The history of zero

Published Juli 3, 2026 · By NumberWiki

Zero feels obvious — it's the first thing we learn to write, the number of cookies left after you eat them all. But zero is one of the most hard-won ideas in the history of mathematics. Most great civilisations counted for millennia without it. Getting from "there is nothing here" to "nothing is a number you can add, subtract, and calculate with" took thousands of years and several independent inventions.

Two different ideas of zero

It helps to separate two things that we now bundle into one symbol. The first is zero as a placeholder — the mark that tells you 205 is not 25, that there's an empty column in the tens place. The second is zero as a number in its own right — a quantity you can do arithmetic with, that sits on the number line to the left of one. The placeholder came first, by a long way. The number came much later.

The Babylonian gap

The Babylonians, writing in base 60 more than 4,000 years ago, ran straight into the placeholder problem: in a positional system, how do you show that a place is empty? For centuries they just left a gap, which was ambiguous. By around 300 BCE they had introduced a special two-wedge symbol to mark an empty position. It was a genuine placeholder — but never a number. You would never see it standing alone as the answer to a calculation, and the Babylonians had no notion of "nothing" as a quantity you could compute with.

The Maya, an ocean away

Completely independently, the Maya of Mesoamerica developed a true zero for their base-20 calendar system, written as a shell-shaped glyph, by at least the 4th century CE (and quite possibly centuries earlier). It let them write long, precise dates in the Long Count. It's one of the earliest full zeros anywhere — but, isolated in the Americas, it never spread to the rest of the world.

India: zero becomes a number

The decisive step happened in India. By the middle of the first millennium CE, Indian mathematicians were treating zero (Sanskrit śūnya, "empty" or "void") not just as a placeholder but as a number. In 628 CE the astronomer and mathematician Brahmagupta wrote down the first known rules for arithmetic with zero: a number minus itself is zero; zero added to a number leaves it unchanged; zero times anything is zero. He even grappled with the deep trouble that has vexed everyone since — what happens when you divide by zero (a question that still has no sensible answer). This is the moment zero graduates from notation to number.

It was no accident that this happened in India. Indian philosophy was comfortable with concepts of the void and the infinite in a way that made a "number for nothing" feel natural rather than paradoxical.

The journey west

From India the idea travelled through the medieval Islamic world, where scholars such as al-Khwārizmī (whose name gives us "algorithm") adopted the Hindu numerals and their zero. The Arabic word for it, ṣifr ("empty"), travelled into Latin as zephirum and eventually gave English both "zero" and "cipher". Europe was slow to accept it: Roman numerals had no zero and worked fine for recording numbers, and merchants and even some authorities were suspicious of the strange new digit. The tipping point came with Leonardo of Pisa — Fibonacci — whose 1202 Liber Abaci showed European readers how much easier calculation became with the ten Hindu-Arabic digits, zero included. Over the following centuries the new system won out precisely because it made arithmetic on paper possible.

Why zero was resisted

Part of the delay was practical — the old systems worked well enough for their purpose. But part was philosophical. A symbol for nothing unsettled people: how can nothing be something? The same discomfort surrounded the related idea of the void and the infinite. Zero forced a genuinely new way of thinking, and new ways of thinking take time.

Zero today

Modern mathematics can't function without it. Zero is the additive identity — add it to any number and nothing changes. It's the origin of the number line and the hinge between positive and negative. It's the only integer that is neither positive nor negative and neither prime nor composite. And it made place-value notation — and with it modern computation, from long multiplication to the binary that runs every computer — possible. Not bad for a number that means nothing at all.