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Lie’s theory of continuous symmetries was originally for differential equations, but turns out to be very useful for physics because symmetries are manifest in many physical systems. This is the start of a series on Lie groups, Lie algebras, and Lie brackets.

Files for download:
Go to https://www.mathemaniac.co.uk/download and enter the following password: lievideoseries

Sources:

History of group theory: https://en.wikipedia.org/wiki/History...

Lie’s theory for differential equations (actually developed further after Lie died):
https://arxiv.org/pdf/1901.01543.pdf
https://www.physics.drexel.edu/~bob/L...
https://www.researchgate.net/profile/...
https://en.wikipedia.org/wiki/Lie_poi...

Lie theory applications to mathematics: https://math.stackexchange.com/questi...

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If you are wondering how I made all these videos, even though it is stylistically similar to 3Blue1Brown, I don't use his animation engine Manim, but I use PowerPoint, GeoGebra, and (sometimes) Mathematica to produce the videos.

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