## Mathematical PapersWilliam 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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### Contents

V | 1 |

VI | 14 |

VII | 17 |

VIII | 20 |

IX | 21 |

X | 23 |

XI | 34 |

XII | 38 |

XLIII | 342 |

XLIV | 346 |

XLVI | 350 |

XLVII | 356 |

XLVIII | 368 |

XLIX | 378 |

L | 385 |

LI | 397 |

XIII | 55 |

XIV | 72 |

XV | 80 |

XVI | 110 |

XVII | 115 |

XVIII | 119 |

XIX | 123 |

XX | 130 |

XXI | 165 |

XXII | 168 |

XXIV | 177 |

XXV | 181 |

XXVI | 201 |

XXVII | 205 |

XXVIII | 218 |

XXIX | 229 |

XXX | 234 |

XXXI | 236 |

XXXIII | 241 |

XXXIV | 255 |

XXXV | 258 |

XXXVII | 266 |

XXXVIII | 277 |

XXXIX | 287 |

XL | 305 |

XLI | 332 |

XLII | 337 |

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### Common terms and phrases

algebra angles apply axes axis becomes body called centre circle coefficients common condition conic consider contains coordinates corresponding cubic curve denote determined dimensions direction distance double drawn elliptic equal equation expression fact factor fixed flat follows four functions geometry given gives harmonic Hence identical infinite infinity intersection joining length linear locus marks means meet motion moving multiplication namely obtain operation origin pair parallel pass perpendicular plane polar position powers projection properties proved quadric quantities ratio regard relation remaining represented respect result right angles rotor round sides space sphere square step straight line suppose surface symbols tangent theorem theory thing third touch transformation triangle types units values vanishes variables vector write

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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...

Page xxviii - CLIFFORD — THE ELEMENTS OF DYNAMIC. An Introduction to the Study of Motion and Rest in Solid and Fluid Bodies.