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Mathematics at TCD 1592-1992

400
years of
MATHEMATICS
by T. D. Spearman

GEORGE
SALMON

The most distinguished of Mac Cullagh's students was George Salmon, also a geometer, whose books on conics sections and on geometry of three dimensions were republished in very many editions and in several languages, and remained in use well into the present century. As well as making significant original contributions in geometry Salmon was actively involved with the English mathematicians Arthur Cayley and J.J. Sylvester in pioneering work in algebra based on the study of invariants under linear transformations. It was through his book Lessons Introductory to the Modern Higher Algebra that his work became widely known. Salmon could carry through the most formidable of calculations and yet his books, the successive editions of which incorporated new and often original results, were models of clarity and elegance. Writing of these books the mathematician Felix Klein said These books are like delightful and instructive walks through forests, fields and gardens, in which the guide points out now this beauty, now that strange phenomenon, without forcing everything together into a rigid system ... We all grew up in these flower gardens; here we gathered the basic knowledge on which we were later to build.'
Apart from his work in algebra Salmon's mathematical interests were confined to geometry, and even the algebraic work may have been largely motivated by its relevance, through the study of invariants, to geometry. He had no taste for physics, despite the excitig work in optics of his three professors, Hamilton, Mac Cullagh and Lloyd. For a while Hamilton thought he had succeeded in interesting him in quaternions but that interest was short lived.
As a Fellow of the College Salmon had been ordained a priest in the Church of Ireland. Theology had always been an interest; in the 1860s this tooks over from mathematics as his primary activity and he was appointed Regius Professor of Divinity in 1866. He was a respected new testament scholar, and wrote a famous critique of papal infallibility. Later he became Provost and presided over the College's tercentenary celebrations in 1892. One of the remarkable geometric results obtained by Salmon: A smooth cubic surface in complex projective 3-dimensional space has exactly 27 complex lines embedded in it. When translated into real space, a smooth cubic surface will have up to 27 real lines embedded in it.


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