"Accountants eventually became comfortable with using negative numbers... but for a long time mathematicians remained wary... the negatives were known as absurd numbers—numeri absurdi...Consider this equation:\frac{-1}{\quad 1} = \frac{\quad 1}{-1}...it states that the ratio of a smaller number, -1, to a larger number, 1, is equal to the ratio of a larger number, 1, to a smaller one, -1. The paradox was much discussed... To make sense of negative numbers, many mathematicians, including Leonhard Euler, came to the bizarre conclusion that they were larger than infinity. ...One voice of clarity among the confusion belonged to... John Wallis, who devised a powerful visual interpretation for the negative numbers. In his 1685 work A Treatise of Algebra, he first described the ","... By replacing the idea of quantity with the idea of position, Wallis argued that negative numbers were neither "Unuseful [nor] Absurd,"...It took a few years for Wallis' idea to hit the mainstream, but... it is the most successful explicatory diagram of all time."