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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 exciting 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 3dimensional
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. 