506 
As one such selection the following may be 
noted: Weber, “ Lehrbuch der Algebra,” three 
volumes; Goursat, “ Cours d’ analyse mathé- 
matique,” three volumes; Veblen and Young, 
“ Projective Geometry,” two volumes—the sec- 
ond by Veblen alone; Hisenhart, “ Differential 
Geometry,” one volume. Those who do not 
read German might substitute for the three 
volumes of Weber’s algebra the following: 
Bécher, “Introduction to Higher Algebra”; 
Miller, Blichfeldt and Dickson, “ Finite 
Groups”; Ried, “ Theory of Algebraic Num- 
bers.” Fortunately the first two volumes of 
‘Goursat’s “Cours” were translated into Eng- 
lish by members of the mathematical depart- 
ment of your state university. 
It may be noted that this list of nine vol- 
umes contains three volumes on each of the 
three broad fields of mathematics—algebra, 
analysis and geometry. Moreover, the mastery 
of these nine volumes would usually be at- 
tended by considerable reference work since 
some subjects are treated therein too concisely 
for the average student. Unfortunately there 
exists at present no good mathematical dic- 
tionary in any language. It is to be hoped 
that the Mathematical Association of America 
will soon remedy this great drawback, espe- 
cially for the private study of mathematics, 
and it is interesting to note that the chairman 
of its committee having this matter under con- 
sideration belongs to your own state univer- 
sity. 
Those who read French and German can not 
be too strongly advised to provide themselves 
with the published parts* of the large mathe- 
matical encyclopedia, whose completion has 
been so much delayed by the world war. The 
French edition of this work is especially com- 
plete, as far as it has been published, and our 
chief objection to the list of 160 library books 
noted above is that it makes no mention of 
this superior work of reference. Almost 
4This publication is not as far advanced as one 
would naturally infer from a reference thereto re- 
cently made by the retiring chairman of the Chi- 
eago Section of the American Mathematical So- 
ciety on the opening page of an address published 
in volume 25 of its Bulletin. 
SCIENCE 
[N. S. Vou. XLVIITI, No. 1249 
equally reprehensible seems to be the omission 
of the very useful Volume I., “Subject, Index, 
Pure Mathematics,” Royal Society of London 
Catalogue of Scientific Papers. Every student 
should have an opportunity to determine the 
limits of our present knowledge along partiec- 
ular lines which may interest him. 
While the careful study of nine such vol- 
umes as were noted above would serve as a 
kind of admission card to the circle of pure 
mathematicians it is necessary to emphasize 
the fact that high standing in this circle would 
imply various other attainments. One of the 
foremost of these is a comprehensive knowl- 
edge of the literature along at least one impor- 
tant line of mathematical work. Such a 
knowledge could scarcely be acquired without 
using French, German and Italian literature. 
Hence a reading knowledge of these languages, 
especially the first two, is very important for 
the prospective mathematician. During the 
last two or three centuries the French have 
contributed more than any other nation 
towards the advancement of mathematics. 
We have thus far failed to mention what 
may appear to many as the foremost qualifica- 
tion for a high position in the circle of mathe- 
maticians; viz., research ability of high order. 
It is true that the highest mathematical honors 
are usually reserved for those who possess 
this ability in a high degree in addition to 
the attainments to which we referred. It is, 
however, equally true that the highest research 
is usually spontaneous and takes care of itself 
provided the proper foundations have been laid 
and the necessary enthusiasm is present. 
It is difficult to see how a man with high 
mathematical attainments and deep mathe- 
matical interest can help doing research work. 
It is the most charming occupation in the 
world even when the results appear unworthy 
of publication. When results are reached 
which seem to be of permanent value and to 
serve as rays of light to all future generations 
the investigator naturally experiences feelings 
of delight that enrich his inner life as few 
things do. 
The view that all mankind has equal mathe- 
matical opportunity in this world is not 
