<aside> 💡 To help students learn proofs and thinking have proof-based understanding.

</aside>

• visual graph or tree connecting all definitions together.
• have some sort of sequential thing. Step by step, choose different paths (contradiction, case, etc), then build out the proof

Workflow is Step by step, choose different paths (contradiction, case, etc), then build out the proof.

At each step, will have all the facts determined at that step, and chat helps you think of next steps given the information at hand.

• Backward helper: Most important feature at a step is highlighting all the current facts or truths, from the axioms, theorems, definitions, and other intermediate truths determined.
  • Each highlight should display a basic definition, an intuitive explanation, an example, an opinionated analysis, and a contexual relationship linking back to the problem at hand.
  • These should be generated on the fly during the current proof problem.
    • We should store definition, intuitive explanation in database, but leave others to be dynamic during each proof.
• Forward helper: List out all the next steps given the information at hand.
• Tracks time if you been away and refreshes your memory with recent definitions and examples.

How LlamaIndex Can Fit into Your Project

1. Integrating Domain-Specific Data:

   • If your educational tool requires specific mathematical content, proofs, or textbooks, LlamaIndex can ingest this data from various sources and make it accessible through natural language queries.

2. Creating a Query Engine:

   • Example: Allow students to ask questions about mathematical concepts or proofs, and use LlamaIndex's query engine to retrieve relevant information from the indexed data.

   typescriptCopy code
   const queryEngine = index.asQueryEngine();
   const response = await queryEngine.query("What is Pythagorean theorem?");
   
   

3. Building a Chat Engine for Interactive Learning:

   • Example: Create a conversational interface for students to interact with mathematical content, enabling a back-and-forth dialogue with the material.

   typescriptCopy code
   const chatEngine = LlamaIndex.createChatEngine(dataIndex);
   const response = await chatEngine.interact("Tell me more about calculus!");
   
   

4. Utilizing Data Agents for Advanced Tasks:

   • Example: Implement LLM-powered knowledge workers to guide students through complex problem-solving or proof-building steps, augmented by specific data and tools.

5. Integration with Other Tools and Platforms:

   • LlamaIndex can be integrated with LangChain, Flask, or other tools, allowing seamless communication and interaction within your ecosystem.

Route that pulls suggestions!

Needs to be interactive! Let user respond and guess a way of thinking around the proof!

• potentially add illustrations later