Clifford, William Kingdon (1845–1879)

English mathematician and scientific philosopher. He developed the theory of biquaternions and made advances in non-Euclidean geometry. It was through a generalization of the quaternions (themselves a generalization of complex numbers) that Clifford derived his theory of biquaternions, associating them specifically with linear algebra. In this way representing motions in three-dimensional non-Euclidean space, and together with his suggestion in 1870 that matter itself was a kind of curvature of space, Clifford may be seen to have foreshadowed in some respects Albert Einstein's general theory of relativity. Clifford parallels and Clifford surfaces are named after him.

Clifford continued his studies in non-Euclidean geometry, with reference particularly to Riemann surfaces, which he proved to be topologically equivalent to a box with holes in it. He further investigated the consequences of adjusting the definitions of parallelism, and found that parallels not in the same place can exist only in a Riemann space – and he proved that they do exist. He showed how three parallels define a ruled second-order surface that has a number of interesting properties.

Clifford was born in Exeter, Devon, and educated at Cambridge, where he spent his academic career until 1871, when he was appointed professor of applied mathematics at University College, London. From 1876 he lived in the Mediterranean region.