'math' 검색 결과

Writes and reviews Lean 4 proofs, machine-checked arguments for mathematics or specifications. Follows Mathlib conventions to organize definitions and lemmas, fill proof gaps, refactor lengthy proofs, and establish automated checks for unproved claims and style.

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• Formalizing mathematics or specifications in Lean 4
• Filling sorry placeholders in proofs
• Splitting long proofs into reusable lemmas

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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Work through one difficult mathematics problem with a single agent, saving established arguments and dead ends as progress notes. Resumes from recorded work after interruptions and writes a self-contained proof file, including any unresolved parts.

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• Work through one difficult mathematics problem
• Resume a proof attempt after an interruption
• Record lemmas, reductions, and dead ends

Investigate one difficult mathematics problem through repeated rounds of independent agent work and review. Track proved, refuted, and unresolved claims, check proposed proofs, and produce a self-contained proof.md that clearly states what remains unproved.

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• Investigate a difficult mathematics problem over multiple rounds
• Check a proposed proof through independent reviews
• Track proved claims and unresolved gaps

Turn mathematical claims into definitions, lemmas, and proofs for Lean 4 and Mathlib. Check proofs with Lean’s trusted core, separately review whether the formal statement matches the original claim, and record verification evidence.

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• Verifying an important lemma with Lean 4
• Breaking a theorem into definitions and supporting lemmas
• Checking proofs for sorry, admit, and unauthorized axioms

Create mathematical and technical explainer videos with Manim Community Edition. The skill guides scene planning, animation code, rendering, and clip assembly to show equations, algorithms, system structures, and data through coordinated visuals.

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• Explaining mathematical concepts through animation
• Showing equation derivations step by step
• Visualizing algorithm execution

Check mathematical expressions, solve equations, and search bounded ranges for counterexamples using symbolic and numerical libraries. Record assumptions, commands, and results so calculations can be repeated, while keeping computational evidence distinct from general mathematical proof.

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• Checking identities and integrals with exact arithmetic
• Searching a defined range for counterexamples
• Cross-checking numerical results at higher precision

Helps write and review mathematical proofs in natural language. It clarifies assumptions, maps dependencies between claims and lemmas, checks counterexamples and edge cases, and produces a traceable draft that identifies unresolved gaps or necessary changes to the statement.

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• Filling gaps in a mathematical proof draft
• Mapping dependencies between claims and lemmas
• Searching for counterexamples and edge cases

Generate scientific chart examples from bundled Python scripts using repeatable simulated data. Choose from templates such as raincloud plots, correlation matrices, and ROC charts, then receive PNG, PDF, SVG, and editable script files.

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• Generating sample scientific charts from templates
• Comparing correlation and prediction chart layouts
• Customizing labels and legends in generated charts

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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Create mathematical and geometric animations in Python with Manim Community Edition. Use guidance, examples, and scene templates to structure animations, display equations, plot graphs, control cameras, and render two-dimensional or three-dimensional scenes.

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• Animating equations and derivations
• Creating function graphs and area visualizations
• Building 3D surfaces with camera movement

Solve competition mathematics problems and examine proofs through independent agents that actively look for gaps, counterexamples, and misused theorems. Produces a checked argument or clearly states what remains unresolved, with optional PDF output.

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• Solve an IMO or Putnam problem
• Check a competition proof for gaps
• Find counterexamples to claims within a proof

Plan Chinese math tutorial videos with clear solution steps, spoken explanations, readable formulas, and matching subtitles. The skill guides lesson structure and pacing, while Creator’s native tools build the visuals, narration, and finished video.

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• Planning a Chinese equation tutorial
• Explaining geometry one step at a time
• Matching math narration with formulas and subtitles

Develop mathematical proofs in Lean, a system that checks formal proofs, continue unfinished projects, or audit existing results. Check that the theorem matches the original claim, examine its assumptions, and prepare sources and commands for reproduction.

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• Turn a mathematical statement into a checked Lean proof
• Continue an unfinished Lean proof project
• Audit whether a theorem proves the original claim

Check mathematical proofs in LaTeX with review by a separate AI model. Identify missing assumptions and unsupported steps, explore counterexamples, repair derivations, and keep an audit record of issues, changes, and follow-up reviews.

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• Checking proofs in a theory paper
• Finding missing assumptions in lemmas
• Repairing gaps in mathematical derivations

Turn scattered formulas and theory notes into a derivation that can be checked step by step. Keep definitions and assumptions consistent, distinguish exact identities from approximations, and make hidden conditions and limits explicit.

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• Organize scattered formulas and theory notes
• Trace the steps behind an algebraic identity
• State conditions and error orders for approximations

Coordinates a mathematical modeling competition project from planning to final checks. It records formatting and language preferences, creates a plan and task checklist, and calls dedicated skills for modeling, coding, diagrams, paper writing, and verification.

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• Starting a mathematical modeling competition project
• Planning work around competition and formatting preferences
• Tracking progress across modeling and paper-writing stages

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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