In 1885 Cayley and Salmon had carried forward the investigations of the earlier German geometers, Hesse, Steiner, Plücker and other; and Salmon had expounded the subject in treatises which for clarity of style are still unrivalled. Further, the Italians, Corrado Segre and Castelnuovo were opening the way into a vast unexplored field, geometry of more than three dimensions. Rarely has a branch of science offered more inviting prospects for a novice hoping to undertake research.

Yet I must now admit that my devotion to this one branch of mathematics has been in some degree unfortunate; for time has shown (what might perhaps have been foreseen) that the elementary algebraic methods, so effective and so admirable when applied to the simpler curves and surfaces, fail to produce results when applied to loci of higher order. Often, no doubt, no relations of an elementary nature exist, and the search for them is bound to end in disappointment. Nevertheless, methods of elementary algebra may still be employed with success both in geometry proper and in applications such as arithmetical properties of rational functions. It is true that the scope of these methods is restricted, but there is compensation in the fact that when geometry is successful in solving a problem the solution is almost invariably both simple and beautiful.

The last sentence explains why so many of my published papers are very short. A result already known is obtained in a simple manner.

Admittedly I have spent much time advocating old-fashioned methods which have fallen into undeserved neglect (in my opinion). This does not imply lack of appreciation of modern methods...

Richmond's mathematical researches lay in the field of pure and algebraic geometry, though he also lectured to generations of undergraduates on differential geometry. His papers always showed the characteristics of elegance and apparent effortlessness. His forte lay in seeing the relations between apparently diverse theorems, and he was especially at home in the projective properties of figures in spaces of more than three dimensions, but he did not disdain the consideration of elementary theorems in plane geometry; he would remark a little sadly that his results were remote from the trends of modern geometry.

But shining through his special interests was his genius for friendships with men of all academic generations. He endeared himself to all of them by his utter sincerity and unpretentiousness, his extreme modesty, his engaging humour..., his faithfulness... . He was a lovely person to know.

No bare recital of his achievements and interests can possibly convey the true flavour of the man, his emphatic modesty, his engaging humour, his humanity, his outstanding sympathy with men of all generations, his impatience with anything pretentious or shoddy.