George Salmon - Mathematics

Mathematics

In the late 1840s and the 1850s Salmon was in regular and frequent communication with Arthur Cayley and J.J. Sylvester. The three of them together with a small number of other mathematicians (including Charles Hermite) were developing a system for dealing with n-dimensional algebra and geometry. During this period Salmon published about 36 papers in journals. In these papers for the most part he solved narrowly defined, concrete problems in algebraic geometry, as opposed to more broadly systematic or foundational questions. But he was an early adopter of the foundational innovations of Cayley and the others. In 1859 he published the book Lessons Introductory to the Modern Higher Algebra (where the word "higher" means n-dimensional). This was for a while simultaneously the state-of-the-art and the standard presentation of the subject, and went through updated and expanded editions in 1866, 1876 and 1885, and was translated into German and French.

Meanwhile back in 1848 Salmon had published an undergraduate textbook entitled A Treatise on Conic Sections. This text remained in print for over fifty years, going though five updated editions in English, and was translated into German, French and Italian. Salmon himself did not participate in the expansions and updates of the more later editions. The German version, which was a "free adaptation" by Wilhelm Fiedler, was popular as an undergraduate text in Germany. Salmon also published two other mathematics texts, A Treatise on Higher Plane Curves (1852) and A Treatise on the Analytic Geometry of Three Dimensions (1862). These too were in print for a long time and went though a number of later editions, with Salmon delegating the work of the later editions to others.

In June 1863 he was elected a Fellow of the Royal Society and in 1868 was awarded their Royal Medal "For his researches in analytical geometry and the theory of surfaces". In 1889 Salmon received the Copley Medal of the society, the highest honorary award in British science, but by 1889 had long ago quit mathematics and science.