Negative Numbers

The need for the concept of negative numbers arose through early accounting methods. They were used by the Hindus and Arabs and came to Western Europe in Arab texts. The Hindus represented negative quantities with a dot. They were not readily accepted by European mathematicians, even in the seventeenth century. For example, Blaise Pascal (1623—1662) commented in his Pensées: ‘I know people who cannot comprehend that if one takes four from zero, zero is left.’ Napier in the early seventeenth century regarded negative numbers as ‘less then nothing’ and as ‘representing a point moving in a direction opposite to positive’. In the eighteenth century the Italian Cardan made use of the modern concept of directed numbers.