[1] He was chosen first Smith prizeman in 1839, beating the senior wrangler, Benjamin Morgan Cowie, his fellow-collegian, and he was elected to a fellowship at St. John's College on 19 March.
He was a man of wide interests and varied attainments, an accomplished pianoforte player, and a successful painter in water-colours.
In 1854, Frost edited the first three sections of Philosophiae Naturalis Principia Mathematica by Isaac Newton.
In 1863 he prepared, in conjunction with Joseph Wolstenholme, A Treatise on Solid Geometry, of which second and third editions, by Frost alone, appeared in 1875 and 1886.
On 7 June 1883, Frost was admitted as a fellow of the Royal Society, and in the same year he was elected by King's College, Cambridge, to a fellowship, which he retained until his death.