 His own major mathematical contributions were on functional and differential equations, and the theory of probability ('On the foundations of the theory of probabilities' (read to the Cambridge Philosophical Society on 14 February 1842; published in the fourth volume of the Proceedings of the Cambridge Philosophical Society of 1844)).Philosophically, Ellis (like George Boole and later John Venn) defended an objective rather than subjective theory of probability.He corresponded with Augustus De Morgan on the conjectured four color theorem.