lthmath: Negative numbers were long denied legitimacy in mathematics. We have no evidence of negativ
lthmath: Negative numbers were long denied legitimacy in mathematics. We have no evidence of negative numbers being recognised in Babylonian, Pharaonic, ancient Greek, or any other ancient civilization. On the contrary, the Greeks considered geometry the only acceptable form of mathematics and since distance cannot be negative, they had no use for negative numbers. In the 7th century, negative numbers were used in bookkeeping in India; positive quantities denoted assets, negative ones debts. The Hindu astronomer Brahmagupta, in a chapter dealing with mathematics in his work on astronomy from about A.D. 630, shows a clear understanding of negative numbers. The earliest documented evidence of the use of negative numbers in European mathematics is the “Arts Magna”, published in 1545 by the Italian mathematician Girolamo Cardano. In the early 17th century, mathematicians began explicitly to use “negative numbers” but met with heavy opposition. Descartes called negative roots “false roots”, and Pascal was convinced that numbers “less than zero” could not exist. Leibniz admitted that negative numbers could lead to absurd conclusions and misconceptions, but defended them as useful aids in calculations. The general acceptance and algebraic use of negative numbers came during the 18th century, although there were still mathematicians who did not feel at home with them and quite often tried to avoid using them. -- source link