dency to disrupt many of the stronger
departments. Hence the question of good teaching forced itself rapidly
to the front. It was commonly recognized that the students of pure
mathematics profit by a study of various applications of the theories
under consideration, and that the students who expect to work along
special technical lines gain by getting broad and comprehensive views
of the fundamental mathematical questions involved. Moreover, it was
also recognized that the investigational work of the instructors would
gain by the broader scholarship secured through greater emphasis on
applications and the historic setting of the various problems under
consideration.

To these fundamental elements relating to the improvement of college
teaching there should perhaps be added one arising from the
recognition of the fact that the number of men possessing excellent
mathematical research ability was much smaller than the number of
positions in the mathematical departments of our colleges and
universities. The publication of inferior research results is of
questionable value. On the other hand, many who could have done
excellent work as teachers by devoting most of their energies to this
work became partial failures both as teachers and as investigators
through their ambition to excel in the latter direction.

=Range of subjects and preparation of students=

It should be emphasized that the college and university teachers of
mathematics have to deal with a wide range of subjects and conditions,
especially where graduate work is carried on. Advanced graduate
students have needs which differ widely from those of the freshmen who
aim to become engineers. This wide range of conditions calls for
unusual adaptability on the part of the college and university
teacher. This range is much wider than that which confronts the
teachers in the high school, and the lack of sufficient adaptability
on the part of some of the college teachers is probably responsible
for the common impression that some of the poorest mathematical
teaching is done in the colleges. It is doubtless equally true that
some of the very best mathematical teaching is to be found in these
institutions.

In some of the colleges there has been a tendency to diminish the
individual range of mathematical teaching by explicitly separating the
undergraduate work and the more advanced work. For instance, in Johns
Hopkins University, L. S. Hulburt was appointed "Professor