In 628 CE, a mathematician sitting somewhere in what is now Rajasthan wrote something that would eventually run every computer on Earth. Brahmagupta, a scholar at the astronomical observatory of Bhillamala, set down rules for arithmetic that included a number no Greek philosopher had dared to formalise: zero. He called it shunya — Sanskrit for empty, void, nothing.
What he could not have known was that he was laying the first stone in the foundation of the digital age.
BEFORE ZERO: THE WORLD IN ROMAN CHAINS
Roman numerals — the number system that dominated Europe well into the medieval period — had no symbol for nothing. To write 2026 in Roman numerals is MMXXVI; to write 2000 is MM. There is no zero, no placeholder, no way to distinguish 21 from 201 without context. The system works acceptably for counting cattle or marking years, but it collapses entirely when you try to do serious mathematics. Multiplication with Roman numerals is an exercise in madness. Long division is nearly impossible. This was not merely an inconvenience. It was a philosophical ceiling. Aristotle had declared that nature hates a vacuum, and this conviction ran deeper than physics — it shaped how educated Europeans thought about numbers. 'Nothing' was a quantity. It could not be operated upon. To ask what seven minus seven equals was almost a theological provocation. The answer implied that nothingness could be named, counted, and manipulated. For centuries, Western scholasticism would not permit it.
INDIA THOUGHT DIFFERENTLY
Indian intellectual tradition had no such prohibition. The concept of shunya — emptiness, the void — had been central to Buddhist and Hindu philosophy for centuries before Brahmagupta. The Upanishads speak of the infinite as the ground of all beings. Buddhist thinkers like Nagarjuna had developed elaborate metaphysical frameworks around sunyata, the doctrine of emptiness, in the 2nd century CE. Nothingness in India was not frightening. It was foundational.
This philosophical comfort with the void gave Indian mathematicians the psychological freedom to treat zero as a legitimate mathematical object. The concept of a placeholder zero a sign used to distinguish 21 from 201— appears in Indian texts as early as the Bakhshali manuscript, dating to somewhere between the 3rd and 7th centuries CE. But Brahmagupta went further. In his Brahmasphutasiddhanta ('The Opening of the Universe'), he defined zero not merely as a placeholder but as a number with its own arithmetic properties: a number added to zero equals itself; a number subtracted from zero becomes its negative; zero multiplied by any number equals zero. He also struggled, with remarkable honesty, with division by zero — and admitted it broke his rules. The question of what any number divided by zero yields would not be satisfactorily answered until the 19th and 20th centuries. The fact that Brahmagupta even asked it was itself extraordinary.
THE JOURNEY WEST
Zero's migration from India to the wider world was slow and contested. Indian mathematicians passed the concept to Persian scholars, most significantly to the polymath Muhammad ibn Musa al-Khwarizmi, who worked in Baghdad's House of Wisdom in the 9th century CE. Al-Khwarizmi incorporated zero into what he called al-jabr — algebra. The word algorithm is a Latinised corruption of his own name. Algebra comes from the title of his book. The entire Western mathematical tradition bears his fingerprints, and his fingerprints bear India's.
From the Arab world, zero entered Europe unwillingly. Italian merchants encountered Hindu-Arabic numerals including zero through trade with North Africa and the Levant. In 1202, the mathematician Leonardo of Pisa, better known as Fibonacci, published Liber Abaci,
urging Europeans to adopt the new numeral system. He demonstrated, with practical commercial examples, that Hindu-Arabic numerals made calculating interest, currency exchange, and profit dramatically easier than Roman numerals.
The reception was hostile. The city of Florence banned the use of Hindu-Arabic numerals in banking records in 1299, because the new symbols were too easy to forge — a zero, city authorities worried, could be altered into a six or a nine. The word cyp, now meaning a secret code, derives from the Arabic sifr, meaning zero: the implication being that these foreign symbols were inherently cryptic, suspicious, not to be trusted. It was merchants, not scholars, who ultimately broke the resistance. Profit is a more persuasive philosopher than Aristotle.
FROM PHILOSOPHY TO BINARY: THE LEAP TO COMPUTING
The distance between Brahmagupta's shunya and a modern microprocessor is enormous, but every step traverses zero. The key figure in this journey is the 17th-century German mathematician Gottfried Wilhelm Leibniz, who in 1679 developed binary arithmetic — a number system using only two digits: 0 and 1. The mathematical machinery he used depended entirely on zero as a number, not a void. Binary arithmetic sat as a mathematical curiosity for over two centuries. Then, in 1854, the English mathematician George Boole published An Investigation of the Laws of Thought, creating a system of logic, Boolean algebra, built entirely on binary values: true and false, 1 and 0. Boole's logic was the architecture; zero was the brick.
The final step came with Claude Shannon's 1937 master's thesis at MIT, in which he demonstrated that Boolean logic could be implemented using electrical circuits. A switch that was either open or closed. A current either flowing or not. One or zero. Shunya or something. Every transistor in every computer, smartphone, and server on Earth today is asking a question that Brahmagupta first answered: can nothing be a number? The binary code running beneath every digital photograph and every financial transaction is nothing more than an extremely fast manipulation of ones and zeroes — Brahmagupta's insight, executed billions of times per second.
WHAT EUROPE'S RESISTANCE COST
The centuries-long European resistance to zero was not merely a philosophical curiosity — it had real costs. While Indian and Arab mathematicians were developing algebra, trigonometry, and early calculus, European scholars remained bound to a number system that made advanced mathematics nearly impossible. The Scientific Revolution, when it finally came, was built on the very tools that European authorities had spent generations suppressing. The story of zero is, among other things, a lesson in how cultural and philosophical assumptions can delay technological progress. Europe's Aristotelian conviction that 'nothing' could be a number was not based on evidence; it was a metaphysical prejudice that happened to have enormous practical consequences. It is a useful reminder that the things we are most certain cannot exist are often precisely the things we most need to think carefully about.
THE CIRCLE CLOSES
There is a poetic geometry to zero's history. The word shunya in Sanskrit shares a root with the Sanskrit word for the sky — the open, unbounded vastness above. The numeral zero, as it evolved through Arabic script into European usage, became a circle: an empty ring, a hole, a form that encloses nothing. The shape of the number encodes its meaning. Brahmagupta, writing in 7th-century India, was not trying to invent computing. He was trying to make his astronomical calculations more rigorous. He was working within a philosophical tradition that had long made peace with emptiness. What he gave the world was not merely a number. It was permission — permission to treat nothing as something, to name the void, to calculate with absence. That permission, passed from India through Arabia to Europe and eventually into the silicon of our machines, is the quiet foundation on which the entire digital world rests. The number Europe feared and called a cipher became the alphabet of the modern age.
Sources:
- Brahmagupta's Brahmasphutasiddhanta (628 CE)
- al-Khwarizmi's Kitab al-mukhtasar fi hisab al-jabr wal-muqabala (c. 820 CE)
- Fibonacci's Liber Abaci (1202)
- George Boole's An Investigation of the Laws of Thought (1854)
- Shannon's A Symbolic Analysis of Relay and Switching Circuits (1937). Historical context drawn from Kim Plofker's Mathematics in India (Princeton University Press, 2009) and Charles Seife's Zero
- The Biography of a Dangerous Idea (Viking, 2000).