124 ANNUAL REPORT SMITHSONIAN INSTITUTION, 1909. 
become an incumbrance and their increase produce an accumulation 
as incomprehensible as all the unknown truth is to the ignorant. 
The historian, the physicist himself, must make his selection from 
among the facts; the brain of the scholar—but a small corner of the 
universe—could never contain this entire universe; so among the 
countless facts which nature presents, some must be passed by, others 
retained. It is as true, a fortiori, in mathematics for neither may 
the mathematician himself gather pellmell all the facts which come 
before him. Rather it is he—I was going to say his caprice—which 
creates them. It is he who constructs from the facts a new combina- 
tion. Nature does not in general bring this to him ready-made. 
Doubtless it happens sometimes that the mathematician ap- 
proaches a problem set by the needs of physics, as when the physicist 
or the engineer asks of him the calculation of some number in view 
of an application. Shall we say, we mathematicians, that we must 
content ourselves to await these commands and, instead of cultivating 
our science for our pleasure, to have no other care than accommodat- 
ing ourselves to the tastes of our clients? If there were no other ob- 
jects for mathematicians than to come to the aid of those who are 
studying nature it would be from them then that we must await the 
word of command. Yet is this the right point of view? Certainly 
not; if we had not cultivated the exact sciences for themselves our 
mathematical machine would not have been created, and on the day 
when the word of command came from the physicist we would have 
been without arms. 
Nor do the physicists, before studying some phenomenon, wait 
until some urgent need of life has made the study a necessity, and 
they are right; had the scientists of the eighteenth century neglected 
the study of electricity because in their eyes it was but a curiosity 
of no practical interest we would not have in the twentieth century 
either the telegraph, or electro-chemistry, or our electrical machinery. 
The physicist, when forced to choose, is not guided in his selection 
solely by utility. What brings about then his selection from among 
the facts of nature? We can not easily say. The phenomena which 
interest him are those which may lead to the discovery of some 
law. Those facts interest him which bear some analogy to many 
other phenomena, which do not appear as isolated facts but closely 
grouped with others. An isolated fact can be observed by all eyes; 
by those of the ordinary person as well as of the wise. But it is the 
true physicist alone who may see the bond which unites several facts 
among which the relationship is important though obscure. The 
story of Newton’s apple is probably not true, but it is symbolical; so 
let us think of it as true. Well, we must believe that many before 
Newton had seen apples fall, but they made no deduction. Facts are 
sterile until there are minds capable of choosing between them and 
