The danger to society is not merely that it should believe wrong things, though that is great enough; but that it should become credulous, and lose the habit of testing things and inquiring into them; for then it must sink back into savagery.

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.