a workflow for turning mathematical conversations into a living, explorable knowledge map — organised by intuition, grown by habit.
A meta-web is a personal knowledge graph for mathematics. Unlike notes or summaries, it is built around intuitions and heuristics — the transferable ways of seeing that survive long after the specific calculation is forgotten. Concepts, results, and open questions orbit these intuitions as supporting structure.
The map grows automatically from conversations you are probably already having with AI assistants. Each conversation generates a structured summary; each summary is merged into a single JSON file; the JSON file renders as an interactive, zoomable graph on your website.
the core philosophy: most mathematical knowledge-capture systems organise by topic or paper. This one organises by how you think. An intuition like “entropy controls large deviations” or “parabolic systems push complexity into parameter space” is more durable than any theorem it supports. Put those first.
The map is most useful when it surprises you — when zooming in reveals a connection you had not consciously made, or when a question from one conversation turns out to illuminate a concept from another.
The system has three layers:
Paste at the end of any AI math conversation. Produces a structured Markdown file extracting intuitions, concepts, connections, open questions, and references.
Paste into Claude along with your current graph and the new summary. Deduplicates, merges, and returns an updated JSON file — the single source of truth for your map.
A standalone HTML file that reads your JSON and renders a force-directed graph with zoom-based depth reveals, clickable nodes, and a description panel. Hosted on GitHub Pages and embedded in your website.
Download all four files. You will only ever need to edit graph.json — everything else stays fixed unless you want to customise the map’s appearance.
All files are available at github.com/nataliajurga/meta-web-build-your-own. You can download each file individually by clicking it in the repository, then clicking the download icon in the top right.
The map is served over HTTP rather than opened as a local file. GitHub Pages is free and takes about five minutes to set up.
Go to github.com and sign up if you don’t have an account.
Click the + icon → New repository. Name it meta-web. Set it to Public. Click Create repository.
Click Add file → Upload files. Drag in index.html and graph.json. Click Commit changes.
Go to Settings → Pages. Under Branch, select main and keep the folder as / (root). Click Save.
After about 60 seconds your map is live at https://yourusername.github.io/meta-web
To embed the map in any website, add an HTML embed block containing:
While iterating on your map, committing to GitHub for every change is slow. VS Code lets you preview everything instantly on your own machine, with no internet required.
Go to code.visualstudio.com and install it. It’s free.
In VS Code: File → Open Folder. Select the folder containing index.html and graph.json. Both files must be in the same folder.
Click the Extensions icon in the left sidebar (or press Cmd+Shift+X on Mac, Ctrl+Shift+X on Windows). Search for “Live Server” by Ritwick Dey and click Install.
Right-click on index.html in the file explorer → “Open with Live Server”. Your browser opens at http://127.0.0.1:5500 showing the map.
Whenever you save a new graph.json, the browser refreshes automatically. No manual reloading needed.
Once you’re happy with how the map looks locally, commit the updated graph.json to GitHub once to publish it live.
Once set up, the full loop takes about five minutes per conversation.
With ChatGPT, Claude, or any AI assistant. Follow your curiosity — the prompt handles extraction.
The AI analyses the conversation and produces a structured .md file. Save it.
Include your current graph.json and the new .md summary. Claude returns an updated graph.json with new nodes, edges, and a change summary.
Claude flags any uncertain merges or inferred edges for your attention before you commit.
On github.com: open graph.json → pencil icon → paste new content → Commit changes. The map updates within 30 seconds.
Nodes have four types, revealed at different zoom levels:
| zoom level | node type | what it represents |
|---|---|---|
| always | intuition | A transferable mental model or heuristic — the permanent core. E.g. “entropy controls large deviations” |
| level 2 | concept | A mathematical object, theorem, technique, or framework. E.g. Lyapunov exponents, Rauzy induction |
| level 3 | question | An open question that emerged from conversation — unresolved, partially answered, or pointing to literature |
| level 3 | paper / person | A load-bearing reference — not just name-dropped but genuinely relevant |
Node size reflects importance: how central the idea was to the conversation, and whether you introduced it or the AI did. Your ideas appear larger.
Edges are directed and typed — is analogous to, is a tool for, is in tension with, unexpectedly relates to — displayed in the panel as readable sentences.
An unconstrained meta-web grows quickly. After a dozen conversations it can accumulate hundreds of nodes, which makes the map harder to read, slower to render, and more expensive to maintain with AI assistance. A few strategies help.
Rather than a single lifelong graph, consider maintaining a separate graph.json for each research project or course. A graph scoped to “my work on Rauzy induction” or “ergodic theory reading group” stays dense and useful rather than sprawling and thin. You can always merge two project graphs later once you see genuine cross-project connections.
After Claude returns an updated graph, read the change summary and ask: do all of these new nodes genuinely earn their place? Deleting a node takes five seconds in the JSON file. Alternatively you can paste the summary into Claude, read the proposed changes, and say “only add the intuitions and skip the peripheral concepts.” The merge prompt accepts natural language instructions.
The quality of your map depends entirely on the quality of your summaries.
An intuition should survive far beyond the specific problem that gave rise to it. “The critical orbit governs everything in quadratic dynamics” is a result, not an intuition. “Recurrence creates structure” is an intuition — it applies to billiards, random walks, and complex dynamics alike.
A connection is not just “these two things appeared in the same paper.” It is a relationship that would surprise a working mathematician — an unexpected analogy, a technical tool crossing fields, a productive tension. If it feels obvious, it belongs in a description rather than an edge.
Resist adding a node for every concept mentioned — only the load-bearing ones. A map with 20 precise nodes is more useful than one with 200 nodes where half are noise.
The summary prompt asks whether each idea came from you or the AI. Your ideas and questions are the structural spine of the map — they should dominate visually. AI-introduced concepts are valuable context but should not crowd out your own thinking.
Each time you run the merge workflow, Claude produces a change summary and a list of review flags — merge decisions or inferred edges that deserve a second look before committing. Reading these takes 60 seconds and keeps the graph honest.
The map never deletes nodes automatically — only adds or updates them. The file is plain JSON and readable without any tools if you ever want to edit it directly.
