gregory was initially recognised for his essay "the foundations of algebra" presented to the royal society of edinburgh in 1838. on completing his degrees, he served as moderator in 1842, examiner through may 1843 and was also appointed assistant tutor. at the suggestion of his friend, archibald smith, he founded and was the first editor of the "cambridge mathematical journal" in november 1837, helped by robert leslie ellis who succeeded him as editor. many of his articles for the "cmj" were collected in "the mathematical writings of d. f. gregory", edited by his friend and colleague william walton. in 1841 he published his "examples of the processes of the differential and integral calculus", which expanded the earlier work of john herschel, george peacock and charles babbage to include the mathematics used to describe discontinuities observed in heat transfer explored by the french mathematician joseph fourier, and the theory of undulatory light, a topic familiar to him. he was elected a member of the philological society 12 may 1843.