Professor Clive Kilmister

Professor Clive Kilmister

Those with access to the JSTOR database of all past copies of the Gazette (up to a 'moving wall' of 5 years ago) will be able to read his Presidential address, published in October 1980.

For those without, it is available to members for a small supplement: contact Marcia Murray at HQ, here are his opening remarks.

Zeno, Aristotle, Weyl and Shuard: Two-and-a-Half Millenia of Worries over Number

It has been common in recent years, if not entirely obligatory, for your President to address you on this occasion about the difficulties and opportunities he has found in the practice of teaching, and this year will be no exception. But following the excellent example of all past Presidents, as far back as I have investigated, I intend to confine my address to that part of the activity about which I am practically conversant. So while I hope that the general ideas and conclusions of my talk will be enjoyable and possibly useful to everyone here, I shall deal in detail only with the narrow problem of first-year undergraduates. I say simply 'problem' because I believe that the various different questions (the 'interface', the content of first-year pure/applied courses, how should the sixth form teacher best prepare the future university entrant,...) are all aspects of a single problem. For the sake of precision I shall deal with only one aspect of this problem, as it arises in analysis. Knowing me, you might have expected rather that I would have discussed the difficulties of teaching mechanics, or of persuading young people of 18 plus (although many of them have been brought up since five years of age on a practical approach to mathematics!) that there is any possibility at all of making an application of mathematics in the external world. My depression about that aspect is too strong, and my involvement in it is probably too deep, for me to see it clearly. But my experiences supervising small groups of students who are making their first genuine acquaintance with the real number field suggest to me the possibility of improving matters.

This brings me to the last of the four names in my title and, for those who are still wondering, it is indeed Hilary Shuard who, though she may feel in strange company amongst such eminent historical personages, has prompted my thinking just as much as the other three. She once remarked to me: "Perhaps they do need to know all about the real numbers, but do they need it all in the first year?" And she has developed some kindred points in the Gazette [1] about the teaching difficulties involved in giving definitions of function, limit, and so on. In digging out her Gazette paper I happened to come across the Association's 1962 Analysis report; its general atmosphere is strikingly different from that reigning now. Eighteen years ago we could expect a majority of first-year students to have been exposed to the further topics suggested in the report; many fewer in 1980. However, it isn't only today's young people who find the real numbers difficult, and this brings me to another of my hobby-horses, the importance of the contribution of the history of mathematics to the understanding of mathematics. I do not suppose I need to argue this here; for any subject which has been going on in a recognisably similar form for over two thousand years neglects its own history at its peril. But the real numbers have a history of discussion and paradox which exceeds most mathematical questions. It seems to me almost certain, in such a situation, that the difficulties of the young in confronting such a system must in part echo these historic troubles, and so we can learn from the past something of use today.