XV 
DARWINISM APPLIED TO MAN 
4G5 
When we turn to the more civilised races, we find the 
use of numbers and the art of counting greatly extended. 
Even the Tongas of the South Sea islands are said to have 
been able to count as high as 100,000. But mere count¬ 
ing does not imply either the possession or the use of any¬ 
thing that can be really called the mathematical faculty, the 
exercise of which in any broad sense has only been possible 
since the introduction of the decimal notation. The Greeks, 
the Romans, the Egyptians, the Jews, and the Chinese had 
all such cumbrous systems, that anything like a science of 
arithmetic, beyond very simple operations, was impossible; 
and the Roman system, by which the year 1888 would be written 
MDCCCLXXXVIII, was that in common use in Europe down 
to the fourteenth or fifteenth centuries, and even much later in 
some places. Algebra, which was invented by the Hindoos, from 
whom also came the decimal notation, was not introduced into 
Europe till the thirteenth century, although the Greeks had some 
acquaintance with it; and it reached Western Europe from Italy 
only in the sixteenth century. 1 It was, no doubt, owing to the 
absence of a sound system of numeration that the mathematical 
talent of the Greeks was directed chiefly to geometry, in which 
science Euclid, Archimedes, and others made such brilliant dis¬ 
coveries. It is, however, during the last three centuries only that 
the civilised world appears to have become conscious of the 
possession of a marvellous faculty which, when supplied with 
the necessary tools in the decimal notation, the elements of 
algebra and geometry, and the power of rapidly communicating 
discoveries and ideas by the art of printing, has developed to 
an extent, the full grandeur of which can be appreciated only 
by those who have devoted some time (even if unsuccessfully) 
to the study. 
The facts now set forth as to the almost total absence of 
mathematical faculty in savages and its wonderful development 
in quite recent times, are exceedingly suggestive, and in regard 
required. But this does not alter the general fact that many low races, 
including the Australians, have no words for high numbers and never require 
to use them. If they are now, with a little practice, able to count much 
higher, this indicates the possession of a faculty which could not have been 
developed under the law of utility only, since the absence of words for such 
high numbers shows that they were neither used nor required. 
1 Article Arithmetic in Eng. Cyc. of Arts and Sciences. 
