The chemist often pursues his investigations into the constitution of 
matter without any thought of any possible utility in his results. He- 
pursues the science for the sake of science, that Man may grow in knowl- 
edge whether or not he can turn that knowledge to practical account in 
the manufacture of steel or the dyeing of silk or the synthesis of nitro- 
genous compounds. 
Yet not seldom in his case, as in the history of pure mathematics, has 
it transpired that a truth sought for truth’s sake has become the neces- 
sary foundation for splendid material achievement. One need but recall 
the labors of an Archimedes or a Newton to note how a searcher for 
higher mathematical truth for its own sake may become an epoch-maker 
in human progress. 
It is not my purpose, however, to dwell upon this part of my subject, 
and I conclude with two quotations from Sylvester. In recommending 
the high living of the mathematician and nature’s provision for his evolu- 
tion he says: “The mathematician lives long and lives young: the wings 
of his soul do not early drop off, nor do his pores become clogged with 
the earthy particles blown from the dusty highways of vulgar life.’ And 
again: “Space is the Grand Continuum from which, as from an inex- 
haustible reservoir, all the fertilizing ideas of modern analysis are de- 
rived, and as Brindley, the engineer, once allowed before a parliamentary 
committee that, in his opinion, rivers were made to feed navigable canals, 
I feel almost tempted to say that one principal reason for the existence of 
space, or at least one principal function which it discharges, is that of 
feeding mathematical invention.” 
-assing, then, with this cursory mention, a theme so inspiring and 
fruitful as the consideration of mathematics from the ground of discipline 
and culture, let us confine our attention to the question of utility alone. 
What has mathematics done that it should commend itself to the great, 
struggling masses of humanity who are busily engaged in adding to the 
surplus products of the race, who are breaking the virgin sod or swing- 
ing the artisan’s hammer or directing the world’s exchanges? Has mathe- 
matics any right to stand with physics, chemistry, botany, zodlogy, geol- 
ogy, whose cultivation has revolutionized civilized life? 
Can a science which begins with assumptions never in perfect accord 
with fact and which ends with conclusions impossible of exact applica- 
tion ever get its feet on the ground sufficiently to secure a leverage for 
pushing along the car of progress? 
