In considering the services of mathematics from this purely utili- 
tarian point of view we shall find it conyenient to speak of 
GEOMETRY AND ANALYSIS. 
The American people are unusually intelligent, but is it not true that 
no more than one per cent. of them ever have any adequate conception of 
the innumerable ways in which geometry enters into their every-day 
life? 
Houses of all kinds, from the humble cottage to the Manufacturers’ 
Building of the White City, from the backwoods meeting house to the 
vaulted cathedral, first grow on paper under the magic of geometry. 
Bridges and everything that rolls over them, shops and every manufac- 
tured product that comes out of them, grow into being in the same way. 
Only a Michael Angelo can hew out a statue without model or draw- 
ing, but Raphael himself must resort to mathematical perspective for 
depth and sky. Not of Muclid do the towering buildings and the diversi- 
fied industries of a teeming city attest, so much as they do of the French- 
man Monge, upon whose discoveries and researches are based our sys- 
tems of industrial drawing now so rapidly and deservedly gaining ground. 
The time. I believe, is not remote when descriptive geometry in some of 
its phases will find a more open way into the high school and will insist 
on recognition whatever else may suffer. The heart of the shop is the 
draughting room, a room without which the trunk line, the ocean steam- 
ship and a thousand and one things necessary to our complex civilization 
can not exist. 
The educational revolt of a generation ago against fossilized methods 
then widely practiced arose from a conviction that we had outgrown 
monastic institutions. The training suitable for a state of society where 
all education was in the hands of the church and all educated men became 
priests was found to be no longer adequate to the needs of a country 
which was rapidly developing into the most powerful nation on the earth 
through the industry, inventive genius and mechanical skill of its people. 
The learning of the college was laughed to scorn. Then came science 
and elective courses, but this was not enough. Technology was trans- 
planted from Russia and Germany. It took quick root and has had a 
marvelous growth in American soil. 
