This article is based on students’ remarks about the introduction of matrices and linear transformations; remarks which provide interesting support to those recorded by M. L. Cornelius [1] in a recent Gazette. However, the purpose of the article is not merely to record students’ opinions, but to consider what implications such responses have for us as teachers.

The following notes arose from a talk given by Professor Halberstam to the South West Wales branch of the Association. In the marriage bureau problem we imagine that n boys and n girls are to be paired off in marriage, that we are able to establish preference lists for each boy of all the girls and vice versa. These preference lists may be displayed in a table such as that given below, which shows the rankings for four boys α, β, γ and δ, and for four girls A, B, C, and D. The boys’ rankings are the first members of the number pairs, in rows, and the girls’ are the second members, in columns.

The word “lesson” came back to Pooh as one he had heard before somewhere. “There’s a thing called Twy-stymes”, he said. “Christopher Robin tried to teach it to me once, but it didn’t.” A. A. Milne.

In assessing the value of the mathematics taught in schools, considerable emphasis is normally given to the use which a minority will later make of it in their jobs. It is the purpose of this article to point out that even those who never use mathematics professionally could better understand important social issues if they had a good basic training in mathematics. This is illustrated by a set of mathematical models related to one such problem— the population explosion.

1. You all remember that in that well-known play, Waiting for Godot, the eponymous hero never actually appears. In the same way my talk should perhaps have been entitled Waiting for transcendental numbers—for while transcendental numbers are at the back of everything that follows, they will not become, for reasons of technical difficulty, proper part of the action.

In the eighteenth century The Ladies’ Diary regularly included mathematical problems. A complete collection of these problems from 1704 to 1760 appears in a volume entitled The Diarian Repository; or Mathematical Register published in 1774 [1]:

“... a collection of more than four hundred and seventy Problems, relating to such various parts of the Mathematics as are here collected from the Diaries, together with their Solutions fully investigated will, we doubt not, prove of considerable service to the young Adventurer in this useful branch of learning...”