Educated at Trinity College of Cambridge University, Clifford, at age 26, was appointed Professor of Appled Mathematics and Mechanics at University College, London, on the recommendation of the great William Clerk Maxwell. (University College was the first in Great Britain to admit women students.)

The Chairman of the Mathematics Department, Joseph L. Sylvester (once math tutor of teen-age Florence Nightingale), had especial praise for a paper of Clifford's which anticipated today's field of geometrodynamics, notably beginning with Einstein's notion of space curved by gravity, and the ideas of Wheeler and Misner about "worm-holes" in space. Clifford wrote: "I hold in fact:

• "(1)That small portions of space are in fact of a nature analogous to litle hills on the surface which is on the average flat: namely, that the ordinary laws of geometry are not valid to them.
• "(2)That this property of being curved or distorted is continually being passed on to another after the manner of a wave.
• "(3)That this variation of the curvature of space is what really happens in that phenomenon which we call the motion of matter.
• "(4)That in the physical world nothing else takes place but this variation, subject (possibly) to the laws of continuity."

Clifford gave a remarkable testimony to the notion of I>stewardship in his essay, "The ethics of personal belief":
"No one man's belief is a private matter which concerns him alone....Our words, our phrases, our forms and processes and modes of thought, are common property, fashioned and perfected from age to age; an heirloom which every succeeding generation as a precious deposit and a sacred trust to be handed on to the next one, not changed but enlarged and purified. Into this, for good or ill, is woven every belief of every man who has speech of his fellows. And awful priviledge and an awful responsibility that we should help to create the world in which posterity will live."

Hestenes says: "Clifford may have been the first person to [realize] ... that two different interpretations of number can be distinguished, the quantitative and the operational ... number as a measure of 'how much' or 'how many' of something ... [contrasted with] a relation between different quantities.... Interpreted quantitatively, [the unit bivector] i is a measure of directed area. Operationally interpreted, i specifies a rotation in the i-plane. Clifford observed that Grassmann developed the idea of directed number from the quantitative point of view, while Hamilton emphasized the operational interpretation. The two approaches are brought together by the geometric product [multiproduct]....[V]ectors are usually interpreted quantitatively, while spinors are usually interpreted operationally."

Clifford wrote two papers setting forth his ideas, but died prematurely of tuberculosis, leaving a young wife and two tiny girls.

The development soon after of the Gibbs-Heaviside vector algebra and analysis diverted attention from his work until Marcel Riesz and David Hestenes revived it.