59 
One, famous for his vigorous championship of Christian thought, chose 
a subject in which he used mathematical methods in theological reason- 
ing. The other two, though splendidly equipped in mathematics, pre- 
ferred to present phases of physics. Our program shows six subdivisions 
of science, among which mathematics has always held a secure place, 
but up to the present time no one has had the inclination or the courage 
to attempt to discuss in a popular manner the oldest science and the one 
second to none in its services to mankind and in the zeal with which it is 
to-day cultivated and enlarged. It is, I confess, with misgivings that I 
break this thirteen years’ silence, for the range of the subject has now be- 
come so vast that no one person can longer hope for an intimate acquaint- 
ance with all of it, and any writer must rely more or less on testimony 
for many results and their bearings upon progress. And yet when we 
consider the extent to which the science of mathematics is cultivated 
among educated people, the large part that it plays in all our lives, are 
we not justified in an occasional attempt to call attention to prominent 
facts concerning it as they appear to some of us who have spent fifteen 
years or more in trying to disseminate its truths? 
In the British Association there have been at least three notable pre- 
sentations of the claims of mathematics by three of its most famous 
exponents. One of these is little less than an inspired plea for his loved 
discipline, by one of its prophets; a second shows how higher ranges of the 
subject have been suggested by other sciences; a third is a classic argu- 
ment for the unrestricted development of mathematics along systematic 
lines both for its own sake and for its possible future utility in fields now 
undreamed of. In the American Association there has been a tendency 
to make mathematical lectures more technical and therefore less interest- 
ing to the general public than in the British. One essayist made a not- 
able attempt to explain modern algebra to the uninitiated, a second spoke 
upon the evolution of algebra, while a third gave a historical disquisition 
upon the origin of our methods with imaginaries. <A fourth was an ex- 
ception to these in that he argued for reform in the choice of subjects in 
college curricula and in the manner of presenting them. 
The essential difficulty in discussing a mathematical topic is the fact 
that this science possesses the most highly developed symbolism and an 
almost perfect technical language. Both these attributes condense our 
reasoning to a minimum and make it unintelligible to the uninitiated. In 
trying to popularize, we are in danger of becoming puerile. Most mathe- 
