The Origin of the Number Zero

Deep in the jungle, an intrepid scholar locates a symbol of power and mystery

This inscription, written in Old Khmer, reads “The Caka era reached year 605 on the fifth day of the waning moon.” The dot (at right) is now recognized as the oldest known version of our zero. Amir Aczel

Four miles from the great temple of Angkor Wat, deep in the Cambodian jungle, I opened the door of a makeshift shed with a corrugated tin roof and walked into a dusty room painted in pale gray. Thousands of chunks and slabs of stone covered the dirt floor: smashed heads of statues of Khmer kings and Hindu gods, broken lintels and door frames from abandoned temples, the remains of steles with ancient writing. After years of searching, I’d finally arrived here, hoping to find a single dot chiseled into a reddish stone, a humble mark of incredible importance, a symbol that would become the very foundation of our number system—our first zero. 

It was a lifelong love that led me to this threshold. I grew up on a cruise ship in the Mediterranean that often called at Monte Carlo, and I was drawn to the alluring numbers on roulette wheels: half of them red, half black. My fascination led to a career as a mathematician, and, dabbling in mathematical archaeology, I’ve tracked down many ancient numerals, including a magic square (those mysterious numerical grids in which the sum of every column, row and diagonal is the same) on the doorway of a tenth-century Jain temple at Khajuraho, India. 

I’m convinced that the creation of numerals to represent the abstract entities we call numbers was our greatest intellectual achievement. The simple sign “3” represents all trios in the universe; it is the quality of “being three”—distinct from “being five” or “being seven.” Numerals allow us to keep track of belongings, record dates, trade goods, calculate so precisely that we are able to fly to the moon and operate on the brain.

We use them with such ease that we take them for granted. Surprisingly, our number system took hold in the West only in the 13th century, after the Italian mathematician Leonardo of Pisa—better known as Fibonacci—introduced the numerals to Europeans. He’d learned them from Arab traders, who presumably adopted them during travels to the Indian subcontinent.

Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers

The invention of numerals is perhaps the greatest abstraction the human mind has ever created. Virtually everything in our lives is digital, numerical, or quantified. The story of how and where we got these numerals, which we so depend on, has for thousands of years been shrouded in mystery. "Finding Zero" is an adventure filled saga of Amir Aczel’s lifelong obsession: to find the original sources of our numerals.

Of all the numerals, “0”—alone in green on the roulette wheel—is most significant. Unique in representing absolute nothingness, its role as a placeholder gives our number system its power. It enables the numerals to cycle, acquiring different meanings in different locations (compare 3,000,000 and 30). With the exception of the Mayan system, whose zero glyph never left the Americas, ours is the only one known to have a numeral for zero. Babylonians had a mark for nothingness, say some accounts, but treated it primarily as punctuation. Romans and Egyptians had no such numeral either.

A circle inscribed at a temple in Gwalior, India, dating to the ninth century, had been widely considered the oldest version of zero in our system, the Hindu-Arabic. At the time it was made, trade with the Arab empire connected East and West, so it could have come from anywhere. I was after an older zero, a particular instance arguing for an Eastern origin.

Found on a stone stele, it was documented in 1931 by a French scholar named George Coedès. Assigned the identifying label K-127, the inscription reads like a bill of sale and includes references to slaves, five pairs of oxen and sacks of white rice. Though some of the writing wasn’t deciphered, the inscription clearly bore the date 605 in an ancient calendar that began in the year A.D. 78. Its date was thus A.D. 683. Two centuries older than the one at Gwalior, it predated wide-ranging Arab trade. But K-127 disappeared during the Khmer Rouge’s rule of terror, when more than 10,000 artifacts were deliberately destroyed. 

I describe my obsession with finding this earliest zero in my forthcoming book, Finding Zero. I spent countless hours poring over old texts in libraries from London to Delhi and emailing and calling anyone who might know someone who could help me locate K-127. I made several unsuccessful trips to Cambodia, spending a significant amount of my own money. On the verge of giving up, I received a grant from the Alfred P. Sloan Foundation and forged ahead. Cambodia’s director general of the Ministry of Culture and Fine Arts, Hab Touch, directed me to the sheds at Angkor Conservation, a restoration and storage site closed to the public. When I was turned away twice, Touch graciously made a phone call, and in early January 2013, I was invited in. I still didn’t know if K-127 had even survived. 

And yet, within two hours, the roulette wheel had spun in my favor. My eye caught a piece of tape with a pencil-scribbled “K-127,” and then I recognized that single dot on the 3- by 5-foot slab, intact but for a rough break at the top. I was elated. I dared not touch the stone surface for fear I might harm it.

Since that fortuitous moment, I’ve pondered the feat that brought us numerals, this time wondering not where and when, but how? I’ve asked dozens of mathematicians a long-debated question: Were numbers discovered or invented? The majority view is that numbers exist outside of the human mind. Unlike Beethoven’s Symphony No. 9, they don’t require a human creator. What gave numbers their power was the very act of naming them and writing them down. I’m now working with Cambodian officials to move K-127 to a museum in Phnom Penh, where a wide audience can appreciate the incredible discovery it represents. 

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