Explore the fascinating world of cyclotomic polynomials in this 24-minute mathematics video. Delve into the importance of these polynomials, also referred to as polynumbers, in algebra, number theory, and geometry. Learn about their origins in factoring the polynomial 1-x^n and discover why calculating Phi_n for large natural numbers can be challenging. Investigate the connection between cyclotomic polynomials and Mersenne primes, and gain insight into the Schoenemann-Eisenstein criterion for irreducibility. Enhance your understanding of number theory and polynomial theory through this in-depth exploration of an essential mathematical concept.