The Rogers-Ramanujan Identities and the Icosahedron - Lecture 1

Explore the fascinating connections between the Rogers-Ramanujan identities and the icosahedron in this lecture by Don Zagier from Max Planck/ICTP. Delve into the beauty of these mathematical formulas, considered by many to be the most striking in all of mathematics. Discover how the unexpected appearance of the number "5" links these identities to the theory of Platonic solids, specifically the icosahedron and dodecahedron. Investigate a wide range of related topics, including number theory, modular forms, combinatorics, continued fractions, conformal field theory, and mirror symmetry. Learn about the connections to other mathematical gems like Apéry's proof of the irrationality of ζ(2). Gain insights into the icosahedral group, Monster group, and the theory of the mirror quintic of Candelas et al. This accessible lecture is designed for mathematicians of all levels and interests, providing a comprehensive survey of these intriguing mathematical concepts without requiring specific prerequisites.

Introduction
From the icosahedron to e8
The golden ratio
The Quaternions
Topics
Two identities
The formula
Modular functions
Oliver Nash
The icosahedron
Platonic solids
Duality
Icosahedron
Icosahedral group
Monster group
Transitively
Coordinates
Quadratic equation
Survey articles