Multiple civilizations independently developed place value systems and the concept of zero, but Indian mathematicians were the first to combine both into a single, fully functional number system. The Babylonians created a place value system around 2000 BCE, the Maya independently developed zero by at least 31 BCE, and Indian scholars brought all the pieces together by defining zero as both a placeholder and a number you could calculate with. That Indian system is the direct ancestor of the one you use today.
Babylonians: Place Value Without Zero
The earliest known place value system emerged in Mesopotamia (modern-day Iraq) around 2000 BCE. The Babylonians used a base-60 system with just two wedge-shaped symbols: one for 1 and one for 10. They combined these to write any number from 1 to 59, then used position to express larger values. The same symbol for “1” could mean 1, 60, 3,600, or even 216,000, depending on where it appeared in a sequence, exactly the way a “3” in our system can mean 3, 30, or 3,000.
The critical weakness was that for most of their history, the Babylonians had no symbol for zero. A gap was sometimes left between groups of symbols to indicate an empty position, but this was inconsistent and easy to misread. A placeholder symbol did eventually appear on tablets from the Seleucid period (around 300 BCE), but it was a late addition and never evolved into a number that could be used in calculations. Most recovered tablets date from either the time of Hammurabi (around 1800 BCE) or the Seleucid dynasty, and scholars still struggle to determine the intended value of numbers on older tablets because of the missing placeholder.
The Maya: An Independent Zero
Across the Atlantic, the Maya civilization developed a base-20 (vigesimal) number system complete with a true zero symbol. The oldest known Mesoamerican zero dates to 31 BCE, carved into Stela C at the Olmec site of Tres Zapotes in Veracruz, Mexico. In Maya writing, zero took several forms: a shell, a flower, a seed, or a stylized human head in profile. It functioned as a well-defined concept within their positional system and was essential to their sophisticated astronomical calendars.
Because the Maya mathematical tradition developed in isolation from Eurasian civilizations, their zero had no influence on the number system that eventually spread worldwide. It stands as remarkable evidence that the idea of zero arose independently more than once in human history.
India: Where Zero Became a Number
Indian mathematicians made the leap that changed everything. Rather than simply using zero as a placeholder (a way to distinguish 305 from 35), they treated it as a number in its own right, with defined rules for how it behaves in arithmetic.
The earliest physical evidence of the zero symbol we use today comes from the Bakhshali manuscript, an ancient Indian mathematical text held at Oxford’s Bodleian Libraries. Radiocarbon dating commissioned by the University of Oxford revealed that portions of the manuscript date to the 3rd or 4th century CE, roughly five centuries older than scholars had previously believed. The zero appears throughout the text as a dot, and that dot is the direct ancestor of our modern “0.” Before this dating, the oldest confirmed zero in India was a circular symbol inscribed in 876 CE on a plaque at the Chaturbhuj Temple in Gwalior Fort, where it appears in the numbers 270 and 50 as part of land grants.
The mathematician who formalized zero’s arithmetic rules was Brahmagupta, writing in 628 CE in his treatise the Brahmasphutasiddhanta. He laid out specific rules: subtracting zero from a positive number leaves it unchanged, subtracting a positive number from zero produces a negative number (he used the terms “fortune” and “debt”), and zero minus zero equals zero. He also tackled multiplication and division involving zero, getting most of it right. His one error, stating that zero divided by zero equals zero, is a problem mathematicians would wrestle with for centuries. But the essential achievement was treating zero as a quantity that participates in equations, not just an empty space between digits.
How the System Reached the Arab World
Indian numerals didn’t travel directly to Europe. They first passed through the Islamic world, where scholars recognized their power. As early as 662 CE, a Nestorian bishop named Severus Sebokht, living on the Euphrates River, wrote admiringly of Indian computation “done by means of nine signs,” arguing that Greek-speaking scholars who thought they had reached the limits of knowledge should read Indian texts.
By 776 CE, the transmission became more formal. According to a later chronicle, an Indian scholar appeared before the Caliph al-Mansur in Baghdad with an astronomical text, most likely Brahmagupta’s Brahmasphutasiddhanta. The Caliph ordered it translated into Arabic. From that point forward, Arab scholars had access to the full Indian number system. The Persian mathematician al-Khwarizmi (around 780 to 850 CE) is often credited with writing the first Arabic text explaining the Indian system. His name gave us the word “algorithm,” and the title of his algebra book gave us the word “algebra.”
Fibonacci and the Spread to Europe
Europe clung to Roman numerals until an Italian mathematician made the case for something better. In 1202, Leonardo Pisano, known as Fibonacci, published Liber Abaci (Book of Calculation). The book introduced the ten Hindu-Arabic numerals, 0 through 9, to a European audience. It also introduced the Arabic word for zero: “zephirum,” which became “zefiro” in Italian, then “zero” in the Venetian dialect, giving English and several other European languages the word used today.
The advantages were practical. Roman numerals work tolerably well for addition and subtraction (you just combine or cancel symbols), but multiplication and division become extremely cumbersome because of the sheer number of individual symbols involved. A place value system with zero makes complex arithmetic vastly more manageable. You need to memorize more multiplication facts (a times table up to 9 × 9 rather than just a handful of symbol conversions), but the tradeoff is that you can multiply, divide, and handle large numbers with consistent, repeatable steps. This efficiency is what ultimately won over European merchants, bankers, and scientists.
Why Both Innovations Had to Come Together
Place value and zero solve different problems, and neither works well without the other. A place value system without zero (like the early Babylonian one) is ambiguous. If position determines a digit’s value, you need a way to mark empty positions, or the number 502 becomes indistinguishable from 52. Zero as a placeholder fixes that ambiguity. But zero as a full number, one you can add, subtract, and multiply with, is what makes the system powerful enough to support algebra, calculus, and modern computing.
The Babylonians contributed the foundational idea of positional notation. The Maya independently proved that zero could anchor a number system. Indian mathematicians synthesized both concepts and defined zero’s arithmetic behavior. Arab scholars preserved and transmitted the system. And Fibonacci delivered it to Europe, where it gradually displaced Roman numerals over the following centuries. The number system on your phone screen is the result of all of these contributions layered across roughly 4,000 years.