Explore the fascinating world of Rogers-Ramanujan identities and their connection to the icosahedron in this comprehensive lecture. Delve into the unexpected appearance of the number "5" in both these identities and the theory of Platonic solids. Discover the intricate relationships between pure number theory, modular forms, combinatorics, continued fractions, conformal field theory, and mirror symmetry. Gain insights into various mathematical gems, including Apéry's proof of the irrationality of ζ(2). Follow along as the lecturer covers topics such as definitions, proofs, least common multiples, L-series, and more, in a manner accessible to mathematicians of all levels and backgrounds.