884 
ical Society (1910), Spanish Mathematical 
Society (1911) and the Russian Congress 
of Mathematicians (1912). In Japan a 
new mathematical periodical, called Tohoku 
Mathematical Journal, was started in 1911, 
and a few years earlier the Journal of the 
Indian Mathematical Society was started 
at Madras, India. The Calcutta Mathe- 
matical Society and the Spanish Mathemat- 
ical Society have also started new period- 
icals during the last two or three years. 
While there has been a very rapid spread 
of mathematical activity during recent 
years, it must be admitted that the greater 
part of the work which is being done in the 
new centers is quite elementary from the 
standpoint of research. The city of Paris 
continues to hold its preeminent mathemat- 
ical position among the cities of the world; 
and Germany, France and Italy continue to 
lead all other countries in regard to the 
quality. and the quantity of research in 
pure mathematics. 
Although America is not yet doing her 
share of mathematical research of a high 
order, we have undoubtedly reached a posi- 
tion of respectability along this line, and it 
should be easier to make further progress. 
Moreover, our material facilities are in- 
ereasing relatively more rapidly than those 
of the countries which are ahead of us, and 
hence many of our younger men start under 
very favorable conditions. Unfortunately, 
there is not yet among us a sufficiently high 
appreciation of scholarly attamments and 
scientific distinction. The honest and out- 
spoken investigator is not always encour- 
aged as he ought to be and the best posi- 
tions do not always seek the best man. 
I coupled outspoken with investigator ad- 
visedly, since research of high order im- 
plies liberty and scorns shams, especially 
shams relating to scholarship. Even along 
these lines there seems to be encouraging 
progress, and this progress may reasonably 
SCIENCE 
[N.8. Vou. XXXV. No. 910 
be expected to increase with the passing of 
those who belong to the past in spirit and 
attainments. What appears to be a very 
serious element in our situation is the fact 
that the American university professor 
does not yet seek and safeguard his free- 
dom with the zeal of his European col- 
league. It is too commonly assumed that 
loyalty implies lying. 
The investigators in pure mathematics 
form a small army of about two thousand 
men and a few women.'2 The question 
naturally arises what is this little army 
trying to accomplish. A direct answer is 
that they are trying to find and to con- 
struct paths and roads of thought, which 
connect with or belong to a network of 
thought roads commonly known as mathe- 
matics. Some are engaged in constructing 
trails through what appears an almost im- 
passable region while others are widening 
and smoothing roads which have been 
traveled for centuries. There are others 
who are engaged in driving piles in the 
hope of securing a solid foundation 
through regions where quicksand and mire 
have combined to obstruct progress. 
A characteristic property of mathematics 
is that by means of certain postulates its 
“ Between five and ten per cent. of the members 
of the American Mathematical Society are women, 
but the per cent. of women in the leading foreign 
mathematical societies is much smaller. Less than 
one per cent. of the members of the national 
mathematical societies of France, Germany and 
Spain are women, according to recent lists of 
members. The per cent. of important mathemat- 
ical contributions by women does not appear to 
be larger, as a rule, than that of their representa- 
tion in the leading societies. The list of about 
three hundred collaborators on the great new 
German and French mathematical encyclopedias 
does not seem to include any woman. Possibly 
women do not prize sufficiently intellectual free- 
dom to become good mathematical investigators. 
Some of them exhibit excellent ability as mathe- 
matical students. 
