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10 THE NATURE OF MATHEMATICS 
CHAPTER I 

THE GROWTH OP MATHEMATICAL SCIENCE IN ANCIENT TIMES 

IN the history of the human race, inventions like those of the 
wheel, the lever, and the wedge were made very early judging 
from the pictures on ancient Egyptian and Assyrian monuments. 
These inventions were made on the basis of an instinctive and 
unreflecting knowledge of the processes of nature, and with the 
sole end of satisfaction of bodily needs. Primitive men had to 
build huts in order to protect themselves against the weather, and, 
for this purpose, had to lift and transport heavy weights, and so 
on. Later, by reflection on such inventions themselves, possibly 
for the purposes of instruction of the younger members of a 
tribe or the newly-joined members of a guild, these isolated 
inventions were classified according to some analogy. Thus we 
see the same elements occurring in the relation of a wheel to its 
axle and the relation of the arm of a lever to its fulcrum the 
same weights at the same distance from the axle or fulcrum, as 
the case may be, exert the same power, and we can thus class 
both instruments together in virtue of an analogy. Here what 
we call " scientific " classification begins. We can well imagine 
that this pursuit of science is attractive in itself; besides 
helping us to communicate facts in a comprehensive, compact, 
and reasonably connected way, it arouses a purely intellectual 
interest. It would be foolish to deny the obvious importance 
to us of our bodily needs; but we must clearly realise two 
things : (1) The intellectual need is very strong, andjs as much 
a fact as hunger or thirst ; sometimes it is even stronger than 
bodily needs Newton, for instance, often forgot to take food 
when he was engaged with his discoveries; (2) Practical 
results of value often follow from the satisfaction of intellectual 
needs. It was the satisfaction of certain intellectual needs in 
the cases of Maxwell and Hertz that ultimately led to wireless 
telegraphy ; it was the satisfaction of some of Faraday's intel- 
lectual needs that made the dynamo and the electric telegraph 
possible. But many of the results of strivings after intellectual 
satisfaction have as yet no obvious bearing on the satisfaction 
of our bodily needs. However, it is impossible to tell whether 
or no they will always be barren in this way. This gives us a