But why is there no quintic formula? | Galois Theory

"The best way to learn a new topic is to teach it" - Grant Sanderson aka 3blue1brown Galois theory is a fascinating topic and I hope you learned as much as I did while making this video. Please leave me any feedback, questions, etc. in the comments. ===Chapters=== 0:00 Introduction 0:24 Groups 1:18 Fields 3:03 The Connection 5:30 Solving a polynomial 9:42 Conclusion 10:46 Why is there no quintic formula 11:38 Outro Ignore the typo at 0:14. It should be "Group Theory" At around 3:25 The last equation should equal -2, not 2. Still it has the same result even if you swap the roots. ===Further material=== https://link.springer.com/book/10.1007/978-3-658-26152-8 (Excellent book about Algebra and Galois Theory) https://youtu.be/zCU9tZ2VkWc (Very good video by @mathemaniac, more technical and in-depth) ===Made with=== Manim (https://www.manim.community/) ===Music=== Music by Vincent Rubinetti Download the music on Bandcamp: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Stream the music on Spotify: https://open.spotify.com/playlist/3zNK20qC96mVSww60lVi1k ===Tags=== #galois #quintic #grouptheory #galoistheory #abelruffini