VI.55 William Kingdon Clifford
b. Exeter, England, 1845; d. Madeira, Portugal, 1879
Geometry; complex function theory; popularization of mathematics
Clifford went up to Trinity College Cambridge in 1863. He graduated from there in 1867 as 2nd Wrangler and also came second in the more demanding Smith’s prize examination. In 1868 he became a Fellow of Trinity, leaving in 1871 to become the professor of applied mathematics at University College London. He died of tuberculosis in 1879.
A versatile mathematician, regarded by many as the best of his generation, Clifford’s favorite field was geometry, over which he ranged widely, proving new results in classical Euclidean geometry as well as in projective and differential geometry. He was the first English mathematician to appreciate the work of RIEMANN [VI.49] on differential geometry, and published a translation of Riemann’s paper “On the hypotheses that lie at the foundations of geometry” in 1873. He endorsed Riemann’s fundamental reformulation of geometry, and went even further in speculating that the curvature of physical space might explain the motion of matter. He also made a significant application of the RIEMANN-ROCH THEOREM [V.31], and was among the first to analyze the complicated topological nature of a RIEMANN SURFACE [III.79] by showing how to dissect any Riemann surface into simple pieces in a standard way. He was the first to study a geometry locally equivalent to plane geometry but topologically distinct (the flat torus, also known today as the Clifford-Klein space form after KLEIN’S [VI.57] later more detailed study of it). In algebra, he invented the biquaternions (these are like quaternions, but have complex numbers as coefficients).
Clifford was regarded as a marvelous lecturer until his health broke, and he was a successful popularizer and essay writer. He forcefully adopted the view that geometry was a matter of experience, not a priori truth. He was a friend of T. H. Huxley and was sympathetic to humanism in philosophy.
Further Reading
Clifford, W. K. 1968. Mathematical Papers, edited by R. Tucker. New York: Chelsea. (First published in 1882.)