Mathematician
"Clifford was above all and before all a geometer." (H. J. S. Smith). In this he was an innovator against the excessively analytic tendency of Cambridge mathematicians. Influenced by Riemann and Lobachevsky, Clifford studied non-Euclidean geometry. In 1870, he wrote On the Space-Theory of Matter, arguing that energy and matter are simply different types of curvature of space. These ideas later played a fundamental role in Albert Einstein's general theory of relativity.
Yet Clifford is now best remembered for his eponymous Clifford algebras, a type of associative algebra that generalizes the complex numbers and William Rowan Hamilton's quaternions and biquaternions. Clifford employed these to study motion in non-Euclidean spaces and on certain surfaces, now known as Klein-Clifford spaces. He showed that spaces of constant curvature could differ in topological structure. He also proved that a Riemann surface is topologically equivalent to a box with holes in it. On Clifford algebras, quaternions, and their role in contemporary mathematical physics, see Penrose (2004).
His contemporaries considered him a man of extraordinary acuteness and originality, gifted with quickness of thought and speech, a lucid style, wit and poetic fancy, and a social warmth. In his theory of graphs, or geometrical representations of algebraic functions, there are valuable suggestions which have been worked out by others. 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. Another important paper is his "Classification of Loci" (1878). He published several papers on algebraic forms and projective geometry and the textbook Elements of Dynamic.
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