back in scotland she resumed her mathematical studies. by that time she had studied plane and spherical trigonometry, conic sections and james ferguson's "astronomy". now she first read isaac newton's "principia", which she continued to study. her inheritance from greig gave her the freedom to pursue intellectual interests. john playfair, professor of natural philosophy at university of edinburgh, encouraged her studies, and through him she began a correspondence with william wallace, with whom she discussed mathematical problems. she started to solve mathematical problems posed in the mathematical journal of the military college at marlow and she eventually made a name for herself when solving a diophantine problem for which she was awarded a silver medal in 1811. somerville had five solutions published in volumes 3 and 4 of the "mathematical repository" under the pseudonym 'a lady'; two of these solutions demonstrated her early adoption of differential calculus, and therefore her contribution to the circulation and visibility of this mathematics in early-nineteenth-century britain.