The Concepts of Zero and Negative Numbers in Math

(Taken from excerpts of Five Ways Ancient India Changed the World – with Maths by Christian Yates)

Zero has a history that goes back a very long time, possibly as early as 3000-2000 BC in Sumerian math.  These are recorded in the Bakshali manuscript and were placeholders, a tool used to distinguish 100 from 10. 

It was only in India that the placeholder symbol for nothing, or zero, progressed to become its own actual number.  The concept of zero allowed numbers to be written efficiently and reliably.  There was a strong and open scholastic and scientific culture around 600 AD, so all the ingredients were in place for an explosion of mathematical discoveries in India. In comparison, these sorts of tools were not popularised in the West until the early 13th century.

In the seventh century, in India, Brahmagupta also demonstrated rules for working with negative numbers. He referred to positive numbers as fortunes and negative numbers as debts. He wrote down rules that have been interpreted by translators as: “A fortune subtracted from zero is a debt,” and “a debt subtracted from zero is a fortune”.

This latter statement is the same as the rule we learn in school, that if you subtract a negative number, it is the same as adding a positive number. Brahmagupta also knew that “The product of a debt and a fortune is a debt” – a positive number multiplied by a negative is a negative

For the large part, European mathematicians were reluctant to accept negative numbers as meaningful, and held them back in math for many years. Many took the view that negative numbers were absurd. They reasoned that numbers were developed for counting and questioned what you could count with negative numbers. Indian and Chinese mathematicians recognised early on that one answer to this question was debts.  Later, Leibniz, did use zero and negatives in his development of Calculus.

The leap, made in India, that transformed zero from a simple placeholder to a number in its own right indicates the mathematically enlightened culture that was flourishing on the subcontinent at a time when Europe was stuck in the dark ages. Although its reputation suffers from the Eurocentric bias, the subcontinent has a strong mathematical heritage, which it continues into the 21st century by providing key players at the forefront of every branch of mathematics.