The beginning of arithmetic is formed by language, & the arithmetical ideas of savages & young children. The names & grammar of numbers show that primitive man could only count – one, two, many; but that in quite recent times he learned to count up to ten on his fingers, – the names of higher numbers being artificial & much more recent.

Place value has arisen in some savage tribes, by a combination of 2 or 3 men counting on their fingers. As people became more civilized the magnitude of numbers which could be realised increased. Children’s exaggeration of numbers often indicates a lack of comprehension of large numbers. Records of numbers began with pebbles, which led to the use of the abacus.

Most early written arithmetic is very cumbersome, the Egyptians understood simple fractions, & could solve simple problems, but for more than 1,000 years made no advance. Babylonian arithmetic has left traces in our methods of dividing time, & dividing angles. The arithmetic of the Greeks was not equal to their geometry. They developed the theory of numbers to which they attributed mystical meanings, but did little pure arithmetic. Their notation was an improvement on the Egyptian & Roman, but was still cumberous. During the Middle Ages arithmetic was purely commercial & was performed by means of the counting-board. Adelard of Bath (1120) introduced Arabic arithmetic which was derived from Greek & Hindu. The Hindu’s had invented the zero symbol & with the hep of this developed our modern notation. This was introduced into Europe after much opposition & then arithmetic advanced rapidly; the most important discovery being that of Decimal Fractions by Stevin in 1585. In later times higher Algebra, & other branches of mathematics have developed from arithmetic.

Primitive people regarded the results of arithmetic with awe, since they did not understand them. Hence the mystical & superstitious ideas connected with numbers.

Many modern people wish to adopt the Decimal System, the advantage being the ease of calculation, & conformity with other nations. The ideal system is the Duodecimal, but as we only possess small fragments of this, & to introduce it would require a revolution of natation & Nomenclature, we fell back on the Decimal System