The number **zero **was first used by the Babylonians in the second millennium BC, before being reinvented by the Mayans and then by the Hindus. But it is the Arabs who will integrate it into their numbering system, to distribute it throughout Europe during the tenth century. Quickly indispensable in mathematics, it will even take on a mystical dimension ...

## The origins of the number zero

Indispensable tool of modern numeration, the **zero **however appeared much later than the other figures. Only three peoples invented it, independently of each other: the **babylonians **first, around 2000 BC, then the **Mayas**, in the third century, and finally the Hindus around the fifth century. What do these peoples have in common? The position number system, which cannot do without a sign indicating an absence.

In addition, if the Greeks appreciated it for astronomy (it would be the symbol of the celestial vault) it is the Indian mathematicians who knew how to exploit the zero as a number but also as an operator.

## Forms and diffusion

The zero did not always have the round shape we know it today: the Mayans used an oval sign in which an arch was inscribed. The Indians alternately described a point or a circle, this last sign having then been taken up by the Arabs who transmitted it to Europeans in the tenth century, along with other numbers. The adoption of the Indian decimal system including zero would greatly facilitate classical arithmetic operations (addition, subtraction, multiplication, division ...). This powerful tool, which for a long time remained confined within the borders of the Indian subcontinent, was to have an international destiny thanks to the circulation of Arabic works of calculation, in particular in Europe from the 12th century. It will revolutionize the history of mathematics.

## A number both empty and infinite

The number 0 of course signifies absence, but it also serves as a point of reference; thus, he arbitrarily fixes the melting point of ice, but also the starting point in geometry. It was not until the beginning of the 20th century that zero was given the status of **number**, with some funny quirks though: it's the only number equal to its opposite, both positive and negative, neutral when added to another number, and absorbing in multiplication. But the most intriguing is its use in the divisions: initially not tolerated because having no meaning, the division by zero allows in modern mathematics to reach infinity. No more no less ! Zero, symbol of both everything and nothing, a true sun filled with energy, is sometimes even considered to be the expression of the divine ...

### For further

*- The great math novel: from prehistory to the present day, by Mickaël Launay. Donot, 2016.*

*- A History of Mathematics: Roads and Mazes, by Amy Dahan-Dalmédico. Point Sciences, 1986.*