Cockle is also remembered for his mathematical and scientific investigations. For instance he invented the number systems of
tessarines and
coquaternions, and worked with
Arthur Cayley (1821–1895) on the theory of
linear algebra. Like many young mathematicians he attacked the problem of solving the
quintic equation, notwithstanding
Abel–Ruffini theorem that a solution by
radicals was impossible. In this field Cockle achieved some notable results, amongst which is his reproduction of Sir
William R. Hamilton's modification of Abel's theorem. Algebraic forms were a favourite object of his studies. He also made contributions to the theory of
differential equations, in particular the development of the theory of
differential invariants or
criticoids. He displayed a keen interest in scientific societies. From 1863 to 1879 he was president of the
Queensland Philosophical Society (now incorporated in the
Royal Society of Queensland); and was elected to Corresponding membership of the
Manchester Literary and Philosophical Society in 1870. On his return to England he became associated with the
London Mathematical Society, of which he was president from 1886 to 1888, and the
Royal Astronomical Society, serving as a member of the council from 1888 to 1892. He died in London on 27 January 1895. An
obituary notice by the Revd.
Robert Harley was published in 1895 in
Proc. Roy. Soc. vol. 59. A volume containing his scientific and mathematical researches made during the years 1864–1877 was presented to the
British Museum in 1897 by his widow. Like his father, Cockle became wealthy during his lifetime, leaving an estate of £32,169, which is approximately £2.7 million if adjusted for inflation as of 2008. ==Works==