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BDD-Driven Mathematical Content Verification Skill Combines Behavior-Driven Development with mathematical formula extraction, verification, and transformation using: - Cucumber/Gherkin for specification - RSpec for implementation verification - mathpix-gem for LaTeX/mathematical content extraction - Pattern matching on syntax trees for formula validation Enables iterative discovery and verification of mathematical properties through executable specifications.

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Mathematical visualization skill for equations, proofs, and geometric concepts. **Triggers when:** - User mentions equations, formulas, or mathematical expressions - Request involves mathematical proofs or derivations - Content includes geometric relationships - User mentions LaTeX, calculus, algebra, geometry, trigonometry - Patterns: "equation", "formula", "prove", "derive", "graph", "plot" **Capabilities:** - LaTeX equation rendering with color-coded components - Function graphing and transformations - Geometric constructions and proofs - 3D mathematical surfaces - Step-by-step derivations with highlights

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Think and work like an expert Mathematical Physicist. Use when a task calls for Mathematical Physicist judgment. Reasons from Hilbert-space domains, Wightman/OS and Haag–Kastler axioms, constructive QFT, Gibbs measures, and spectral/scattering theory; uses Reed–Simon, Glimm–Jaffe, MathSciNet/math-ph, while treating wrong self-adjoint extensions, invalid Wick rotation, limit-order swaps, and lattice-as-continuum claims as first-class failure modes.

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Real-world problem formulation, mathematical abstraction, and applied mathematics for translating between practical problems and mathematical frameworks. Covers the modeling cycle (problem identification, assumptions, formulation, analysis, validation, interpretation), Polya's framework adapted for modeling, common model types (linear, exponential, logistic, periodic, power-law), dimensional analysis (Buckingham Pi theorem), optimization (linear programming, gradient descent, constraint satisfaction), probability models (Markov chains, queuing theory, Monte Carlo simulation), statistical modeling (regression, hypothesis testing, model selection), model criticism (overfitting, underfitting, sensitivity analysis), and real-world case studies. Use when formulating mathematical models, performing dimensional analysis, optimizing systems, running simulations, or evaluating model validity.

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Use this skill in the MathModel LaTeX sandbox when the user asks to reproduce built-in scientific visualization templates, especially prompts from the Improve tab mentioning $mathmodel-figure-templates, 科研绘图模板, SHAP蜂群柱状图, 配对云雨图, 交叉验证ROC, 泰勒图, 相关矩阵组合图, 预测真实值边缘分布图, TPE调参3D曲面, 下三角相关矩阵半边小提琴图, 分组环形热图, 城市公园降温组合图, or Nature和弦图. It provides ready-to-run Python scripts bundled inside the skill.

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Deterministic mathematical computation using SymPy. Use for ANY math operation requiring exact/verified results - basic arithmetic, algebra (simplify, expand, factor, solve equations), calculus (derivatives, integrals, limits, series), linear algebra (matrices, determinants, eigenvalues), trigonometry, number theory (primes, GCD/LCM, factorization), and statistics. Ensures mathematical accuracy by using symbolic computation rather than LLM estimation.

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Design a Concrete-Pictorial-Abstract learning sequence for a mathematical concept using manipulatives. Use when teaching maths through Singapore method or when students struggle with abstraction.

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Generate a coherent, whole-paper mathematical modeling solution framework from a complete contest problem. Use after the user supplies a CUMCM or other modeling problem and asks for modeling ideas, an overall solution plan, question-by-question analysis, candidate-model comparison, model-selection reasons, innovations, validation, or cross-question linkage. For every question, explain the task and mathematical essence, compare multiple feasible models in tables, recommend a route with explicit reasons, and keep all questions connected through shared data, variables, parameters, constraints, and validation.

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Design a Concrete-Pictorial-Abstract learning sequence for a mathematical concept using manipulatives. Use when teaching maths through Singapore method or when students struggle with abstraction.

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The logical structure of mathematical proof -- how first-order logic, natural deduction, and semantic reasoning combine to produce rigorous mathematical arguments. Covers the logical skeleton of direct proof, contraposition, contradiction, cases, and induction; the role of definitions, lemmas, and theorems; how informal mathematical prose maps to formal deductive structure; and the difference between proof-as-object and proof-as-activity. Use when the question is "why is this a valid proof?" rather than "what proof technique applies?"

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Generate satirical "math slop" ragebait formulas that connect famous constants (φ, π, e, i) in trivially true but profound-looking equations. Outputs LaTeX. Use for math memes or when someone asks for "math slop."

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数学の概念や数式の導出、アルゴリズムの動きをアニメーション動画にします。構成づくりから描画、動画の結合まで、図形で理解を促す解説を制作します。

• 数学の概念を図形で説明したいとき
• 数式の導出を順に見せたいとき
• アルゴリズムの動きを可視化

Solve competition math problems (IMO, Putnam, USAMO, AIME) with adversarial verification that catches the errors self-verification misses. Activates when asked to 'solve this IMO problem', 'prove this olympiad inequality', 'verify this competition proof', 'find a counterexample', 'is this proof correct', or for any problem with 'IMO', 'Putnam', 'USAMO', 'olympiad', or 'competition math' in it. Uses pure reasoning (no tools) — then a fresh-context adversarial verifier attacks the proof using specific failure patterns, not generic 'check logic'. Outputs calibrated confidence — will say 'no confident solution' rather than bluff. If LaTeX is available, produces a clean PDF after verification passes.

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Production pipeline for mathematical and technical animations using Manim Community Edition. Creates 3Blue1Brown-style explainer videos, algorithm visualizations, equation derivations, architecture diagrams, and data stories. Use when users request: animated explanations, math animations, concept visualizations, algorithm walkthroughs, technical explainers, 3Blue1Brown style videos, or any programmatic animation with geometric/mathematical content.

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Use this skill when working with symbolic mathematics in Python. This skill should be used for symbolic computation tasks including solving equations algebraically, performing calculus operations (derivatives, integrals, limits), manipulating algebraic expressions, working with matrices symbolically, physics calculations, number theory problems, geometry computations, and generating executable code from mathematical expressions. Apply this skill when the user needs exact symbolic results rather than numerical approximations, or when working with mathematical formulas that contain variables and parameters.

日本語の概要は準備中です。原文の説明を表示しています。

Use this skill when working with symbolic mathematics in Python. This skill should be used for symbolic computation tasks including solving equations algebraically, performing calculus operations (derivatives, integrals, limits), manipulating algebraic expressions, working with matrices symbolically, physics calculations, number theory problems, geometry computations, and generating executable code from mathematical expressions. Apply this skill when the user needs exact symbolic results rather than numerical approximations, or when working with mathematical formulas that contain variables and parameters.

日本語の概要は準備中です。原文の説明を表示しています。

Use this skill when working with symbolic mathematics in Python. This skill should be used for symbolic computation tasks including solving equations algebraically, performing calculus operations (derivatives, integrals, limits), manipulating algebraic expressions, working with matrices symbolically, physics calculations, number theory problems, geometry computations, and generating executable code from mathematical expressions. Apply this skill when the user needs exact symbolic results rather than numerical approximations, or when working with mathematical formulas that contain variables and parameters.

日本語の概要は準備中です。原文の説明を表示しています。

Production pipeline for mathematical and technical animations using Manim Community Edition. Creates 3Blue1Brown-style explainer videos, algorithm visualizations, equation derivations, architecture diagrams, and data stories. Use when users request: animated explanations, math animations, concept visualizations, algorithm walkthroughs, technical explainers, 3Blue1Brown style videos, or any programmatic animation with geometric/mathematical content.

日本語の概要は準備中です。原文の説明を表示しています。

Generate and render-verify publication-quality mathematical-modeling figures from saved evidence, using the approved figure plan, source data, claim, type, and consistent visual system.

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Creates a Check for Understanding (CFU) for a math topic or standard: 1–3 targeted formative items whose distractors come from documented student misconceptions, plus a teacher guide routing each likely response to a specific next instructional step. Load BEFORE asking any clarifying question about grade, standard, or topic. This skill is for math; for other subjects, help as you normally would and don't mention the skill to the user. Triggers on asks to create, write, generate, or design a check for understanding, formative check, quick check, or exit ticket for a math concept or standard, and on implicit signals like "I need to see who got it before I move on." Not a quiz, test, or practice set — a CFU is read for what it reveals, not scored, so a numbered quiz or a bare answer key is a different job. Does not create a lesson (k12-lesson-plan-creation, which brings its own exit ticket), tier one (k12-lesson-differentiation), or prepare a teacher to teach one (k12-lesson-prep).

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Calculate simple mathematical expressions using shell commands. Use when the user asks to perform arithmetic calculations like addition, subtraction, multiplication, division, or more complex math expressions.

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Review the model establishment, numerical solution, result analysis, model validation, and sensitivity or robustness sections of a mathematical-modeling paper against the complete problem. Use for core-model-section diagnosis, not automatic full-paper scoring or unsupported recomputation.

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Review the symbol-notation section of a mathematical-modeling paper against the full paper. Check table coverage, symbol meanings, units, overloading, case and subscript consistency, first-use definitions, formula usage, and visible table formatting. Use for symbol-table diagnosis, not general paper review.

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Check a mathematical-modeling paper's in-text citations, bibliography, appendix length and content, code, supporting files, reproducibility, consistency, and anonymity. Use when the user provides a paper or related materials and wants one consolidated P0-P3 audit; do not generate or invent missing sources or programs.

日本語の概要は準備中です。原文の説明を表示しています。