Duncan F. Gregory (1813-1844) was a proponent of the Calculus of Operations and a founding editor of the Cambridge Mathematical Journal. Extant is a series of six letters that Gregory wrote to a friend in 1839. This correspondence provides a glimpse into life at early-Victorian Cambridge, reveals something of the character of Gregory and his dedication to the CMJ, and shows some of the mathematical problems he pondered. In this talk, we will look briefly at Cambridge, Gregory and the CMJ, and will examine several of the problems.