Explore the fascinating world of Galois theory in this 45-minute video that delves into the famous Abel-Ruffini theorem, explaining why quintic equations are not solvable. Learn about Galois groups, cyclotomic and Kummer extensions, and tower of extensions as you uncover the mathematical reasoning behind this groundbreaking concept. Follow along with the step-by-step explanation, from the initial setup to the final intuitive stretch, and gain a deeper understanding of the core principles behind the unsolvability of quintic equations. Suitable for math enthusiasts of all levels, this video simplifies complex algebraic concepts while maintaining the essence of the theory, making it accessible to a wide audience.