This lecture captures the Retiring Presidential Address of G. D. Mostow, who served as AMS president from 1986 to 1988. The subject of his lecture illustrates how various branches of mathematics, while seeming quite separate, can in fact have profound connections. The story begins with diagrams for finite groups generated by complex reflections, which were introduced by Coxeter in 1966. Mostow describes how this line of research eventually led him and his colleagues to the Kummer identities for hypergeometric functions, which were originally introduced in 1836. Mostow's years of research experience and deep understanding illuminate this remarkable mathematical excursion. The lecture would be suitable for advanced undergraduate mathematics majors, graduate students, and researchers.