# The numbers that rule them all

Zero and infinity **cast **long **shadows in** mathematics, making and breaking equations. But these strange beasts can also explain what numbers really are

**Zero**

The number that’s not a number

YOU could be forgiven for thinking that zero is not a proper number. After all, numbers are the things we use to count, and you can’t count nothing.

We have evidence for counting going back five **millennia**, but the history of zero only began with the Babylonians in about 1800 BC. Even then, it was not a fully fledged number. The point of zero for them was like the zero in our modern representation of a number like 3601 – it’s a position-setting symbol that distinguishes the number from 361.

The Babylonians’ symbol was two **diagonal** arrows; the familiar squashed egg shape only came into being around AD 800, still as an accounting symbol. It was the work of Indian mathematicians that sparked the **genesis** of zero as a number, when they first appreciated that numbers can have an abstract existence distinct from counting physical objects. The astronomer Brahmagupta, for example, **laid out** a number line that included positive and negative numbers and zero.

This line of thought wasn’t embraced in the West until much later, partly because zero was considered a gateway to the negative numbers, where debt and **fraud** lay. By the late 19th century, however, mathematicians had become interested in establishing rules of mathematical logic. When the Italian mathematician Giuseppe Peano set out a list of rules for **arithmetic**, his first **axiom** insisted that zero must be a number.