[At the evening meeting of the Annual Meeting of the Mathematical Association on 5th January, 1937, Mr. A. W. Siddons took the chair, and in calling upon Professor Wolff for his paper said: Professor Georg Wolff came to England in 1913, and I believe I am right in saying that Harrow was the first school to which he came and that the last educational institute he was at in England was this Institute of Education in Southampton Row, where he talked with Sir Percy Nunn. When he was in England on that occasion Professor Wolff spent much of his time learning about the teaching of mathematics in this country. He has more recently been lecturing at Columbia University, New York.]

Population trends are determined by fertility and mortality. The crudest method of measuring fertility and mortality consists in relating the number of births and of deaths to the total population. The birth and death rates thus obtained show the proportion by which a population increases through births and decreases through deaths. But since these rates are calculated without regard to the sex and age composition of the population they do not afford an adequate gauge for the measurement of fertility and mortality The disturbing influence of the sex and age composition is eliminated by computing fertility tables and life tables.

I want to begin with an explanation as to my position in coming here to address you. I am not an expert upon the history of mathematics. I have come in order to tell you something of my experiences in trying to teach a little of the history of mathematics to sundry university students. This had its origin in the determination of Professor Milne, even while he was teaching at Clifton, to propagate a knowledge of the history of mathematics amongst students who, as a rule, know absolutely nothing of it. He continued on that crusade in a true missionary spirit at the University of Leeds.

Some years ago there was a vogue for a series of books dealing imaginatively with the future and bearing such titles as Daedalus, or the Future of Science, Icarus, or the Future of Flying, and the like. I do not recall whether arithmetic was among the topics considered by the ingenious authors, but a further title, Archimedes, or the Future of Calculation, might certainly have been suggested by the developments of modern arithmometers.

The aim of this article is to convey the impressions received by a French Professor of Mathematics on reading the book referred to in the title, and thus to throw some light on similarities and differences between methods of teaching in the two countries.

From some viewpoints the beginnings of Analysis were marked by the publication, in 1656, by J. Wallis of the Arithmetica Infinitorum, in which he obtains the product ad inf.

He defines, very early in the book, a “limit” in this way (considering a series which tends to the value ⅓) “When the number of terms increases, the excess above ⅓ decreases, so that at length it becomes less than any assignable quantity; moreover, if the number of terms becomes infinite, the excess will have vanished completely”. We still use substantially the same definition.

The eternal question of the distinction to be drawn, in teaching elementary Mechanics to youngsters, between mass and weight has recently thrust itself upon me in discussing with a Science colleague the choice of a textbook on General Science suitable for pupils, aged about 11 or 12 years, beginning the subject. The first year General Science syllabus which he has drawn up excludes as far as possible all quantitative work, my own Mathematics department is left to deal with the fundamental teaching of all work involving units, not only of mere length, area, and such things as invariably occur in elementary mathematical teaching, but also of such others as temperature and our old friends mass, force, weight, density, and so on, which will in time be used in the Mechanics course for which the Mathematics department assumes responsibility and to which the Science department will refer incidentally as it feels the need.