Our Association was founded deliberately to “improve” the teaching of geometry, and its work has extended to cover every branch of the mathematics taught in the pre-undergraduate years. It is no surprise that, among the many distinguished mathematicians who have contributed to this development, a few stand apart clearly for the extent of their influence. Judged by any standards, E. H. Neville was one of the greatest of them all, and this tribute, by one of his earliest pupils at University College, Reading, is written with a sense of deep personal affection and gratitude.

The Mathematical Association was founded in 1871, as an Association for the Improvement of Geometrical Teaching, by teachers who had lost faith in the educative value of learning by rote the words of Euclid's sacred text; indeed, one suggested name was the Anti-Euclid Society Progress was at first slow, until in the early years of this century Oxford and Cambridge agreed to accept, in their entrance requirements, any system of geometry which exhibited some logical coherence.

E. H. Neville was Librarian of the Mathematical Association for over thirty years, from 1923 to 1954.For more than half of that time Neville was not only Librarian but custodian of the books which were handsomely shelved and displayed in his own home, first in his house on Castle Hill, Reading, and then in his first house in Sonning.

Through the kindness of Mr. Langford we are able to publish a mathematical note by Neville and some extracts from his letters, mainly on teaching problems.Those who knew Neville will almost hear him speak through these informal (and unedited) comments on topics where his keen enthusiasm helped so vitally to clarify issues that were becoming needlessly obscure.

You are all mathematicians, but almost all of you are something more than mathematicians; you are astronomers, meteorologists, physicists, or whatever it may be. Few mathematicians who are nothing but mathematicians attend the meetings of our Association regularly, and in this Chair I am not only a fish out of water, but a very small fish at that. you should see the ones that got away! An enquiry into the reasons for this state of affairs might lead to interesting observations on the purpose of conferences in general and of our own meetings in particular, as well as on the differences between one subject and another in respect of semi-vulgarisation, but it would be in the worst of taste to offer you who are here nothing but a disquisition making excuses for those who are not. Let us agree with the French that being absent they are in the wrong, and leave it at that.

§1. The problem is to evaluate, with an absolute error o(l) or better,

where m and n are large and positive and c is a positive constant.

The following is an account of a method of addition and some methods of subtraction which may appeal to teachers who like to lace their teaching with enrichment material, but who sometimes refrain from doing so because of a fear that an “off beat” treatment of a topic may confuse rather than clarify.

It has been argued from time to time [1] that the special theory of relativity is suitable for first year undergraduates reading mathematics or physics at British Universities. The pedagogical value of this subject is considerable, since it introduces conceptual problems, whose solutions require clear thought, but only elementary mathematics. The teaching of this subject can therefore bring about a useful broadening in a student’s intellectual equipment.