381,784 Collected SKILL.md files

Explore AI Agent Skills & Claude Prompts

Discover open-source agent skills for Claude Code, Codex, ChatGPT, and any tool that uses SKILL.md.

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mathematical science teachers postsecondary
Showing 12 of 476 skills
danielmiessler

systemsthinking

by danielmiessler
star 16.0k

Structural analysis of complex systems grounded in Donella Meadows, Peter Senge, Jay Forrester, Russell Ackoff, and the Santa Fe Institute tradition. Five workflows: Iceberg (walk Events → Patterns → Structures → Mental Models to find why the same thing keeps happening), CausalLoop (build causal loop diagrams with reinforcing R and balancing B loops), FindArchetype (match behavior to ~10 canonical patterns — Limits to Growth, Shifting the Burden, Tragedy of the Commons, Fixes That Fail, etc. — then apply the documented canonical intervention), FindLeverage (Meadows' 12 leverage points ordered by impact — parameters are weakest, paradigm transcendence is strongest), ConceptMap (Novak-style entity-relationship mapping). Core axiom: behavior is generated by structure; events are visible, structure is not. At Extended+ effort on anything with recurring behavior or cross-component coupling, systems thinking is the structural lens, not optional enrichment. NOT FOR incident causal chains (use RootCauseAnalysis). USE

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schedule Updated 1 month ago
parcadei

math-intuition-builder

by parcadei
star 3.8k

Develops mathematical understanding through examples, visualization, and analogy

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schedule Updated 5 months ago
OpenLAIR

aris-proof-writer

by OpenLAIR
star 992

Writes rigorous mathematical proofs for ML/AI theory. Use when asked to prove a theorem, lemma, proposition, or corollary, fill in missing proof steps, formalize a proof sketch, 补全证明, 写证明, 证明某个命题, or determine whether a claimed proof can actually be completed under the stated assumptions.

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schedule Updated 2 months ago
MathClaw-ruc

memory

by MathClaw-ruc
star 443

Structured daily and weekly learning memory with dual graph snapshots.

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schedule Updated 2 months ago
shuyicc

mathlens

by shuyicc
star 378

专业的数学老师辅导技能,用于深入浅出的解答数学题,生成HTML讲解文档和带配音的Manim动画视频, 解答细致,深入浅出,浅显易懂,比较适合一般学情的学生。 核心工作流:数学分析 → HTML可视化 → 分镜脚本 → TTS音频 → 验证更新 → 脚手架 → Manim代码 → 渲染验证 触发条件:学生粘贴数学题图片、需要教学视频、需要HTML讲解资料

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schedule Updated 3 months ago
aiskillstore

desmos-graphing

by aiskillstore
star 360

Create interactive Desmos graphs in Obsidian using desmos-graph code blocks. Use when visualizing functions, parametric curves, inequalities, or mathematical relationships with customizable styling and settings.

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schedule Updated 5 months ago
GarethManning

erroneous-example-designer

by GarethManning
star 321

Design deliberately flawed examples that develop error-detection skills and deepen understanding. Use when students make characteristic errors and need practice spotting mistakes.

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schedule Updated 2 months ago
yogsoth-ai

contradiction-derivation

by yogsoth-ai
star 312

Negate a claim, derive logical consequences step by step, detect whether a genuine contradiction or absurdity emerges.

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schedule Updated 1 month ago
jamesrochabrun

math-teacher

by jamesrochabrun
star 159

Interactive math teacher that instantly generates playful, gamified learning experiences. Creates visual playgrounds, interactive artifacts, and engaging games for kids and adults to learn math concepts from basic arithmetic to advanced calculus.

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schedule Updated 7 months ago
curiositech

knot-theory-educator

by curiositech
star 122

Expert in visualizing and explaining braid theory, knot mathematics, and topological concepts for educational purposes. Use for creating interactive visualizations, explainer cards, step-wise animations, and translating abstract algebra into intuitive understanding. Activate on keywords: braid theory, knot visualization, σ notation, crossing diagrams, Yang-Baxter, topological education. NOT for general math tutoring, pure knot invariant computation, or non-educational knot theory research.

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schedule Updated 3 months ago
lyndonkl

concept-rediscovery-walk

by lyndonkl
star 121

Guides a learner to invent a math or ML concept themselves through a Socratic walk — a sequence of small guessable questions that ends with the learner stating the formal definition unprompted. The 3Blue1Brown signature move. Use when the learner is meeting a foundational concept (eigenvectors, gradient, attention, softmax, KL divergence) for the first time, when prior exposure produced memorization without understanding, or when the user says "explain it from scratch", "I want to really get it", "build it up for me", or "where does this come from".

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schedule Updated 1 month ago
lyndonkl

geometric-algebraic-bridge

by lyndonkl
star 121

Presents a math or ML concept simultaneously in geometric form (picture, transformation, region, surface) and algebraic form (formula, matrix, derivation), then writes the explicit one-sentence bridge that says "these are the same thing because…". The signature 3Blue1Brown move applied to any vector/matrix concept. Use when a learner has one view but not the other ("I understand the formula but not what it means" or "I see the picture but can't write it down"), when introducing a concept that genuinely needs both views to land (eigendecomposition, SVD, dot product, attention, gradient, covariance), or when the user mentions "geometric meaning", "intuition behind", "picture for", or "why does the formula look like that".

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schedule Updated 1 month ago
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Browse Agent Skills by Occupation

23 major groups · 867 SOC occupations

Browse by Category

Explore agent skills organized by their primary use case

SKILLMD / CREATORS AND OCCUPATION CATEGORIES

Explore the agent skills ecosystem by occupation and creator

SkillMD is not just a keyword search box. It is an open map that organizes public skills by occupation, creator, and repository, helping you see which workflows, judgment criteria, and domain habits people are writing for AI agents.

Then follow creators and GitHub repositories back to the source: compare the skills a team maintains, whether the repo is active, and how the README frames the work before you open, install, or reuse anything.

Use it three ways: learn an unfamiliar field by occupation, study how creators organize skills, then use source context to decide what is worth opening or reusing.

01 Map a field

Browse 23 occupation groups and 867 SOC roles to learn what skills exist in adjacent domains and how they break down real work.

02 Follow creators

Use creator and repository pages to inspect maintained skill collections, recent updates, and source context before trusting a result.

03 Search with sources

Search 1.7M+ collected skills, then use occupation tags, creators, and GitHub source context to decide what is worth opening.

Start with the occupation map, then follow creators and repositories back to real code. SkillMD helps explain why a skill is worth opening, not only what it is named.

SEO KNOWLEDGE HUB & TECHNICAL OVERVIEW

Standardizing Agent Capabilities with SKILL.md and Model Context Protocol (MCP)

In the rapidly evolving landscape of artificial intelligence, LLM agents (Large Language Model agents) have transitioned from simple text predictors to autonomous problem solvers. To orchestrate complex, multi-step agentic workflows, developers require a standardized format to specify agent capabilities, prompt instructions, system rules, and database bindings. This is where SKILL.md and the Model Context Protocol (MCP) have emerged as standard developer paradigms. SkillMD serves as the central directory for indexing, exploring, and sharing these critical agent configurations.

Our open-source registry currently tracks over 1.7 million collected SKILL.md configurations and system prompts. By compiling agent configurations from active developers on GitHub, we bridge the gap between prompt engineering research and production execution. Whether you are building agents with Anthropic's Claude Code, OpenAI's GPT-4, Google's Gemini, or local models using Ollama and LlamaIndex, standardized skill definitions ensure your agents behave predictably across different runtime environments.

What is the Model Context Protocol (MCP)?

The Model Context Protocol (MCP) is an open-source standard designed to connect LLMs to data sources, developer tools, and external environments. MCP establishes a bidirectional communication channel between client applications (like Cursor, Claude Desktop, or custom agent systems) and servers hosting data or capabilities. Standardizing instructions via SKILL.md enables LLMs to query databases, read local files, execute terminal commands, and integrate third-party APIs. SkillMD allows you to find ready-to-run MCP servers and prompt instructions for various occupations and technical tasks.

The Structure of a Professional SKILL.md File

A valid SKILL.md configuration is designed to be easily read by humans and parsed by LLMs. It contains precise system instructions, trigger conditions, required parameters, and execution examples. Below is the typical architectural blueprint of a professional agent skill:

  • Metadata & Core Scope: Declares the name of the skill, author details, target models, and a description of the capability.
  • Triggers & Intent Detection: Details semantic triggers that help the agent decide when to invoke this skill.
  • System Prompts: Explicit system-level instructions that direct the agent's behavior, personality, safety guardrails, and formatting preferences.
  • Capabilities & Tools: Lists the files, databases, or APIs the agent must access to complete the tasks.
  • Few-Shot Examples: Demonstrates real inputs and outputs, helping the model generalize behavior through in-context learning.

Optimizing Agent Workflows for Modern LLMs

Writing effective agent skills requires deep knowledge of prompt engineering. With the release of advanced reasoning models like Claude 3.5 Sonnet, ChatGPT o1, and DeepSeek-V3, prompt templates must focus on structured thinking. Developers are encouraged to use XML tags (e.g., <thought>, <context>, and <rules>) to isolate execution boundaries. Standardized prompts prevent agents from suffering from context drift, ensuring that long-running tasks remain aligned with the initial system parameters.

Exploring by SOC Occupations and Creator Profiles

What makes SkillMD unique is its taxonomy. Instead of simple text search, we parse and organize files according to the Standard Occupational Classification (SOC) system. This means you can discover skills written for Computer and Mathematical roles, Business and Financial operations, Legal, Design, and and Educational Instruction fields. By tracking creator profiles, developers can study how different teams organize their custom instructions, compare version updates, and fork public configs for specialized enterprise use cases.

SkillMD operates as a high-performance index running on a fast Go backend and a highly responsive Astro SSR frontend. All search queries execute in milliseconds, featuring smart debouncing to prevent multiple API requests while keeping user data secure. Join our community of developers to standardize your AI agent instructions and optimize your LLM prompting workflows today.

8 QUESTIONS

Frequently Asked Questions

A practical guide to agent skills: what they are, how to inspect them, and how SkillMD helps you explore the ecosystem.