Math-To-Manim: Transforming Simple Prompts into Advanced Manim Animations

What is Math-To-Manim, and how does it turn a basic prompt like “explain quantum field theory” into a complete, mathematically accurate animation? This article explores a tool that uses recursive reasoning to generate verbose, LaTeX-rich descriptions for Manim animations, building from foundational concepts without relying on training data.

Project Overview

What problem does Math-To-Manim solve for users who want to visualize complex math and physics concepts? It automates the creation of detailed Manim animations from simple text prompts, ensuring mathematical precision and narrative flow through a structured agent pipeline.

Math-To-Manim takes everyday prompts, such as “explain cosmology,” and produces elaborate animations complete with LaTeX equations, visual metaphors, and smooth transitions. Unlike traditional methods that depend on pattern matching from datasets, this tool employs a reverse knowledge tree to recursively identify prerequisites, starting from basic ideas and building up to the target concept. For instance, explaining cosmology might begin with high school physics like Galilean relativity before advancing to general relativity and cosmic microwave background radiation.

This approach results in animations that are not only visually appealing but also educationally sound, as they layer concepts logically. In practice, users can input a prompt and receive a Manim-compatible Python script that renders scenes with precise camera movements and color-coded elements.

From my perspective as the creator, one key insight is how forcing precision through LaTeX in prompts eliminates common rendering errors—it’s a lesson in how specificity drives better AI-generated code.

See It in Action

How can I visualize the power of Math-To-Manim through real examples? By examining generated animations like ULTRA QED, which demonstrates the tool’s ability to create comprehensive visualizations from a single prompt.

Consider the ULTRA QED animation, a 4-minute journey through quantum electrodynamics generated without manual edits. It spans 11 scenes, starting with a cosmic starfield and progressing through spacetime foundations, Maxwell’s equations, the QED Lagrangian, Feynman diagrams, and more, ending in a grand synthesis.

In this example, the animation visualizes the relativistic metric ( ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2 ), electromagnetic waves via the wave equation ( \nabla^2 \vec{E} – \frac{1}{c^2} \frac{\partial^2 \vec{E}}{\partial t^2} = 0 ), and the full QED Lagrangian ( \mathcal{L}{\text{QED}} = \bar{\psi}(i\gamma^\mu D\mu – m)\psi – \frac{1}{4}F_{\mu\nu}F^{\mu\nu} ). Each term is color-coded for clarity, showing fermion fields in orange, gamma matrices in teal, and more.

Another case is the ProLIP animation, which illustrates probabilistic vision-language models, focusing on contrastive learning and uncertainty quantification.

Here, the tool maps abstract concepts like probabilistic embeddings to visual elements, making it easier for researchers to communicate ideas in presentations or tutorials.

Similarly, the GRPO animation depicts group relative policy optimization in reinforcement learning, with visuals of policy updates and gradient flows through neural networks.

These examples highlight how Math-To-Manim excels in scenarios like educational content creation, where a single prompt yields a ready-to-render animation, saving hours of manual scripting.

Reflecting on these outputs, I’ve learned that unedited one-shot generations often include minor overlaps during transitions, but this preserves the natural flow— a trade-off that emphasizes authenticity over polished perfection.

The Innovation: Reverse Knowledge Tree

What is the reverse knowledge tree, and why does it outperform traditional pattern-matching methods in generating animations? It’s a recursive method that breaks down a prompt by identifying prerequisites, ensuring animations build from basics to advanced topics.

For a prompt like “explain cosmology,” the process starts by asking: What must be understood before cosmology? This leads to general relativity, Hubble’s law, redshift, and CMB radiation. Then, it drills deeper: Before general relativity? Special relativity, differential geometry, gravitational fields. This continues until reaching foundational concepts like the speed of light or Lorentz transformations.

The tree forms a conceptual dependency graph, which is then traversed from foundation to target to construct the animation. In application, this means an animation on quantum field theory might begin with classical waves before introducing the QED Lagrangian, making it accessible for students or self-learners.

Compared to data-driven approaches, this method avoids brittleness with new concepts and doesn’t require massive datasets. Instead, it relies on reasoning to handle edge cases.

In my experience developing this, the recursive nature revealed how interconnected knowledge is—often, what seems advanced boils down to layered basics, which makes teaching through animations more intuitive.

To visualize such a tree, imagine a branching diagram where nodes represent concepts, and edges show prerequisites. While not yet interactive, future integrations could map entire learning paths from algebra to quantum field theory.

How It Works: The Agent Pipeline

How does the agent pipeline in Math-To-Manim process a prompt to produce a working animation? It uses six specialized agents (with a seventh planned) to analyze, explore, enrich, design, compose, and generate content step by step.

The pipeline begins with the ConceptAnalyzer agent, which parses the prompt to identify the core concept, domain, and visualization style. For example, for “visualize optimal transport theory,” it might detect a mathematics domain and suggest gradient flow visuals.

Next, the PrerequisiteExplorer— the core innovation— builds the reverse knowledge tree by recursively querying prerequisites, creating a graph of dependencies.

The MathematicalEnricher then adds LaTeX equations to each node, ensuring rigor. In a quantum mechanics scenario, it might insert the Schrödinger equation and link it to wave function visuals.

Following that, the VisualDesigner specifies aesthetics: camera pans, colors (e.g., red for electric fields), and transitions, mapping concepts to metaphors like undulating waves for fields.

The NarrativeComposer weaves a story by walking the tree, producing a 2000+ token verbose prompt that describes the entire animation in detail.

Finally, the CodeGenerator translates this into Manim Python code, handling LaTeX correctly for rendering.

A planned VideoReview agent will automate quality checks on the output MP4, extracting frames for iteration.

In practice, for a prompt like “show me the Pythagorean theorem,” the pipeline generates code for a visual proof, complete with animated squares on triangle sides.

This modular setup, powered by Claude Sonnet 4.5, manages context automatically and integrates tools seamlessly. From building it, I’ve reflected that separating concerns into agents mirrors human collaboration—each focuses on one strength, leading to more robust outputs.

Quick Start Guide

How do I get started with installing and running Math-To-Manim? Follow these steps to set up the environment and launch the interface for generating animations.

First, clone the repository:

git clone https://github.com/HarleyCoops/Math-To-Manim
cd Math-To-Manim

Install dependencies:

pip install -r requirements.txt

Set up your API key by creating a .env file:

echo "ANTHROPIC_API_KEY=your_key_here" > .env

Install FFmpeg based on your OS:

• Windows: choco install ffmpeg
• Linux: sudo apt-get install ffmpeg
• macOS: brew install ffmpeg

To launch the Gradio interface:

python src/app_claude.py

Enter a prompt like “explain quantum mechanics” and watch the agents generate the verbose prompt and code.

For running pre-built examples, such as a quantum electrodynamics journey:

manim -pql examples/physics/quantum/QED.py QEDJourney

Use flags like -p for preview and -ql for low quality. This setup works well for quick tests in educational settings, like preparing lecture visuals.

One lesson from my setup process: Ensuring FFmpeg is installed early prevents rendering failures—it’s a small step but critical for video output.

Repository Structure and Examples

What does the repository structure look like, and how can I find examples for different topics? It’s organized by categories, with over 55 animations spanning physics, mathematics, computer science, and more.

The structure includes:

• src/: Core agents and interfaces, like prerequisite_explorer_claude.py for the knowledge tree.
• examples/: Categorized animations.

  • physics/quantum/: 13 QED/QFT files, e.g., QED.py.
  • mathematics/geometry/: Proofs like pythagorean.py.
  • computer_science/machine_learning/: Neural nets such as AlexNet.py.
  • Other folders for cosmology, finance, and misc.
• docs/: Guides like ARCHITECTURE.md and EXAMPLES.md.
• tests/: Unit, integration, and e2e tests.

For beginners, try the Pythagorean theorem example:

manim -pql examples/mathematics/geometry/pythagorean.py PythagoreanScene

This visualizes a simple proof, ideal for learning Manim basics.

Intermediate users might explore fractal patterns:

manim -pql examples/mathematics/fractals/fractal_scene.py

Advanced cases include optimal transport:

manim -pql examples/mathematics/analysis/diffusion_optimal_transport.py

In a classroom scenario, an instructor could use these to demonstrate concepts like Wasserstein distance visually.

Reflecting on organizing this, categorizing by difficulty and topic made it more accessible—it’s satisfying to see users navigate from beginner to advanced seamlessly.

The Secret: LaTeX-Rich Prompting

Why does using detailed, LaTeX-rich prompts lead to better animations than simple English descriptions? Because they provide precision in mathematics and cinematography, reducing ambiguity in code generation.

A vague prompt like “create an animation showing quantum field theory” often results in broken or generic output. Instead, Math-To-Manim generates detailed descriptions: “Begin by slowly fading in a panoramic star field… Display the relativistic metric ( ds^2 = -c^2 dt^2 + dx^2 + dy^2 + dz^2 ) with each component highlighted…”

This includes exact symbols, colors, and movements, ensuring the Lagrangian ( \mathcal{L}{\text{QED}} = \bar{\psi}(i \gamma^\mu D\mu – m)\psi – \tfrac{1}{4}F_{\mu\nu}F^{\mu\nu} ) renders correctly.

In application, for teaching Maxwell’s equations, the prompt morphs notations from vector calculus to four-vector form ( \partial_\mu F^{\mu \nu} = \mu_0 J^\nu ), with animations dissolving symbols.

My unique insight: LaTeX forces mathematical accuracy, which self-corrects errors when fed back to the model— a loop that refines outputs iteratively.

Why This Works: Technical Insights

What makes Math-To-Manim effective in producing coherent animations? It builds from foundations, ensures precision, and handles cinematography without training data.

By traversing the knowledge tree, animations explain prerequisites first, creating narrative flow. LaTeX adds rigor, while detailed specs for visuals eliminate vagueness.

For instance, in a Feynman diagram gallery, it visualizes electron scattering with spacetime lines, using gold for photon exchanges.

No datasets are needed; reasoning via Claude handles recursion. If code breaks, re-prompting with errors fixes issues.

In scenarios like research presentations, this enables quick prototyping of complex visuals, like running couplings ( \alpha(Q^2) ).

From my development, I’ve seen how this method adapts to levels—from high school geometry to graduate physics—automatically scaling complexity.

Current Status and Future Plans

Where is Math-To-Manim now, and what developments are planned? Currently refactored to Claude Sonnet 4.5, with 55+ examples and a core algorithm, future steps include completing agents and integrations.

Short-term: Finalize the pipeline, add tests, and visualize knowledge trees.

Medium-term: Integrate semantic graphs for faster discovery, caching relationships for 10x speed, and enabling interactive paths.

Long-term: Build a community platform for sharing animations and graphs.

In use, this could mean faster generations for prompts like “visualize gravitational waves.”

Reflecting, switching to Claude improved reasoning— a reminder that tool choice impacts scalability.

Key Features

What standout features does Math-To-Manim offer for cross-model support and adaptive complexity? It supports multiple AI models and generates dual outputs, adjusting depth automatically.

Models like Claude, DeepSeek, Gemini, Grok, Qwen, and Mistral generate examples, each adding unique angles.

It produces Manim code and LaTeX notes; re-prompt for explanations to get PDF-ready docs.

Complexity adapts via the tree: Basic for geometry, advanced for QED.

In financial scenarios, it visualizes option pricing with adaptive depth.

One lesson: Dual outputs bridge visuals and text, enhancing learning.

Common Pitfalls and Solutions

What common issues arise in animation generation, and how does Math-To-Manim address them? Problems like LaTeX errors or vague specs are solved through enriched prompts and consistent notation.

For LaTeX issues, verbose prompts verify notation. Vague cinematography is fixed by detailed designs. Missing prerequisites are caught by the explorer. Inconsistent notation is maintained across the tree.

In practice, for a broken QED render, re-prompt with errors.

My insight: These pitfalls stem from ambiguity—structuring prompts eliminates them.

Performance Notes

How long does it take to generate and render animations with Math-To-Manim? The pipeline takes 1-2 minutes, with rendering varying by quality.

Tree generation: 30-60 seconds. Prompt composition: 20-40 seconds. Code: 15-30 seconds.

Rendering: Low quality 10-30 seconds; high 1-5 minutes; 4K 5-20 minutes.

For a cosmology prompt, this means quick iterations in development.

Why Claude Agent SDK?

What advantages does using Claude Agent SDK provide in Math-To-Manim? It offers superior reasoning, context management, and tools for robust agents.

Reasons: Better recursion, no context limits, built-in ops, MCP integration, production readiness.

In migration from DeepSeek, it scaled better for complex prompts.

Reflecting, this switch taught me about framework maturity—essential for autonomous systems.

Contributing Guidelines

How can I contribute to Math-To-Manim? By adding examples, improving agents, or fixing bugs, following simple steps.

Create categorized files with docstrings, test renders, and submit PRs.

For a new quantum animation: Place in examples/physics/quantum/, name descriptively, add explanation.

This builds the community, like sharing learning paths.

Conclusion

Math-To-Manim revolutionizes animation creation by turning prompts into precise, layered visuals via recursive reasoning. It empowers users to explain complex ideas effortlessly, from quantum fields to algorithms.

Practical Summary / Operation Checklist

• Clone repo and install dependencies.
• Set API key and FFmpeg.
• Launch Gradio: python src/app_claude.py.
• Input prompt and generate.
• Run examples with manim -pql path/to/file.py SceneName.
• For errors, re-prompt with details.
• Explore categories for inspiration.
• Contribute via PRs.

One-Page Speedview

Overview: Automates Manim from prompts using reverse knowledge tree.

Pipeline: 6 agents for analysis to code.

Install: Git clone, pip install, .env, FFmpeg.

Examples: 55+ in physics/math/CS.

Features: LaTeX-rich, adaptive, dual outputs.

Future: Semantic graphs, community platform.

Performance: 1-2 min pipeline, variable render.

FAQ

How do I install Math-To-Manim? Clone the repo, pip install requirements, set .env with API key, and install FFmpeg.

What prompts work best? Simple ones like “explain quantum mechanics” or “visualize Pythagorean theorem.”

Can I run examples without the pipeline? Yes, use manim commands on files in examples/.

What if LaTeX renders wrong? Re-prompt the model with the error and code.

Is GPU required? No, but it speeds rendering.

How accurate are animations? High, thanks to LaTeX validation.

Can I use other models? Yes, examples from DeepSeek, Gemini, etc.

What’s the license? MIT, free for commercial use with attribution appreciated.