DECEMBER 6, 1918] 
we can render our students is a function of 
many variables but among these variables our 
own knowledge of the subject which we try 
to teach is doubtless the most significant. Our 
enthusiasm for the subject is likely to grow 
with this knowledge and is another important 
variable upon which our success will depend. 
It should also be noted that an enthusiam 
which is expressed only in words is not likely 
to reach the student’s heart. 
It is somewhat like the enthusiasm of our 
pro-German fellow citizens who had a change 
of tongue immediately after our entrance into 
the world war. While we were glad to see 
these changes we were inclined to await a 
change of mind and still more a change of 
heart. The change of tongue is the easiest hu- 
man transformation, then comes a change of 
mind and finally a change of heart. The en- 
thusiasm coming from the heart of the teacher 
is the only one which is apt to reach the heart 
of the student, and if your heart is in your 
subject you will want to know more about it. 
While the summer sessions of our universi- 
ties offer important facilities for the scientific 
development of our teachers there are other 
facilities which are less expensive and more 
permanent. Among these the high-school li- 
brary deserves especial emphasis. Books are 
the cheapest educational factors in the world 
and most young teachers do not buy enough 
books relating to their own fields of work. 
What is more important they do not provide 
enough mathematical reading matter for their 
students. 
The number of popular mathematical books 
is not very large, but this number is increasing 
fairly rapidly, and all high-school students 
should have access to at least a few of them. 
A few books on the history of mathematics, on 
mathematical recreation and on general mathe- 
matical expositions should be in every high 
school library. Such mathematical journals 
as School Science and Mathematics and the 
American Mathematical Monthly should also 
come regularly to every such library. High 
school students should be frequently encour- 
aged to read mathematical articles in the gen- 
ral encyclopedias. 
SCIENCE 
555 
While the books and journals to which we 
referred should be accessible to the students 
of every high school, they should especially be 
used by the teachers, and they afford important 
facilities for the scientific development of 
these teachers. Those interested in larger col- 
lections and more explicit references should 
consult “A list of mathematical books for 
schools and colleges,” containing titles of 160 
books suitable for the school or college library, 
which was prepared by the library committee 
of the Mathematical Association of America, 
and published in the American Mathematical 
Monthly, volume 24, 1917, page 368. 
It should be emphasized that this list of 160 
books is for reference and not for intensive 
study. One of the greatest dangers which be- 
set those of us who are anxious to become 
strong mathematicians is scientific dissipation. 
General mathematical reading is extremely 
useful but the backbone of the equipment of 
‘the mathematician is a profound knowledge of 
a few subjects, and the mastery of a compara- 
tively small number of books. In fact, I be- 
lieve that if a man would secure a thorough 
knowledge of certain nine mathematical books 
beyond a first course in elementary caleulus he 
would be much better informed than the aver- 
age candidate for the Ph.D. degree. 
The mastery of nine volumes does not ap- 
pear to be an insurmountable barrier between 
many young teachers of mathematics and the 
important goal of holding a place in the ranks 
of the real mathematicians of our land. I 
take it that there are many here whose views 
are in accord with the following words of 
Bacon, printed for years on the covers of the 
Mathematical Gazette: “I hold every man a 
debtor to his profession, from the which as 
men of course do seek to receive countenance 
and profit, so ought they of duty to endeavor 
themselves by way of amends to be a help and 
an ornament thereunto.” 
The nine mathematical books whose mastery, 
together with a fair amount of general mathe- 
matical reading, and a development of some 
of the thoughts contained in these books, would 
make us an ornament unto our profession 
could be selected with considerable latitude. 
