If I steal money from any person, there may be no harm done from the mere transfer of possession; he may not feel the loss, or it may prevent him from using the money badly. But I cannot help doing this great wrong towards Man, that I make myself dishonest.

He was the first to suggest that gravitation might be a manifestation of an underlying geometry. He was much interested too in universal algebra and elliptic functions his papers "Preliminary Sketch of Biquaternions" (1873) and "On the Canonical Form and Dissection of a Riemann's Surface" (1877) ranking as classics. This paper was famously attacked by pragmatist philosopher William James in his "Will to Believe" lecture.

In his philosophical writings he coined the expression "mind-stuff". Building on the work of Hermann Grassmann he introduced what is now termed geometric algebra a special case of the Clifford algebra named in his honour with interesting applications in contemporary mathematical physics and geometry.