Visual Explanations of Mathematics (2020)

There is also Joyce's Java Version of Euclid's Elements:

https://mathcs.clarku.edu/~djoyce/java/elements/elements.htm...

and I'm still impressed by the custom Unity tools which Freya Holmér uses for her videos:

https://www.youtube.com/watch?v=jvPPXbo87ds

Wish Geogebra was both more capable and widely used:

https://www.geogebra.org/

That said, these days if I need to plot out something I just use OpenSCAD: https://openscad.org/ (or, the Python-enabled version: https://pythonscad.org/ )

I've seen physical-sciences research talks by people from Caltech, where the format is putting up a single equation, and then walking through it piece by piece. That's the entire talk, all the slides, and how the talk is organized. I've never seen that from elsewhere, and so think of it as a "caltech style". Does this have a real name? Can anyone flesh this out?

I don’t think visual explanation should be about writing colored versions of formulas or adding notes, it’s providing a visual that immediately unlocks the core idea. Many examples are given here: https://math.stackexchange.com/questions/733754/visually-stu...

> We have lots of tools to write better mathematics: LaTeX, markdown, Jupyter Notebooks, and so on. But it feels like nothing has really converged yet. Technology that seamlessly mixes symbolic equations, illustrative-and-explicative annotation, and runnable code is, I am sure, not far off. [2020; emphasis added]

Back in the 1990's, we had lots of tools to write better mathematics: LaTeX, HTML, Mathematica notebooks, and so on. But it felt like nothing had really converged yet. Technology that seamlessly mixes symbolic equations, illustrative-and-explicative annotation, and runnable code is, I then expected, not to be anticipated before my distant retirement and death. Given the preceding decades of cripplingly underfunded and glacial programming language evolution - that seemed a similar kind of society-hobbling infrastructure challenge that we just don't handle well. Now here we are, 3 decades later, and languages are in a far better place... though with pace still throttled by poor funding. Perhaps someday math tech will be too. Large-scale hypertext, and GUIs, also managed the "and now, what you've lonnnng been waiting for, tada!" transition.

link to the book in the website takes you here https://lacathospital.com/ ?

Might a multimodal LLM be taught to generate illuminated equations and descriptions?