It has always been my wish to maintain a friendly connection with my College, and I am delighted to receive this response from the College.  The peculiar form in which the reference to the Statute enables them to put it renders it doubly pleasing.

As the Statute is new, I should be obliged by a copy of it.  And, at any convenient time, I should be glad to know the name of the person with whom I am so honorably associated.

I am, My dear Master,
Very faithfully yours,
G.B.  AIRY.

* * * * *

Consequent on Airy’s proposals in 1866 for the introduction of new physical subjects into the Senate-House Examination and his desire that the large number of questions set in Pure Mathematics, or as he termed it “Useless Algebra,” should be curtailed, there was a smart and interesting correspondence between him and Prof.  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.E.
1867, Nov. 8.

MY DEAR SIR,

I think it best to put in writing the purport of what I have said, or have intended to say, in reference to the Mathematical Studies in the University.

First, I will remark on the study of Partial Differential Equations.  I do not know that one branch of Pure Mathematics can be considered higher than another, except in the utility of the power which it gives.  Measured thus, the Partial Differential Equations are very useful and therefore stand very high, as far as the Second Order.  They apply, to that point, in the most important way, to the great problems of nature concerning time, and infinite division of matter, and space:  and are worthy of the most careful study.  Beyond that Order they apply to nothing.  It was for the purpose of limiting the study to the Second Order, and at the same time working it carefully, philosophically, and practically, up to that point, that I drew up my little work.