The use of Mathematics we understand as not merely utilitarian applications, such as those by which astronomy is employed in navigation, “whereby our nautical logbooks can be better kept, and water transport of all kinds has grown more commodious”; flight too can be made in the air, but also the cultivation at the same time of the intellect, to think correctly, and arrive at the right conclusion from data which are certain ; and the enlargement generally of the interest in this life.

And so our subject received its name from MA⊖HMATA, meaning disciplined exact knowledge, and formed an important branch in the old University ideal, to teach how to live a life, not merely to make a living. To keep the soul alive, body and soul together, and to cure intellectual timidity, the worst form of cowardice.

To introduce the proposed rule we make use of it to settle the signs of terms in the expansion of determinants such as :

where the symbol for the element has superscript r denoting rows and subscript s denoting columns.

For many years candidates (and teachers) involved in A-level work have quoted Newton’s experimental law of restitution as one of the principles enabling collision problems to be solved. It had always seemed to me that it is fortunate that such a simple law holds and also that it is a great pity that there is no simple relationship between the initial and final kinetic energies. Recently, however, I realised that, viewed in terms of invariance, the law is not at all surprising and also that there is a very simple way of dealing with the loss of kinetic energy.