Why did it take so long to invent the number zero?

Answer

Dear Saujan,

It is actually not correct to say that it took thousands of years “to find the number zero”. The earliest mathematical civilization was that of the Babylonians and they already knew zero. Their earliest mathematical tablets date back to 1600 BC. Perhaps we should first distinguish between zero as a digit in a positional number system and zero as a quantity (number). The Babylonians had a positional number system much like ours but with base 60 instead of 10. They implicitly used a zero at the end of a unit, only they had no symbol for it. It was an empty place. But they also recognized zero as a quantity. On three tablets there is a subtraction with zero as a result. They gave it the name ma-ti which means something like ‘unknown’.

The Egyptians had no positional number system, so there was no need for a symbol for zero. However, according to recent studies, they did have a notion of a null quantity dating back to 1770 BC. They used the sign for nfr which means ‘good’, ‘complete’ or ‘beautiful’.

The civilization that had the most complete concept of zero as a number was the Indian and especially the Jaina tradition (from 200 BC to 400). Our symbol for zero ultimately comes from Sanskrit. Around 800 they used the symbol for zero that we would now recognize as zero. It is believed that the Chinese and Arabic use of zero comes from the Indian tradition.

Not all use of zero is derived from Indian mathematics. In all likelihood, zero was invented in multiple civilizations. A good example is the Maya civilization which also had a positional number system and a symbol for zero.

A good introduction to the cultural diversity of mathematics is the book “The Crest of the Peacock” by GG Joseph published in 1991.