Item 16 - Letter from George Biddell Airy to Arthur Cayley

2 folded sheets.

Royal Observatory, Greenwich, London S. E. - Thinks 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'; comments first on the study of partial differential equations, which 'are very useful and therefore stand very high., as far as the Second Order. They apply... to the great problems of nature concerning time, and infinite division of matter, and space.. Beyond that Order they apply to nothing'.

Discusses 'what I may call the moral part' of mathematical studies: thinks a 'heavy responsibility' lies on those responsible for the course of education in the University to direct it 'in the way in which it will be most useful to the students' by 'disciplining their powers and habits' and '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'; does not think that the 'mere personal taste of a teacher is sufficient justification for a special course' unless these aspects are taken into consideration.

Has for some years inspected the examination papers, and considers that except for the very best students there is currently 'a prodigious loss of time without any permanent good whatever', since only a very few such as Adams and Stokes retain their study of abstract analytical geometry. Believes that in contrast 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' and therefore remain in the mind and 'raise the national character'.

Is 'old enough to remember the time of more geometrical processes' and believes that 'for the cultivation of accurate mental discipline they were far superior to the operations in vogue at the present day. There is no subject in the world more favourable to logical habit than the Differential Calculus in all its branches...'; thinks a return to study of it would be 'far more advantageous... than the simple applications to Pure Equations and Pure Algebraical Geometry now occupying so much attention'.