Math-To-Manim: Reverse Knowledge Tree Animation Pipeline

Transform any concept into professional mathematical animations using a six-agent workflow that requires NO training data - only pure LLM reasoning.

Core Innovation: Reverse Knowledge Tree

Instead of training on example animations, this system recursively asks: "What must I understand BEFORE this concept?" This builds pedagogically sound animations that flow naturally from foundation concepts to advanced topics.

When to Use This Skill

Invoke this workflow when:

• Creating mathematical or scientific animations
• Building educational visualizations with Manim
• Generating code from conceptual explanations
• Needing pedagogically structured content progression

The Six-Agent Pipeline

Agent 1: ConceptAnalyzer

Parse user intent to extract:

• Core concept (specific topic name)
• Domain (physics, math, CS, etc.)
• Level (beginner/intermediate/advanced)
• Goal (learning objective)

Agent 2: PrerequisiteExplorer (Key Innovation)

Recursively build knowledge tree:

1. Ask: "What are the prerequisites for [concept]?"
2. For each prerequisite, recursively ask the same question
3. Stop when hitting foundation concepts (high school level)
4. Build DAG structure with depth tracking

Foundation detection criteria: Would a high school graduate understand this without further explanation?

Agent 3: MathematicalEnricher

For each node in the tree, add:

• LaTeX equations (2-5 key formulas)
• Variable definitions and interpretations
• Worked examples with typical values
• Complexity-appropriate rigor

Agent 4: VisualDesigner

For each node, design:

• Visual elements (graphs, 3D objects, diagrams)
• Color scheme (maintain consistency)
• Animation sequences (FadeIn, Transform, etc.)
• Camera movements and transitions
• Duration and pacing

Agent 5: NarrativeComposer

Walk tree from foundation to target:

1. Topologically sort nodes
2. Generate 200-300 word segment per concept
3. Include exact LaTeX, colors, animations
4. Stitch into 2000+ token verbose prompt

Agent 6: CodeGenerator

Generate working Manim code:

• Use Manim Community Edition
• Handle LaTeX with raw strings: r"$\frac{a}{b}$"
• Implement all visual specifications
• Produce runnable Python file

Workflow Execution

To execute this workflow for a user request:

Step 1: Analyze the Concept

# Extract intent
analysis = {
    "core_concept": "quantum tunneling",
    "domain": "physics/quantum mechanics",
    "level": "intermediate",
    "goal": "Understand barrier penetration"
}

Step 2: Build Knowledge Tree

Recursively discover prerequisites with max depth of 3-4 levels:

Target: quantum tunneling
├─ wave-particle duality
│   ├─ de Broglie wavelength [FOUNDATION]
│   └─ Heisenberg uncertainty
├─ Schrödinger equation
│   ├─ wave function
│   └─ probability density
└─ potential barriers [FOUNDATION]

Step 3: Enrich with Mathematics

Add to each node:

• Primary equations in LaTeX
• Variable definitions
• Physical interpretations

Step 4: Design Visuals

Specify for each concept:

• Elements: ['wave_function', 'potential_barrier']
• Colors: {'wave': 'BLUE', 'barrier': 'RED'}
• Animations: ['FadeIn', 'Create', 'Transform']
• Duration: 15-30 seconds per concept

Step 5: Compose Narrative

Generate verbose prompt with:

• Scene-by-scene instructions
• Exact LaTeX formulas
• Specific animation timings
• Color and position details

Step 6: Generate Code

Produce complete Python file:

from manim import *

class ConceptAnimation(ThreeDScene):
    def construct(self):
        # Implementation following verbose prompt
        ...

Critical Implementation Details

LaTeX Handling

Always use raw strings for LaTeX:

equation = MathTex(r"E = mc^2")

Color Consistency

Define color palette at scene start and reuse throughout.

Transition Pattern

Connect concepts with smooth animations:

• Previous concept fades
• New concept builds from prior elements
• Use Transform or ReplacementTransform

Verbose Prompt Format

Structure prompts with:

1. Overview section with concept count and duration
2. Scene-by-scene instructions
3. Exact specifications (no ambiguity)

See references/verbose-prompt-format.md for complete template.

Output Files

The pipeline generates:

• {concept}_prompt.txt - Verbose prompt
• {concept}_tree.json - Knowledge tree structure
• {concept}_animation.py - Manim Python code
• {concept}_result.json - Complete metadata

Additional Resources

Reference Files

• references/reverse-knowledge-tree.md - Detailed algorithm explanation
• references/agent-system-prompts.md - All six agent prompts
• references/verbose-prompt-format.md - Complete prompt template
• references/manim-code-patterns.md - Code generation patterns

Example Files

• examples/pythagorean-theorem/ - Complete workflow example

Quick Start

For immediate use, follow this simplified pattern:

1. Parse: Extract the core concept from user input
2. Discover: Build prerequisite tree (depth 3-4)
3. Enrich: Add math and visual specs to each node
4. Compose: Generate verbose prompt (2000+ tokens)
5. Generate: Produce working Manim code

The key insight: verbose, specific prompts with exact LaTeX and visual specifications produce dramatically better code than vague descriptions.