Synapse Three

Margin is a voice-and-pen calculus tutor that brings AI assistance directly into the student's notebook. Students often lose their train of thought when they get stuck solving mathematics. Existing AI tools require them to switch to a separate chat interface, explain their problem, and often receive complete solutions instead of guidance that helps them learn. Margin rethinks this interaction. Students write naturally using a stylus or keyboard, ask questions through voice or text, and receive contextual assistance directly on the notebook page. Margin reads handwritten mathematical working, identifies incorrect steps, diagnoses mistakes, and writes concise hints beside the exact line that needs attention. What makes Margin different is its separation of AI reasoning from mathematical verification. Meta AI models handle multimodal understanding, interaction, and tutoring workflows, while a deterministic SymPy-based mathematical referee verifies supported calculus operations and corrections. Margin features progressive hints, verified next-step suggestions, rule explanations, graph sketching, mathematical typesetting, and editable handwritten AI annotations. Students can accept, reject, erase, or modify the AI's suggestions just like ordinary notebook ink. The notebook also supports offline use, optional cloud synchronization, and integration with external AI agents through an MCP server. Our goal is to make AI a learning companion that works alongside the student, rather than another chatbot that replaces their thinking. Margin — No chat box. Just ink in the margin.