Ladies and Gentlemen,

There are many different forms of Presidential Address. To glance back at those delivered to this Association is at once an exhilarating and a humbling procedure. Indeed, at one stage during it I toyed with the notion of filling this session with an amalgam of abstracts. You might have been better served had I done so; as it is I shall be quoting from three only and the reasons for that particular selection should become apparent before long.

We have already explained pp. (25-31) that there are two types of uniform three-dimensional space, viz., finite or elliptic space, in which the geodesies or straight lines are closed and of constant length, and infinite or hyperbolic space, in which the geodesies are unclosed and of infinite length. Euclidean or parabolic space may be regarded as a special third type, or as the dividing case between the two general types; but it is best to regard it as a variety of hyperbolic space, owing to the reality of the infinite. In elliptic space all geodesies through a point either return without intersecting again, or have at most one other fixed point of intersection. In hyperbolic space it does not appear necessary that a geodesic should consist of only a single branch, though this is of course the simplest case; if the geodesies have several branches, all geodesies through a point will have a fixed point on each branch, and two geodesies which intersect will have as many points of intersection as they have branches. When we consider two-dimensional space we find that, even in the elliptic type, the geodesies may have any number of intersections, and may be unclosed and infinite. The proof to the contrary on p. 31 does not apply when the geometry is confined to a surface.

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.

A few years ago, an experiment was made at Marlborough (1) to begin the teaching of statistics with a discussion of rank correlation because “within a few periods and without any complicated arithmetic, it was possible to discuss the main items in a statistician’s philosophy”. What I want to do in this article is to show how the same can be done with one of the commonest situations in elementary statistics, when we wish to compare populations from which two samples are drawn and decide whether one is “better” than the other. In the classical approach, this is often done by Student’s t test which is highly sophisticated compared with the Mann-Whitney U test, to which I now turn.

Since due recognition is now being more and more widely given to the importance of Vector Analysis for three-dimensional work in mechanics, geometry and mathematical physics, the time is opportune to consider the place which that subject merits in a University degree course. A student who undertakes anything like research work in applied subjects is considerably handicapped if he has had no training in Vector Analysis; but the need for it is felt much earlier than the stage at which research is generally begun. Every University course contains subjects which are less useful than Vector Analysis; and on the ground of utility alone there is no question that the latter deserves a place in the curriculum. It will, however, be found quite unnecessary to displace anything else, because the time occupied in teaching the essential parts of vector algebra and calculus will be saved, even during a three years’ course, by the application of this method to the three-dimensional parts of mechanics and mathematical physics.

During my year as President of The Mathematical Association the government began a review of the curriculum across all subjects taught in school. Given the constant tinkering with the education system by every government, this is probably a sentence that any MA president could write during their tenure. But 2013 saw government really trying to layout their vision for what education should deliver in the coming decade.

In English, an aim of the curriculum review is to develop a student's love of literature through widespread reading for enjoyment. Students will get to read Shakespeare, romantic poetry, the great novels of the nineteenth century together with seminal works of world literature. It is hoped that this will expose students to the great works of literature and allow them to acquire an appreciation of ‘our rich and varied literary heritage’ [1, p. 13].

In science, by building on fundamental ideas and concepts, the curriculum review aims to foster in students ‘a sense of excitement and curiosity about natural phenomena’ [1, p. 99]. Students will study the fundamental mechanics of the cell, learn about stem cells, photosynthesis and genomics; they will be exposed to radiation (in a theoretical sense) and the evidence for the Big Bang. Such fundamental ideas will give students the scientific knowledge to be able to understand the uses and implications for the impact of science on society.