William Clifford (1845-1879) was an important mathematician of his day. He is most remembered today for his invention of Clifford algebras, which are fundamental in modern differential geometry and mathematical physics. His ideas on the connection between energy and matter and the curvature of space were important in the eventual formulation of general relativity. Clifford was particularly interested in non-Euclidean geometry. However, in his relatively brief career, he made contributions to diverse fields of mathematics: elliptic functions, Riemann surfaces, biquaternions, motion in Euclidean and non-Euclidean space, spaces of constant curvature, syzygies, and so on. He was also well-known as a teacher and for his ideas on the philosophy of science. This work covers the life and mathematical work of Clifford, from his early education at Templeton (Exeter) to King's College (London), to Trinity (Cambridge) and ultimately to his professorship at University College (London)--a post which he occupied until the time of his death. Tucker discusses Clifford's Fellowship at the Royal Society and his Council post at the London Mathematical Society. His papers and talks are presented and peppered with entertaining anecdotes relating Clifford's associations with his private tutor, family members, and his wide circle of personal friends and professional colleagues.
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algebra asymptotes axes axis bitangent body called centre chord circle circular points Clifford coefficients conic conicoids conies conjugate consider coordinates corresponding cubic curvature curve of order denote determined diagonal dimensions distance drawn elliptic elliptic functions equal equation expression factor fixed point foci formula functions geometry given harmonic Hence hyperbola intersection involution Jacobian length line at infinity line joining linear locus London Mathematical Society meet motion multiplication n-gram obverse orthotomic pair parabola parallel parameters pass perpendicular plane points at infinity points of contact polar polygon position quadric quadric surface quantities quartic quaternion radical axis ratio regard relation represented respect result Riemann's surface right angles rotor shew sides space sphere square straight line suppose surface symbols tetrahedron theorem theory Theta functions touch triangle values vanishes variables vector velocity vertices zero
Page xliv - But after that would come again a changeless eternity, which was fully accounted for and described. But in any case the Universe was a known thing. Now the enormous effect of the Copernican system, and of the astronomical discoveries that have followed it, is that, in place of this knowledge of a little, which was called knowledge of the Universe, of Eternity and Immensity, we have now got knowledge of a great deal more; but we only call it the knowledge of Here and Now.
Page xlv - ... or a future eternity. He knows, indeed, that the laws assumed by Euclid are true with an accuracy that no direct experiment can approach, not only in this place where we are, but in places at a distance from us that no astronomer has conceived; but he knows this as of Here and Now; beyond his range is a There and Then of which he knows nothing at present, but may ultimately come to know more.
Page xliv - For the laws of space and motion . . . implied an infinite space and infinite duration, about whose properties as space and time everything was accurately known. The very constitution of those parts of it which are at an infinite distance from us, 'geometry upon the plane at infinity...