886 
inestimable amount of good for the growth 
of knowledge and the spread of the spirit 
of investigation. At the present time more 
than 2,000 articles which are supposed to 
be contributions to knowledge in pure 
mathematics appear annually in such 
periodicals. In addition to these there is a 
growing annual list of books. 
The great extent of the fields of mathe- 
matics and the rapid growth of this litera- 
ture have made it very desirable to secure 
means of judging more easily the relative 
merit of various publications. Along this 
line our facilities are still very meager and 
many serious difficulties present themselves. 
In America we have the book reviews 
and the indirect means provided by the 
meetings of various societies and by such 
publications as the ‘‘American Men of 
Science.”’ 
The most important aid to judge con- 
temporaneous work is furnished by a Ger- 
man publication known as the Jahrbuch 
liber die Fortschritte der Mathematik. In 
this work there appear annually about 
1,000 pages of reviews of books and articles 
published two or three years earlier. These 
reviews are prepared by about 60 different 
mathematicians who are supposed to be well 
prepared to pass judgment on the par- 
ticular books and articles which they un- 
dertake to review. While these reviews are 
of very unequal merit, they are rendering a 
service of the greatest value. 
The main object of such reviews is to 
enable the true student to learn easily what 
progress others are making, especially in 
his own field and in those closely related 
thereto. They serve, however, another very 
laudable purpose in the case that they are 
reliable. We have the pretender and the 
unscrupulous always with us, and it is al- 
most as important to limit their field of 
operation as to encourage the true investi- 
gator. ‘‘Companions in zealous research’”’ 
SCIENCE 
[N.S. Vou. XXXV. No. 910 
should be fearless in the pursuit of truth 
and in the disclosure of falsehood, since 
these qualities are essential to the atmos- 
phere which is favorable to research. 
While the mathematical investigator is 
generally so engrossed by the immediate 
objects in view that he seldom finds time to 
think of his services to humanity as a 
whole, yet such thoughts naturally come to 
him more or less frequently, especially 
since his direct objects of research seldom 
are well suited for subjects of general con- 
versation. If these thoughts do come to 
him they should bring with them great 
inspiration. Who can estimate the amount 
of good mathematics has done and is doing 
now? If all knowledge of mathematics 
could suddenly be taken away from us 
there would be a state of chaos, and if all 
those things whose development depended 
upon mathematical principles could be re- 
moved, our lives and thoughts would be 
pauperized immeasurably. This removal 
would sweep away not only our modern 
houses and bridges, our commerce and 
landmarks, but also most of our concepts 
of the physical universe. 
Some may be tempted to say that the 
useful parts of mathematics are very ele- 
mentary and have little contact with mod- 
ern research. In answer we may observe 
that it is very questionable whether the 
ratio of the developed mathematics to that 
which is finding direct application to things 
which relate to material advantages is 
greater now than it was at the time of the 
ancient Greeks. The last two centuries 
have witnessed a wonderful advance in 
the pure mathematics which is commonly 
used.1# While the advance in the extent 
4 Jn 1726, arithmetic and geometry were studied 
during the senior year in Harvard College. Nat- 
ural philosophy and physies were still taught be- 
fore arithmetic and geometry. Cajori, ‘‘The 
Teaching and History of Mathematics in the 
United States,’’ 1890, p. 22. 
