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Given the situation we are in (pandemic) I have looked for the best way to make math videos for teaching. I have tried with digital whiteboards, notes in LaTeX but they do not convince me at all.

Browsing YouTube I found this channel that is dedicated to sharing math topics. His videos are lovely and I would like to do something similar with my students. Do you know what kind of programs this guy uses to make those kinds of animations?

https://www.youtube.com/watch?v=O85OWBJ2ayo

Rdch
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Yes, he developed his own Python library called manim (math animations) for making math videos.

He has his own library still, but it has been branched off to a community edition which is where you want to start.
https://www.manim.community/

It's fairly easy to use and there is a lot of examples you can find in the documentation. It's also very fun to use!