last quarter of the nineteenth century, and the
wave of enthusiasm which attended this introduction was unfortunately
not sufficiently tempered by emphasis on good teaching and breadth of
knowledge, especially as regards applications. In fact, the leading
mathematician in America during the early part of this period was
glaringly weak along these lines. By means of his bountiful enthusiasm
he was able to do a large amount of good for the selected band of
gifted students who attended his lectures, but some of these were not
so fortunate in securing the type of students who are helped more by
the direct enthusiasm of their teacher than by the indirect enthusiasm
resulting from good teaching.

The need of good mathematical teaching in our colleges and
universities began to become more pronounced at about the time that
the wave of research enthusiasm set in, as a result of the growing
emphasis on technical education which exhibited itself most
emphatically in the development of the schools of engineering. While
the student who is specially interested in mathematics may be willing
to get along with a teacher whose enthusiasm for the new and general
leads him to neglect to emphasize essential details in the
presentation, the average engineering student insists on clearness in
presentation and usability of the results. As the latter student does
not expect to become a mathematical specialist, he is naturally much
more interested in good teaching than in the mathematical reputation
of his teacher, even if his reputation is not an entirely
insignificant factor for him.

During the last decade of the nineteenth century and the first decade
of the present century the mathematical departments of our colleges
and universities faced an unusually serious situation as a result of
the conditions just noted. The new wave of research enthusiasm was
still in its youthful vigor and in its youthful mood of
inconsiderateness as regards some of the most important factors. On
the other hand, many of the departments of engineering had become
strong and were therefore able to secure the type of teaching suited
to their needs. In a number of institutions this led to the breaking
up of the mathematical department into two or more separate
departments aiming to meet special needs.

In view of the fact that the mathematical needs of these various
classes of students have so much in common, leading mathematicians
viewed with much concern this ten