648 skills · sorted by relevance
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.
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.
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.
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.
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.
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.
Build understanding of mathematical ideas before calculating. The skill guides you through concrete examples, diagrams, simpler cases, and analogies, then summarizes the intuition and suggests a next step with a check.
Guides work on categories and functors by checking definitions, composition rules, and structure-preserving properties. Explains common functor types and provides examples for verifying proofs with Lean 4 and Mathlib.
Review progress while solving a math problem by organizing previous attempts, checking intermediate results, and assessing growing complexity. The skill recommends whether to continue, adjust the approach, switch strategies, or tackle a smaller problem first.
Work with mathematical formulas in Python to solve equations, calculate derivatives and integrals, and manipulate matrices. Keep exact results using symbols, then turn expressions into executable code or formatted LaTeX equations.
Provides a starting structure for work on formal logic and mathematical foundations, with source checks and a review of unresolved gaps. The material is a legacy template awaiting research and validation.
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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Create animated explanations of mathematical concepts, equation derivations, and algorithms with Manim Community Edition. The skill guides scene planning, Python animation code, rendering, and clip assembly into a finished explainer video.
Turn a math or science video idea into a detailed scene plan. Research the topic, clarify the audience, and outline visuals, narration, transitions, and implementation notes for Manim, an animation tool.
Combine capabilities from multiple fine-tuned LLMs without retraining using mergekit. Choose a merging method, configure how models are blended, and evaluate the resulting model on tasks such as math, code generation, and conversation.
Review mathematical proofs in LaTeX for logical gaps, missing assumptions, and unjustified steps. Attempt counterexamples, develop explicit repairs, and repeat the review, producing an audit report that distinguishes completed fixes from assumptions and unresolved proof obligations.
Clarify the next step in a mathematical research task by identifying what is blocking progress. Select one specialist skill for discovery, derivation, computation, proof, or formal verification, with required inputs and clear stopping conditions.
Write and edit Quarkdown documents, an extended form of Markdown, to produce reports, articles, slides, and other formatted content. Add layouts, math, diagrams, and themes, then compile the source to check for errors.
Turn a complete mathematical modeling competition paper into an English conference manuscript. Reorganize the research argument, track evidence, and prepare figures using an included IEEE LaTeX template, delivering source files and a PDF when compilation succeeds.
Provides shared reference material for mathematical modeling competitions, covering writing conventions, problem-specific pitfalls, and chart guidelines. Other skills consult relevant sections during their work; this resource does not run independently.