Visual explanations of mathematics (2020)
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Visual explanations of mathematics (2020)
1–10 of 28 posts
Re: Visual explanations of mathematics (2020)
#2I'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?
Re: Visual explanations of mathematics (2020)
#3There 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:
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/ )
Re: Visual explanations of mathematics (2020)
#4[deleted]
Re: Visual explanations of mathematics (2020)
#5> 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.
Re: Visual explanations of mathematics (2020)
#6I 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...
Re: Visual explanations of mathematics (2020)
#7Might a multimodal LLM be taught to generate illuminated equations and descriptions?
Re: Visual explanations of mathematics (2020)
#8I 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...
Or, the famous AoPS Proofs Without Words:
https://artofproblemsolving.com/wiki/index.php/Proofs_withou...
Re: Visual explanations of mathematics (2020)
#9There 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://ope…
Grant Sanderson's YouTube channel 3blue1brown and his Manim package have made it significantly easier to visualize math computationally: https://www.youtube.com/c/3blue1brown
https://3b1b.github.io/manim/index.html
There's also a well supported community version as well: https://www.manim.community/
Re: Visual explanations of mathematics (2020)
#10> 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,…
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