researchers, graduate students, and technical writers preparing papers who want mathematically sound derivations and proofs expressed in idiomatic LaTeX. Use cases include writing a proofs section, building a paper's notation table, formalizing an experimental setup, and selecting and reporting the right statistical test for an evaluation.