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.
On the general question of Mathematical Studies, I will first give my leading ideas on what I may call the moral part. I think that a heavy responsibility rests on the persons who influence most strongly the course of education in the University, to direct that course in the way in which it will be most useful to the students—in the two ways, of disciplining their powers and habits, and of giving them scientific knowledge of the highest and most accurate order (applying to the phenomena of nature) such as will be useful to them through life. I do not think that the mere personal taste of a teacher is sufficient justification for a special course, unless it has been adopted under a consideration of that responsibility. Now I can say for myself that I have, for some years, inspected the examination papers, and have considered the bearing of the course which they imply upon the education of the student, and am firmly convinced that as regards men below the very few first—say below the ten first—there is a prodigious loss of time without any permanent good whatever. For the great majority of men, such subjects as abstract Analytical Geometry perish at once. With men like Adams and Stokes they remain, and are advantageous; but probably there is not a single man (beside them) of their respective years who remembers a bit, or who if he remembers them has the leisure and other opportunities of applying them.
I believe on the other hand that a careful selection of physical subjects would enable the University to communicate to its students a vast amount of information; of accurate kind and requiring the most logical treatment; but so bearing upon the natural phenomena which are constantly before us that it would be felt by every student to possess a real value, that (from that circumstance) it would dwell in his mind, and that it would enable him to correct a great amount of flimsy education in the country, and, so far, to raise the national character.