which can scarcely be attained in any other way, yet the early attack on research problems has not been free from undesirable results. If the mind is centered on one line of thought it is less apt to be in condition to receive deep impressions of other fields which may be equally important. Only the greatest minds have been able to attain to those broad and impressive views which comprehend the true correlation of the different lines of mathematical activity, in addition to making important contributions along any one line. In recent years there has been a tendency to encourage breadth of scholarship even at the expense of research in early years,—a tendency which Klein has aptly named encyclopedic.[1]
In American mathematical research activity was very limited until recent years. Within the last decade the mathematical productivity has more than doubled, both as to quality and as to quantity. This has been largely due to foreign training, as only very few of our larger institutions have a sufficient number of research men on their faculties to afford their students opportunities to enter upon fields of research which are best suited to their tastes and ability. Hence the encyclopedic tendency of German mathematics, and possibly also of that of France, should not affect us for a number of years.
The tendencies which have been mentioned relate principally to university instruction. During the last few years there has been an unprecedented activity along lines which relate principally to secondary schools. This movement is sometimes called the Perry movement, in view of the great activity of Professor John Perry, of the Royal College of Science, London. Perry's paper at the recent Glasgow meeting of the British Association for the Advancement of Science provoked a great deal of discussion, and was followed by the appointment of a committee with Professor Forsyth, of Cambridge, as chairman, 'to report upon improvements that might be effected in the teaching of mathematics, in the first instance in the teaching of elementary mathematics, and upon such means as they think likely to effect such improvements.'
In our own country the movement has been brought into prominence largely through the efforts of Professor Moore, who devoted a part of his presidential address before the American Mathematical Society to questions related to this movement. That the time was ripe for such a movement seems evidenced by the numerous organizations of teachers of mathematics with a view to the discussion of questions related to the improvements in teaching and in the selection of subject matter.[2]
