who seek
similar degrees. In view of the fact that in America as well as in
Germany the student often receives much direct assistance while
working on his Ph.D. thesis, this supposition is frequently not in
accord with the facts.[11]

The emphasis on the Ph.D. degree for college teachers has in many
cases led to an improvement in ideals, but in some other cases it has
had the opposite effect. Too many possessors of this degree have been
able to count on it as accepted evidence of scientific attainments,
while they allowed themselves to become absorbed in non-scientific
matters, especially in administrative details. Professors of
mathematics in our colleges have been called on to shoulder an unusual
amount of the administrative work, and many men of fine ability and
scholarship have thus been hindered from entering actively into
research work. Conditions have, however, improved rapidly in recent
years, and it is becoming better known that the productive college
teacher needs all his energies for scientific work; and in no field is
this more emphatically true than in mathematics. Some departmental
administrative duties will doubtless always devolve upon the
mathematics teachers. By a careful division of these duties they need
not interfere seriously with the main work of the various teachers.

=The mathematical textbook=

The American teachers of mathematics follow the textbook more closely
than is customary in Germany, for instance. Among college teachers
there is a wide difference of view in regard to the suitable use of
the textbook. While some use it simply for the purpose of providing
illustrative examples and do not expect the student to begin any
subject by a study of the presentation found in the textbook, there
are others who expect the normal student to secure all the needed
assistance from the textbook and who employ the class periods mainly
for the purpose of teaching the students how to use the textbook most
effectively. The practice of most teachers falls between these two
extremes, and, as a rule, the textbook is followed less and less
closely as the student advances in his work. In fact, in many advanced
courses no particular textbook is followed. In such courses the
principal results and the exercises are often dictated by the teacher
or furnished by means of mimeographed notes.

The close adherence to the textbook is apt to cultivate the habit on
the part of the student of trying to understand what