The Annual Meeting of the Mathematical Association was held on Friday, 5th January, 1917, at the London Day Training College, Southampton Row, London, W.C., the President, Professor A. N. Whitehead, Sc.D., F.R.S., in the chair.

The subject of this address is Technical Education. I wish to examine its essential nature and also its relation to a liberal education. Such an enquiry may help us to realise the conditions for the successful working of a national system of technical training. It is also a very burning question among mathematical teachers; for mathematics is included in most technical courses.

It would not be possible in the short time allotted to me for this paper to discuss any scheme of Educational Reconstruction which might appear to me as ideal. Indeed it is doubtful, notwithstanding the constant use which is made of the term, whether any reconstruction of our educational system, in the full sense of the word, is probable or even possible. But many reforms, some of them fundamental and far-reaching in their effects, are both possible and probable. It is with certain of these which, directly or indirectly, will materially affect the position of mathematics, that I propose to deal as far my limited time allows.

Geometry in a Mathematical Syllabus seems to me to occupy much the same position that Greek does in the Classical. The two have similar merits and similar defects, and I am doubtful whether either deserves its place except in specialist classes.

Aim. I take it that the object of teaching mathematics in a boys’ school is to develop, in combination, the power (i) to apply mathematics successfully to matters of human interest, (ii) to appreciate in some measure that ‘realm of order’ (the expression is borrowed from Professor Nunn) in which mathematical ideas exist.

Euclid’s definition of two parallel straight lines seems to be the correct one for the absolute ideal of a plane and of a straight line. The conception of a line at infinity, it would seem, should be stated if used in some such words as these. Points may be supposed to exist at such a distance from the points generally considered in a plane that their distances from all such points in the plane may be regarded as equal, i.e. the differences of these distances may in general be regarded as negligible. These points, as a first approximation, may, under certain circumstances, be regarded, when considered in relationship to points at a finite distance, as lying on a straight line. Parallel straight lines may be regarded—for most practical purposes—as far as points at a finite distance are concerned, as intersecting at one of these points.