SEPTEMBER 20, 1918] 
great map of our country—the seats of our 
stronger universities. The spirit of research 
should penetrate many other institutions. 
Young men of ability, now doomed to pass 
their lives with broken wings through the 
erushing weight of excessive hours of teach- 
ing, should find relief in the future and be 
encouraged to accomplish the highest that is 
in them to do. Professor Bjerknes, of Stock- 
holm, when lecturing at Columbia University, 
ventured the statement that had his teaching 
schedule at home been as onerous as is that 
of American professors, then he would never 
have been invited to lecture in America in a 
difficult branch of science. 
To earry the enterprise we are considering 
into successful operation calls for the united 
efforts of three groups of men: The mathema- 
tician, eager to enter arich but difficult field of 
research, the administrator, willing to provide 
the mathematician with the necessary leisure, 
and the philanthropist, ready to supply the 
funds necessary for the publication of the re- 
sults of research. Has America the ideals 
and the genius of organization for the creation 
of such a triumvirate? 
In recent years a new ideal for the history 
of mathematics has arisen. The new move- 
ment calls for a much more careful and com- 
prehensive scrutiny of historical material; it 
demands higher standards of historical ac- 
euracy. This ideal has been championed in 
the Bibliotheca Mathematica, a journal edited 
by Gustav Enestrém, of Stockholm. Accord- 
ing to the standards set by Enestrém, the labors 
of Moritz Cantor, of Heidelberg, especially the 
third volume of his well-known history, hardly 
reach the high mark of excellence demanded. 
Cantor worked diligently and persistently for 
many years until finally failing eyesight 
lessened his powers and, more recently, com- 
pelled him to enter the darkened universe of 
the blind. If his third volume is inferior to 
his first two, an additional cause thereof is 
found in the fact that in the seventeenth and 
eighteenth centuries so many new mathe- 
matical subjects were introduced that the task 
of setting forth their history almost trans- 
cended the powers of a single individual. 
SCIENCE 
283 
Necessity compelled the fourth volume to be 
prepared on the cooperative plan, by a group 
of men. 
The present danger is that, in the effort to 
attain extreme accuracy in historical detail, 
we shall lose sight of literary quality. The 
publications of Huxley and Tyndall have 
demonstrated that scientific writing admits of 
combination with literary finish. The two 
ideals are not incompatible. Good literary 
form challenges attention and provokes ad- 
miration. Macaulay, the great master of 
words, made history enjoyable to thousands 
who otherwise would have shunned historical 
reading. Arago’s biographies of scientific men 
have a charm their own. 
In order to make the history of mathematics 
interesting, it is desirable to consider not only 
literary finish, but also the amplitude of topics 
selected. In writing the mathematical history 
of the ninetenth century, it does not seem to 
me sufficient merely to endeavor to trace the 
line of scientific progress, the evolution of new 
concepts. That much is done by the “ En- 
eyklopiidie” and the “ Encyclopédie,” which 
we hope may be earried to completion soon 
after the termination of the great war. The 
mathematical reader does not subsist on logic 
alone. He is eager for color. He desires to 
know the personality of great mathematicians, 
the environment in which they worked, their 
idiosyneracies, their struggles with scientific 
difficulties, the circuitous route by which they 
reached their results, the influence which 
mathematicians exerted, one upon another. 
The heroism of some scientific men makes a 
tremendous appeal to the reader. These topics 
create not only interest but enthusiasm. In 
fact, if we consult our experience, as well as 
that of others, we are forced to admit that 
the best that we have from history is the 
enhusiasm which it generates. The mathe- 
matician, like the warrior, is a hero worship- 
per. In the case of Archimedes, the reader 
expects the historian not only to state ac- 
curately the connection of the writings of 
Archimedes with those of his predecessors, the 
advances that he made and the relations that 
his writings bear to the modern mathematics, 
