Why study Lie theory? | Lie groups, algebras, brackets #1

Next video:    • How to rotate in higher dimensions? Comple...   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... Other than commenting on the video, you are very welcome to fill in a Google form linked below, which helps me make better videos by catering for your math levels: https://forms.gle/QJ29hocF9uQAyZyH6 If you want to know more interesting Mathematics, stay tuned for the next video! SUBSCRIBE and see you in the next video! 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. Social media: Facebook:   / mathemaniacyt   Instagram:   / _mathemaniac_   Twitter:   / mathemaniacyt   Patreon:   / mathemaniac   (support if you want to and can afford to!) Merch: https://mathemaniac.myspreadshop.co.uk Ko-fi: https://ko-fi.com/mathemaniac [for one-time support] For my contact email, check my About page on a PC. See you next time!