Cambridge is honoured this year by its selection for the first meeting held in England by the International Congress of Mathematicians. The Cambridge School has played a notable part in the development of mathematics in Britain, and it may be of interest if I briefly summarize the leading facts of its history, which is indeed closely connected with that of the University. The School is of more than respectable antiquity and inevitably it has been sometimes flourishing and sometimes the reverse. Here I desire rather to bring out the salient features in its history than to discuss details or individual achievements.

I desire in the first place to express my thanks to the members of the London Branch of the Mathematical Association for the honour they have done me in electing me to the office of president. I esteem it a privilege to take part in the efforts the Association is making to bring about improvements in the methods of teaching Mathematics.

In what position does the work of the Association now stand ? Is it in fact in the position described by Sir J. J. Thomson in his address to the Association of Public School Science Masters? He is reported to have said that he had come to the conclusion that if you have intelligent masters and small classes it does not matter much what theory of education you adopt, and if you have not these, well, it does not much matter either.

(In reference to A. C. Dixon’s note on lm + 2m + 3m +...+nm, on pp. 283-4 of this volume, the following further notes may be of interest. They are taken, with some alterations, from a paper communicated to the London Mathematical Society in February, 1910.)