Science becomes professionalised in the nineteenth century. It is only in 1834, with the coinage of the word ’scientist,’ that its practitioners are formally distinguished from philosophers, while the rest of the century sees their efforts to establish dedicated university degrees and qualifications in science, professional bodies and journals, and more broadly to extricate themselves from a priori religious beliefs, from phrenology and spiritualism, and from metaphysical entities, such as phlogiston and the ether, as well as from gifted amateurs. In the hard sciences professionalisation involved shifts from verbal to mathematical language and modelling. It is an index of this rapid and radical cultural transition that some of the greatest physicists and mathematicians of the mid-Victorian period also wrote poetry, and indeed found radical affinities between their practices of science and poetry. This paper focuses upon work by two of these scientists, the physicist James Clerk Maxwell and the mathematician James Joseph Sylvester, to explore their convictions that poetry and mathematics share common epistemological grounds that enable them to grasp the truth of the object world.