The Invention of Nothing

Zero seems obvious now, but it was a radical idea. The Romans had no symbol for nothing at all — try doing long division with X, V, and I. Zero as a written digit grew up in India in the 5th century, then traveled to Europe through Arab mathematicians, and it quietly rebuilt the way the world does arithmetic.

Zero does two very different jobs. As a placeholder, the 0 in 502 tells you there are no tens, so the 5 and the 2 land in the right columns. As a number in its own right, it is the additive identity: any number plus zero stays exactly the same. Both ideas sound simple, yet most ancient cultures never made either leap.