Imagine yourself in a bustling Babylonian marketplace around 400 BCE. You’re a fish merchant tallying the day’s trades on a clay tablet. Twenty-four fish for some grain? No problem! You press your wedge-shaped stylus into the soft clay: 𒌋𒌋𒌋𒌋 (that’s 24).
But wait, what about recording 204 fish? Without a symbol for “nothing,” you’d write the same marks for 2 and 4, with nothing in between. How would anyone know if that’s twenty-four or two-hundred-and-four? Did you just lose 180 fish in your accounting?
This was a real headache for ancient record-keepers. The Babylonians, who counted in base-60 (which, fun fact, is why we have 60 seconds in a minute and 60 minutes in an hour), eventually developed a solution. Around 400 BCE, they began using two tiny angled wedges to indicate “nothing here” in their number system. It wasn’t zero as we know it, just a placeholder that meant “empty spot.” You couldn’t add it, subtract it, or do anything mathematical with it. Truly, just nothing.
Meanwhile, across the ocean, the Maya were having similar thoughts. By 36 BCE, monuments at Chiapa de Corzo and Tres Zapotes displayed a stylized shell symbol that meant “completed cycle” in their complex calendar system. It’s the earliest known zero symbol in the Americas, used in their base-20 positional system. Apparently, the concept of “nothing” was something multiple civilizations needed to figure out independently.
From Placeholder to Actual Number
Let’s fast-forward a few centuries and travel to India, where zero’s story gets really interesting.
Picture this: It’s the 3rd century CE, and an Indian mathematician is working on a birch-bark manuscript, using dots to mark empty places in calculations. This is the famous Bakhshali manuscript, which radiocarbon dating has shown is much older than we once thought. These dots weren’t just placeholders anymore, they were evolving into something more.
By 628 CE, a mathematician named Brahmagupta took a revolutionary step. In his work Brahmasphuṭasiddhānta (try saying that five times fast), he defined zero as an actual number and wrote rules for using it in calculations:
- When you add zero to a number, you get the same number (a + 0 = a)
- When you multiply a number by zero, you get zero (a × 0 = 0)
This might seem obvious to us today, but back then, it was mind-blowing. Brahmagupta was also working with negative numbers at the same time, imagine figuring out both zero AND negative numbers. Insane.
By 876 CE, zero had earned enough respect to be carved in stone. At the Chaturbhuj Temple in Gwalior, India, an inscription contains the numbers 270 and 50 with round zeros that look remarkably like our modern 0. This is the oldest known stone carving of the circular zero we recognize today.
Zero’s Journey West
Zero might have remained an Eastern mathematical concept if not for cultural exchanges along trade routes. Arabic scholars encountered Indian mathematics and recognized its brilliance. Around 825 CE, a Persian mathematician named Al-Khwarizmi wrote a book explaining Hindu positional arithmetic, including zero, to the Islamic world. His name, when Latinized, gave us the word “algorithm.” Talk about a lasting legacy.
Then along came Leonardo of Pisa, better known as Fibonacci (yes, the sequence guy), who published his book Liber Abaci in 1202. After learning Arabic numerals during his travels in North Africa, Fibonacci became Europe’s most enthusiastic zero evangelist. His book showed European merchants how much easier calculation could be with this new number system.
But Europe wasn’t immediately convinced. In fact, in 1299, Florence’s guild statutes banned Arabic numerals in accounting ledgers. Why? They feared fraud. A zero could too easily be changed to a 6 or a 9, they argued. Padua went even further and outlawed zero altogether. Quite backwards to think about it now.
Of course, pragmatic merchants quickly realized the benefits of this efficient system. Many kept two sets of books, one with Roman numerals to satisfy regulations, and another with Arabic numerals to actually get work done. Eventually, the practical advantages of zero and its numerical companions became impossible to ignore, and Europe finally embraced what India had known for centuries.
Zero Gets Infinitely Small
Zero’s next big breakthrough came in the 17th century, when mathematics took a giant leap forward with the invention of calculus. Both Isaac Newton and Gottfried Wilhelm Leibniz (working independently) faced a fascinating problem: how do you calculate the exact rate of change at a specific instant?
Imagine you’re tracking a falling apple. You can easily calculate its average speed over one second, but what about its exact speed at the 0.5-second mark? This is where zero became truly transformative.
Newton and Leibniz developed the concept of infinitesimals, quantities that could become arbitrarily small, approaching zero without ever quite reaching it. Newton called them “fluxions” and described them as “vanishing quantities.” You keep dividing a time interval into smaller and smaller pieces, getting closer and closer to zero, but never quite getting there.
This brain puzzle with zero led to the derivative, a way to find instantaneous rates of change, and the integral, which adds up infinitely many infinitesimal pieces. Both relied on a radical idea: we can work with quantities that are not quite zero, but so close to zero that they’re smaller than any number you can name.
The concept was controversial. Bishop Berkeley famously mocked these “ghosts of departed quantities” as logically incoherent. How could something be so small it’s practically zero, but still not zero? It seemed like mathematical sleight of hand.
It wasn’t until the 19th century that mathematicians like Cauchy and Weierstrass formalized these ideas with the concept of limits, a rigorous way of describing what happens as quantities approach zero. The expression “approaching zero” became precise: for any small positive number you choose, I can make my quantity smaller than that.
This breakthrough unleashed a wave of scientific advances. Without the ability to calculate with near-zero quantities, we couldn’t have developed modern physics, engineering, or most of our technological world. From modeling planetary orbits to designing airplane wings to calculating electron behavior, calculus, and its intricate relationship with zero, became the language of nature itself.
From Empty Space to Digital Age
Zero’s final transformation came in the 20th century. In 1948, Claude Shannon published “A Mathematical Theory of Communication,” coining the term “bit” (binary digit) as the basic unit of information, explicitly a choice between 0 and 1. Every text message you send, every movie you stream, every article you read online (including this one!) is ultimately encoded as strings of zeros and ones. Zero had completed its journey from “nothing” to half of everything.
So there you have it, the remarkable journey of zero. It began as a humble placeholder for empty spaces in Babylonian accounting, became a proper number thanks to Indian mathematicians, traveled westward on Arabic parchment, overcame European resistance, revolutionized calculus by becoming infinitely small, and eventually became a cornerstone of both higher mathematics and digital technology.
Not bad for something that represents nothing!
Further Reading:
- Kaplan, Robert. The Nothing That Is: A Natural History of Zero
- Ifrah, Georges. The Universal History of Numbers
- Aczel, Amir D. Finding Zero: A Mathematician’s Odyssey to Uncover the Origins of Numbers
- Seife, Charles. Zero: The Biography of a Dangerous Idea