A paper diagram visualizer

Mathematician Terence Tao developed an interactive web app that visualizes the logical flow of mathematical papers using JSON dependency files, leveraging large language models to generate diagrams for demonstration. The app allows users to explore, edit, and export diagrams, though Tao cautions that LLM-generated diagrams may not be fully accurate.

I am finding the newly revealed capability to code old applet ideas into reality to be very tempting to sink more time into, though I am certainly encountering the common “vibe coding” experience that the process can produce something that superficially resembles a finished product well before a satisfactory level of testing and review has been completed; indeed, it is the review process which is now the most time-consuming, to the point where I think any further advances in coding agent capability will have little impact on the new bottlenecks in the design process. In any event, I spent a few hours https://teorth.github.io/tao-web/apps/paper-diagram-making-of.html working to realize a proposal I had made back in 2023 https://terrytao.wordpress.com/2023/02/18/would-it-be-possible-to-create-a-tool-to-automatically-diagram-papers/ to automatically create diagrams to visually illustrate the logical flow of a given mathematical paper. At the time, Freddie Manners, extrapolating from the half-decent capability of the then-newly released ChatGPT 3.5 at this task, presciently predicted https://terrytao.wordpress.com/2023/02/18/would-it-be-possible-to-create-a-tool-to-automatically-diagram-papers/ comment-674333 that “by the time a dedicated tool had been completed, the next general purpose engine would be better than it”. With that in mind, I decided to focus not on the generation of the diagram – which now can be done at various levels of quality by any number of large language models – but on its presentation. The result is the following app https://teorth.github.io/tao-web/apps/paper-diagram.html , which can take a certain formatted JSON file of dependencies between theorem objects and produce an interactive graph which can be explored, edited and also exported somewhat lossily into other standard formats such as SVG, TikZ, quiver, or Mermaid. Here is a screenshot of a diagramming https://teorth.github.io/tao-web/apps/paper-diagram.html?paper=kakeya of the celebrated proof by Wang and Zahl https://arxiv.org/abs/2502.17655 of the three-dimensional Kakeya conjecture: Using an LLM, I generated diagrams for eight papers for demonstration purposes, including for instance a diagram for Wiles’s proof of Fermat’s last theorem https://teorth.github.io/tao-web/apps/paper-diagram.html?paper=wiles-flt , or of Szemeredi’s proof of his famous theorem on arithmetic progressions https://teorth.github.io/tao-web/apps/paper-diagram.html?paper=szemeredi which sports a notoriously convoluted such diagram in the original paper https://eudml.org/doc/205339 , as well as a few papers https://teorth.github.io/tao-web/apps/paper-diagram.html?paper=gilbreath of my https://teorth.github.io/tao-web/apps/paper-diagram.html?paper=2605.00301 own https://teorth.github.io/tao-web/apps/paper-diagram.html?paper=2605.00301 . If there are other requests to diagram particular papers, I can try to use an LLM to generate more examples; but my intention is for users of the app to create their own such diagrams, either by manually constructing them, or by directing their own AI tools to build the diagram in the required format which is a JSON, with the precise specification given here https://teorth.github.io/tao-web/apps/paper-diagram.html format . I mentioned in the previous post that for these sorts of visualization apps, which work deterministically for a given set of inputs, the downside risk of LLM use to build the app is acceptably low. For this particular app, there is a complicating factor, which is that while the app does remain deterministic, the data I used to populate the app – namely, the above diagrams – are also LLM-generated. I have done spot checks comparing the diagrams against the source papers, and did not find any errors; however, they are not guaranteed to be 100% accurate, and should only be used as approximations to the logical structure of these papers rather than completely exact representations. The latter might become deterministically extractable should the results of these papers become formalized in a proof assistant language, but this is not currently the case. Still, I hope these sorts of diagrams can serve as a helpful initial guide when first trying to read and understand a complex paper.