Cayley, who was
the great exponent and advocate of Pure Mathematics at Cambridge. Both
of them were men of the highest mathematical powers, but diametrically
opposed in their views of the use of Mathematics. Airy regarded
mathematics as simply a useful machine for the solution of practical
problems and arriving at practical results. He had a great respect for
Pure Mathematics and all the processes of algebra, so far as they
aided him to solve his problems and to arrive at useful results; but
he had a positive aversion to mathematical investigations, however
skilful and elaborate, for which no immediate practical value could be
claimed. Cayley on the contrary regarded mathematics as a useful
exercise for the mind, apart from any immediate practical object, and
he considered that the general command of mathematics gained by
handling abstruse mathematical investigations (though barren in
themselves) would be valuable for whatever purpose mathematics might
be required: he also thought it likely that his researches and
advances in the field of Pure Mathematics might facilitate the
solution of physical problems and tend to the progress of the
practical sciences. Their different views on this subject will be
seen from the letters that follow:
ROYAL OBSERVATORY, GREENWICH,
LONDON, S.
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