Does Nothing Matter? The Transnational Story of Zero
- Kiruba Murugaiah
- Feb 27
- 6 min read
Updated: Mar 8
By Kiruba Murugaiah
Crossing continents and cultures, zero took millennia for the world to be ready for it. One of the most consequential intellectual achievements in human history, zero bears the marks of the ways of knowing the world chose to honor—and those it chose to bury.
The story that continues to be taught begins in Greece, leaps to Newton, and names European men at every milestone. The Mayan shell glyph, the Indian Shunya, the Chinese rod numeral, the Islamic transmission: these are footnoted away, misattributed, or simply omitted. The result, as Joseph (2010) documents with painstaking care in The Crest of the Peacock: Non-European Roots of Mathematics, is a mathematics curriculum that systematically erases the non-European origins of the field’s most foundational ideas. This is not a matter of incomplete history. It is epistemicide.
The fuller story is one every mathematics teacher should know—and share. What follows is only an invitation. For the full account, you will need to do some digging yourself!
Empty Spaces
As early as 2000 BCE, Mesopotamian mathematicians in present-day Iraq had developed a positional numbering system. Their sexagesimal system, operating in base 60 (the ancestor of our 60-minute hour and 360-degree circle), encoded place value implicitly. But it lacked a true zero. Ambiguity about empty positions was often resolved by context or by a small gap. It was a workaround, not a solution.
The Egyptian use of nfr (meaning “beautiful” or “complete”) dates to roughly 1770 BCE, with examples found in accounting and architectural drawings. Their use of zero-like notation in astronomical texts continued through the later Ptolemaic period (around 300–100 BCE), when Egyptian astronomers used a small circle, or “o,” to denote an absent quantity. This later period overlaps with Greek influence in Egypt, so there is some debate about which influence influenced the other in that development.
Nevertheless, the Egyptians, for whom geometry and arithmetic were highly practical and precise, passed their number traditions on to the Greeks.
Fearing the Void
For the Greeks, the universe was governed by ratio, shape, and harmony. Numbers were not abstract objects but living properties of things—the music of the spheres, the geometry of the cosmos. Within such a worldview, the void had no natural place.
As Charles Seife (2000) explains in Zero: The Biography of a Dangerous Idea, “Even if zero were a number in the Greek sense, the act of taking a ratio with zero in it would seem to defy nature…For everything in the universe to be governed by ratios, as the Pythagoreans hoped, everything that made sense in the universe had to be related to a nice, neat proportion. It literally had to be rational” (35).
Consider Zeno of Elea and his famous paradoxes. To cross a room, he argued, you must first cross half the distance, then half of what remains, and so on without end. How can an infinite number of steps ever be completed? The paradox unsettled the Greeks because they lacked the conceptual tools for the infinite or the infinitesimal. They had no zero; they could not sum an infinite series to a finite value.
Aristotle built his physics on the assumption that velocity is proportional to force divided by resistance—a formula that collapses entirely if resistance equals zero, yielding infinite velocity, an absurdity.
Embracing Shunya
Where there is the Infinite, there is joy. There is no joy in the finite. Chandogya Upanishad
It was not ignorance that kept the Greeks from zero but a philosophical system that would anchor Western thought for nearly two thousand years. Meanwhile, civilizations to the east and west of Europe embraced the metaphysical and practical potential of zero.
The Maya: Place Value and the Shell of Emptiness
As early as the 4th century BCE, long before any contact with the Old World, the Maya of Mesoamerica made two of the most remarkable independent discoveries in the history of mathematics: the principle of place value and a symbol for zero. Working in a vigesimal (base 20) system, Mayan astronomers and mathematicians used a shell glyph — beautiful, deliberate, unmistakable — to represent the absence of a quantity in a given position. The Maya did not stumble upon zero. They needed it, invented it, and used it with confidence, enabling calendrical calculations that produced extraordinarily accurate estimates of solar, lunar, and planetary cycles, rivaling modern computations.
China: The Rod and the Empty Column
Between the 1st and 5th centuries CE, Chinese mathematicians using rod numerals operated within a positional system in which an empty column on the counting board represented the absence of a quantity. The concept was functional and systematic, even before a dedicated symbol existed. Here, too, zero was born from practical necessity, not philosophical debate.
India: Where Zero Became a Number
It is in India, between roughly the 3rd and 7th centuries CE, that the story reaches its most philosophically radical turn. Indian mathematicians did not merely use zero as a placeholder. They asked: What is zero? What happens when you compute with it?
The answer emerged from a cultural soil uniquely prepared to receive it. Hindu and Buddhist philosophy had long engaged with the concept of Shunya — emptiness, the void — not as an absence to be feared but as a profound and generative state of being. The void was not nothing. It was the ground from which something arises.
In the 7th century CE, the astronomer and mathematician Brahmagupta, writing in the Brahma Sphuta Siddhanta, laid out the first formal system of arithmetic with zero. He treated zero as a number equal in standing to positive and negative quantities — a boundary between them, the point where two equal and opposite forces meet and cancel. His rules:
Zero added to or subtracted from a number leaves it unchanged.
Any number multiplied by zero gives zero.
Zero divided by zero equals zero.
Brahmagupta’s last rule (zero ÷ zero = 0) would later be contested, but his achievement was epochal— zero had entered arithmetic as a full citizen.
In the 12th century, Bhaskaracharya pushed further. What happens when you divide a number by zero — not zero by itself, but something like 1 ÷ 0? His answer was visionary: the result is a quantity “as infinite as the god Vishnu”!
Bhaskaracharya intuited the concept of infinity as the reciprocal of zero centuries before Western calculus would formalize the same idea through limits.
Zero Today
The zero we use today — the Hindu-Arabic numeral system, including its zero — traveled from India through the Islamic world, carried and refined by scholars such as al-Khwārizmī in the 9th century, from whose name we derive the word algorithm, before entering Europe through medieval Spain and Italy. By the 13th century, Fibonacci was promoting the Hindu-Arabic system in Europe. By the 17th century, zero had unlocked calculus in the hands of Newton and Leibniz, who finally solved Zeno’s paradox by summing infinite series to finite limits. The rest is history, as the saying goes.
Two Zeros
Zero has two distinct and equally important roles in mathematics.
The first is as a placeholder — a positional marker that gives meaning to every other digit. Consider 108. That zero is doing critical work: it tells us we have 1 hundred, no tens, and 8 ones. Without it, 108 collapses into 18, or becomes confused with 180, 81, or 810. Where zero sits changes everything about the number’s meaning. This is the genius of place value: the position of a digit, not just its face value, determines its worth.
The second role is zero as a number in its own right — a quantity with its own arithmetic properties, occupying its rightful place to the left of 1 on the number line. As we have seen, this second zero was far more philosophically dangerous.
Genealogy of “Zero”
Sanskrit śūnya ("empty/void") → Arabic ṣifr ("cipher/nothing") → Medieval Latin zephirum → Italian zefiro, contracted to zero.
Chronology of Zero
Period | Civilization | Contribution |
2000 BCE | Mesopotamia (Iraq) | Positional base-60 system; empty position implied but no true zero symbol |
300 BCE – 900 CE | Maya (Mesoamerica) | Independent invention of zero (shell glyph) and place value in base 20; precise astronomical calendars |
1st – 5th CE | China | Rod numerals with empty column as placeholder zero |
3rd – 5th CE | India | Earliest symbolic zero as placeholder in Hindu astronomical texts |
628 CE | India (Brahmagupta) | First formal arithmetic of zero in Brahma Sphuta Siddhanta |
9th CE | Islamic world (al-Khwārizmī) | Transmission and systematization of Hindu-Arabic numerals including zero |
1202 CE | Europe (Fibonacci) | Introduction of Hindu-Arabic numeral system to European merchants |
17th century | Europe (Newton, Leibniz) | Calculus resolves Zeno's paradox using limits built on zero and infinity |
What This Means for the Mathematics Classroom
Zero is a gift from civilizations that Western education has largely refused to name. When we teach number systems without this history, we do more than leave out interesting facts — we quietly confirm to students from non-European backgrounds that their ancestors did not build the world of ideas. We also deprive every student of the richer, truer, and frankly more wondrous
Comments