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.