JUNE 7, 1912] 
appeal to a large number of mathematical 
intellects of the present or of the future. 
Some isolated facts may be of great in- 
terest, but as long as they are isolated they 
have little or no real mathematical interest. 
One object of mathematics is to enable us 
to deal with infinite sets with the same ease 
and confidence as if they were individuals. 
In this way only can our finite mind treat 
systematically some of the infinite sets of 
objects of mathematical thought. 
In comparatively recent years the spirit 
of organization has made itself felt among 
mathematicians with rapidly increasing 
power, and it has already led to many 
important results. Beginning with small 
informal organizations in which the social 
element was often most prominent, there 
have resulted large societies, national and 
even international, with formal organiza- 
tions and with extensive publications. In 
reference to one of these early organiza- 
tions, the mathematical society of Spital- 
fields in London, which lasted for more 
than a century (1717-1845), it is said that 
each member was expected to come to the 
meetings with his pipe, his mug and his 
problem. 
The modern mathematical society is dom- 
inated by a different spirit. It generally 
supports at least one organ for publication, 
and scholarly publicity develops scholarly 
cooperation as well as scholarly ambitions. 
This cooperation has led to movements 
which could not have been undertaken by a 
few individuals. One may recall here the 
Revue Semestrielle, published under the 
auspices of the Amsterdam Mathematical 
Society ; the extensive movement to examine 
and compare methods and courses of mathe- 
matical instruction in various countries, 
u<<Hs wurde von jedem erwartet, dass er seine 
Pfeife, seinen Krug und sein Problem mitbringe.’’ 
Cantor, ‘‘ Vorlesungen ueber Geschichte der Math- 
ematik,’’ Vol. 4, 1908, p. 59. 
SCIENCE 
883 
inaugurated at the fourth international 
congress, held at Rome in 1908; and, espe- 
cially the great mathematical encyclopedias 
whose start was largely influenced by the 
support of the deutschen Mathematiker- 
Vereinigung as expressed at the Vienna 
meeting in 1894, The French edition of 
the latter work, which is now in the course 
of publication, is expected to include 
thirty-four large volumes, besides those 
which are to be devoted to questions of the 
philosophy, the teaching and the history of 
mathematics. 
These encyclopedias and other large 
works of reference are doing much to ex- 
pedite travel in the mathematical field. In 
fact, it would probably not be exaggerating 
if we should say that by these encyclo- 
pedias alone the distances, in time and 
effort, between many points of the mathe- 
matical field have been cut in two. In this 
connection, it may be fitting to recall, with 
a deep sense of obligation, the great work 
which is being done by the Royal Society 
of London—not only for mathematics, but 
also for a large number of other sciences— 
in providing bibliographical aids on a large 
scale. If the increase in knowledge will 
always be attended by a corresponding in- 
crease in means to learn readily what is 
known, even the young investigator of the 
future will have no reason to regret the 
extent of the developments. On the con- 
trary, these should make his task easier, 
since they furnish such a great richness of 
analogies and of tried methods of attack. 
The last two or three decades have wit- 
nessed a great extension of mathematical 
research activity. As a result of this we 
have a large number of new mathematical 
societies. A few of the most recent ones 
are as follows: Calcutta Mathematical So- 
ciety (1908), Manchester Mathematical So- 
ciety (1908), Scandinavian Congress of 
Mathematicians (1909), Swiss Mathemat- 
