essay on invention of zero

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The history of zero.

From placeholder to the driver of calculus, zero has crossed the greatest minds and most diverse borders since it was born many centuries ago. Today, zero is perhaps the most pervasive global symbol known. In the story of zero, something can be made out of nothing.

Zero, zip, zilch - how often has a question been answered by one of these words? Countless, no doubt. Yet behind this seemingly simple answer conveying nothing lays the story of an idea that took many centuries to develop, many countries to cross, and many minds to comprehend. Understanding and working with zero is the basis of our world today; without zero we would lack calculus, financial accounting, the ability to make arithmetic computations quickly, and, especially in today’s connected world, computers. The story of zero is the story of an idea that has aroused the imagination of great minds across the globe.

When anyone thinks of one hundred, two hundred, or seven thousand the image in his or her mind is of a digit followed by a few zeros. The zero functions as a placeholder; that is, three zeroes denotes that there are seven thousands, rather than only seven hundreds. If we were missing one zero, that would drastically change the amount. Just imagine having one zero erased (or added) to your salary! Yet, the number system we use today - Arabic, though it in fact came originally from India - is relatively new. For centuries people marked quantities with a variety of symbols and figures, although it was awkward to perform the simplest arithmetic calculations with these number systems.

The Sumerians were the first to develop a counting system to keep an account of their stock of goods - cattle, horses, and donkeys, for example. The Sumerian system was positional; that is, the placement of a particular symbol relative to others denoted its value. The Sumerian system was handed down to the Akkadians around 2500 BC and then to the Babylonians in 2000 BC. It was the Babylonians who first conceived of a mark to signify that a number was absent from a column; just as 0 in 1025 signifies that there are no hundreds in that number. Although zero’s Babylonian ancestor was a good start, it would still be centuries before the symbol as we know it appeared.

The renowned mathematicians among the Ancient Greeks, who learned the fundamentals of their math from the Egyptians, did not have a name for zero, nor did their system feature a placeholder as did the Babylonian. They may have pondered it, but there is no conclusive evidence to say the symbol even existed in their language. It was the Indians who began to understand zero both as a symbol and as an idea.

Brahmagupta, around 650 AD, was the first to formalize arithmetic operations using zero. He used dots underneath numbers to indicate a zero. These dots were alternately referred to as ‘sunya’, which means empty, or ‘kha’, which means place. Brahmagupta wrote standard rules for reaching zero through addition and subtraction as well as the results of operations with zero. The only error in his rules was division by zero, which would have to wait for Isaac Newton and G.W. Leibniz to tackle.

But it would still be a few centuries before zero reached Europe. First, the great Arabian voyagers would bring the texts of Brahmagupta and his colleagues back from India along with spices and other exotic items. Zero reached Baghdad by 773 AD and would be developed in the Middle East by Arabian mathematicians who would base their numbers on the Indian system. In the ninth century, Mohammed ibn-Musa al-Khowarizmi was the first to work on equations that equaled zero, or algebra as it has come to be known. He also developed quick methods for multiplying and dividing numbers known as algorithms (a corruption of his name). Al-Khowarizmi called zero ‘sifr’, from which our cipher is derived. By 879 AD, zero was written almost as we now know it, an oval - but in this case smaller than the other numbers. And thanks to the conquest of Spain by the Moors, zero finally reached Europe; by the middle of the twelfth century, translations of Al-Khowarizmi’s work had weaved their way to England.

The Italian mathematician, Fibonacci, built on Al-Khowarizmi’s work with algorithms in his book Liber Abaci, or “Abacus book,” in 1202. Until that time, the abacus had been the most prevalent tool to perform arithmetic operations. Fibonacci’s developments quickly gained notice by Italian merchants and German bankers, especially the use of zero. Accountants knew their books were balanced when the positive and negative amounts of their assets and liabilities equaled zero. But governments were still suspicious of Arabic numerals because of the ease in which it was possible to change one symbol into another. Though outlawed, merchants continued to use zero in encrypted messages, thus the derivation of the word cipher, meaning code, from the Arabic sifr.

The next great mathematician to use zero was Rene Descartes, the founder of the Cartesian coordinate system. As anyone who has had to graph a triangle or a parabola knows, Descartes’ origin is (0,0). Although zero was now becoming more common, the developers of calculus, Newton and Lebiniz, would make the final step in understanding zero.

Adding, subtracting, and multiplying by zero are relatively simple operations. But division by zero has confused even great minds. How many times does zero go into ten? Or, how many non-existent apples go into two apples? The answer is indeterminate, but working with this concept is the key to calculus. For example, when one drives to the store, the speed of the car is never constant - stoplights, traffic jams, and different speed limits all cause the car to speed up or slow down. But how would one find the speed of the car at one particular instant? This is where zero and calculus enter the picture.

If you wanted to know your speed at a particular instant, you would have to measure the change in speed that occurs over a set period of time. By making that set period smaller and smaller, you could reasonably estimate the speed at that instant. In effect, as you make the change in time approach zero, the ratio of the change in speed to the change in time becomes similar to some number over zero - the same problem that stumped Brahmagupta.

In the 1600’s, Newton and Leibniz solved this problem independently and opened the world to tremendous possibilities. By working with numbers as they approach zero, calculus was born without which we wouldn’t have physics, engineering, and many aspects of economics and finance.

In the twenty-first century zero is so familiar that to talk about it seems like much ado about nothing. But it is precisely understanding and working with this nothing that has allowed civilization to progress. The development of zero across continents, centuries, and minds has made it one of the greatest accomplishments of human society. Because math is a global language, and calculus its crowning achievement, zero exists and is used everywhere. But, like its function as a symbol and a concept meant to denote absence, zero may still seem like nothing at all. Yet, recall the fears over Y2K and zero no longer seems like a tale told by an idiot.

References: 1. Kaplan, Robert (2000). The Nothing that Is: A Natural History of Zero. New York: Oxford University Press.

2. Seife, Charles (2000). Zero: The Biography

Rights: © Copyright Yale Center for the Study of Globalization 2002

The Invention of Zero: How Ancient Mesopotamia Created the Mathematical Concept of Nought and Ancient India Gave It Symbolic Form

By maria popova.

If the ancient Arab world had closed its gates to foreign travelers, we would have no medicine, no astronomy, and no mathematics — at least not as we know them today.

Central to humanity’s quest to grasp the nature of the universe and make sense of our own existence is zero, which began in Mesopotamia and spurred one of the most significant paradigm shifts in human consciousness — a concept first invented (or perhaps discovered) in pre-Arab Sumer, modern-day Iraq, and later given symbolic form in ancient India. This twining of meaning and symbol not only shaped mathematics, which underlies our best models of reality, but became woven into the very fabric of human life, from the works of Shakespeare, who famously winked at zero in King Lear by calling it “an O without a figure,” to the invention of the bit that gave us the 1s and 0s underpinning my ability to type these words and your ability to read them on this screen.

Mathematician Robert Kaplan chronicles nought’s revolutionary journey in The Nothing That Is: A Natural History of Zero ( public library ). It is, in a sense, an archetypal story of scientific discovery, wherein an abstract concept derived from the observed laws of nature is named and given symbolic form. But it is also a kind of cross-cultural fairy tale that romances reason across time and space

Kaplan writes:

If you look at zero you see nothing; but look through it and you will see the world. For zero brings into focus the great, organic sprawl of mathematics, and mathematics in turn the complex nature of things. From counting to calculating, from estimating the odds to knowing exactly when the tides in our affairs will crest, the shining tools of mathematics let us follow the tacking course everything takes through everything else – and all of their parts swing on the smallest of pivots, zero With these mental devices we make visible the hidden laws controlling the objects around us in their cycles and swerves. Even the mind itself is mirrored in mathematics, its endless reflections now confusing, now clarifying insight. […] As we follow the meanderings of zero’s symbols and meanings we’ll see along with it the making and doing of mathematics — by humans, for humans. No god gave it to us. Its muse speaks only to those who ardently pursue her.

With an eye to the eternal question of whether mathematics is discovered or invented — a question famously debated by Kurt Gödel and the Vienna Circle — Kaplan observes:

The disquieting question of whether zero is out there or a fiction will call up the perennial puzzle of whether we invent or discover the way of things, hence the yet deeper issue of where we are in the hierarchy. Are we creatures or creators, less than – or only a little less than — the angels in our power to appraise?

Like all transformative inventions, zero began with necessity — the necessity for counting without getting bemired in the inelegance of increasingly large numbers. Kaplan writes:

Zero began its career as two wedges pressed into a wet lump of clay, in the days when a superb piece of mental engineering gave us the art of counting. […] The story begins some 5,000 years ago with the Sumerians, those lively people who settled in Mesopotamia (part of what is now Iraq). When you read, on one of their clay tablets, this exchange between father and son: “Where did you go?” “Nowhere.” “Then why are you late?”, you realize that 5,000 years are like an evening gone. The Sumerians counted by 1s and 10s but also by 60s. This may seem bizarre until you recall that we do too, using 60 for minutes in an hour (and 6 × 60 = 360 for degrees in a circle). Worse, we also count by 12 when it comes to months in a year, 7 for days in a week, 24 for hours in a day and 16 for ounces in a pound or a pint. Up until 1971 the British counted their pennies in heaps of 12 to a shilling but heaps of 20 shillings to a pound. Tug on each of these different systems and you’ll unravel a history of customs and compromises, showing what you thought was quirky to be the most natural thing in the world. In the case of the Sumerians, a 60-base (sexagesimal) system most likely sprang from their dealings with another culture whose system of weights — and hence of monetary value — differed from their own.

Having to reconcile the decimal and sexagesimal counting systems was a source of growing confusion for the Sumerians, who wrote by pressing the tip of a hollow reed to create circles and semi-circles onto wet clay tablets solidified by baking. The reed eventually became a three-sided stylus, which made triangular cuneiform marks at varying angles to designate different numbers, amounts, and concepts. Kaplan demonstrates what the Sumerian numerical system looked like by 2000 BCE:

This cumbersome system lasted for thousands of years, until someone at some point between the sixth and third centuries BCE came up with a way to wedge accounting columns apart, effectively symbolizing “nothing in this column” — and so the concept of, if not the symbol for, zero was born. Kaplan writes:

In a tablet unearthed at Kish (dating from perhaps as far back as 700 BC), the scribe wrote his zeroes with three hooks, rather than two slanted wedges, as if they were thirties; and another scribe at about the same time made his with only one, so that they are indistinguishable from his tens. Carelessness? Or does this variety tell us that we are very near the earliest uses of the separation sign as zero, its meaning and form having yet to settle in?

But zero almost perished with the civilization that first imagined it. The story follows history’s arrow from Mesopotamia to ancient Greece, where the necessity of zero awakens anew. Kaplan turns to Archimedes and his system for naming large numbers, “myriad” being the largest of the Greek names for numbers, connoting 10,000. With his notion of orders of large numbers, the great Greek polymath came within inches of inventing the concept of powers, but he gave us something even more important — as Kaplan puts it, he showed us “how to think as concretely as we can about the very large, giving us a way of building up to it in stages rather than letting our thoughts diffuse in the face of immensity, so that we will be able to distinguish even such magnitudes as these from the infinite.”

This concept of the infinite in a sense contoured the need for naming its mirror-image counterpart: nothingness. (Negative numbers were still a long way away.) And yet the Greeks had no word for zero, though they clearly recognized its spectral presence. Kaplan writes:

Haven’t we all an ancient sense that for something to exist it must have a name? Many a child refuses to accept the argument that the numbers go on forever (just add one to any candidate for the last) because names run out. For them a googol — 1 with 100 zeroes after it — is a large and living friend, as is a googolplex (10 to the googol power, in an Archimedean spirit). […] By not using zero, but naming instead his myriad myriads, orders and periods, Archimedes has given a constructive vitality to this vastness — putting it just that much nearer our reach, if not our grasp.

Ordinarily, we know that naming is what gives meaning to existence . But names are given to things, and zero is not a thing — it is, in fact, a no-thing. Kaplan contemplates the paradox:

Names belong to things, but zero belongs to nothing. It counts the totality of what isn’t there. By this reasoning it must be everywhere with regard to this and that: with regard, for instance, to the number of humming-birds in that bowl with seven — or now six — apples. Then what does zero name? It looks like a smaller version of Gertrude Stein’s Oakland, having no there there.

Zero, still an unnamed figment of the mathematical imagination, continued its odyssey around the ancient world before it was given a name. After Babylon and Greece, it landed in India. The first surviving written appearance of zero as a symbol appeared there on a stone tablet dated 876 AD, inscribed with the measurements of a garden: 270 by 50, written as “27°” and “5°.” Kaplan notes that the same tiny zero appears on copper plates dating back to three centuries earlier, but because forgeries ran rampant in the eleventh century, their authenticity can’t be ascertained. He writes:

We can try pushing back the beginnings of zero in India before 876, if you are willing to strain your eyes to make out dim figures in a bright haze. Why trouble to do this? Because every story, like every dream, has a deep point, where all that is said sounds oracular, all that is seen, an omen. Interpretations seethe around these images like froth in a cauldron. This deep point for us is the cleft between the ancient world around the Mediterranean and the ancient world of India.

But if zero were to have a high priest in ancient India, it would undoubtedly be the mathematician and astronomer Āryabhata, whose identity is shrouded in as much mystery as Shakespeare’s. Nonetheless, his legacy — whether he was indeed one person or many — is an indelible part of zero’s story.

Āryabhata wanted a concise way to store (not calculate with) large numbers, and hit on a strange scheme. If we hadn’t yet our positional notation, where the 8 in 9,871 means 800 because it stands in the hundreds place, we might have come up with writing it this way: 9T8H7Te1, where T stands for ‘thousand’, H for “hundred” and Te for “ten” (in fact, this is how we usually pronounce our numbers, and how monetary amounts have been expressed: £3.4s.2d). Āryabhata did something of this sort, only one degree more abstract. He made up nonsense words whose syllables stood for digits in places, the digits being given by consonants, the places by the nine vowels in Sanskrit. Since the first three vowels are a, i and u, if you wanted to write 386 in his system (he wrote this as 6, then 8, then 3) you would want the sixth consonant, c, followed by a (showing that c was in the units place), the eighth consonant, j, followed by i, then the third consonant, g, followed by u: CAJIGU. The problem is that this system gives only 9 possible places, and being an astronomer, he had need of many more. His baroque solution was to double his system to 18 places by using the same nine vowels twice each: a, a, i, i, u, u and so on; and breaking the consonants up into two groups, using those from the first for the odd numbered places, those from the second for the even. So he would actually have written 386 this way: CASAGI (c being the sixth consonant of the first group, s in effect the eighth of the second group, g the third of the first group)… There is clearly no zero in this system — but interestingly enough, in explaining it Āryabhata says: “The nine vowels are to be used in two nines of places” — and his word for “place” is “kha”. This kha later becomes one of the commonest Indian words for zero. It is as if we had here a slow-motion picture of an idea evolving: the shift from a “named” to a purely positional notation, from an empty place where a digit can lodge to “the empty number”: a number in its own right, that nudged other numbers along into their places.

Kaplan reflects on the multicultural intellectual heritage encircling the concept of zero:

While having a symbol for zero matters, having the notion matters more, and whether this came from the Babylonians directly or through the Greeks, what is hanging in the balance here in India is the character this notion will take: will it be the idea of the absence of any number — or the idea of a number for such absence? Is it to be the mark of the empty, or the empty mark? The first keeps it estranged from numbers, merely part of the landscape through which they move; the second puts it on a par with them.

In the remainder of the fascinating and lyrical The Nothing That Is , Kaplan goes on to explore how various other cultures, from the Mayans to the Romans, contributed to the trans-civilizational mosaic that is zero as it made its way to modern mathematics, and examines its profound impact on everything from philosophy to literature to his own domain of mathematics. Complement it with this Victorian love letter to mathematics and the illustrated story of how the Persian polymath Ibn Sina revolutionized modern science .

— Published February 2, 2017 — https://www.themarginalian.org/2017/02/02/zero-robert-kaplan/ —

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Who Invented the Zero?

By: History Staff

Updated: June 6, 2023 | Original: January 22, 2014

It might seem like an obvious piece of any numerical system, but the zero is a surprisingly recent development in human history. In fact, this ubiquitous symbol for “nothing” didn’t even find its way to Europe until as late as the 12th century. 

Zero’s origins most likely date back to the “fertile crescent” of ancient Mesopotamia. Sumerian scribes used spaces to denote absences in number columns as early as 4,000 years ago, but the first recorded use of a zero-like symbol dates to sometime around the third century B.C. in ancient Babylon. The Babylonians employed a number system based around values of 60, and they developed a specific sign—two small wedges—to differentiate between magnitudes in the same way that modern decimal-based systems use zeros to distinguish between tenths, hundreds and thousandths. A similar type of symbol cropped up independently in the Americas sometime around A.D. 350, when the Mayans began using a zero marker in their calendars.

These early counting systems only saw the zero as a placeholder—not a number with its own unique value or properties. A full grasp of zero’s importance would not arrive until the seventh century A.D. in India. There, the mathematician Brahmagupta and others used small dots under numbers to show a zero placeholder, but they also viewed the zero as having a null value, called “sunya.” Brahmagupta was also the first to show that subtracting a number from itself results in zero. 

From India, the zero made its way to China and back to the Middle East, where it was taken up by the mathematician Mohammed ibn-Musa al-Khowarizmi around 773. He studied and synthesized Indian arithmetic and showed how zero functioned in the system of formulas he called ‘al-jabr’—today known as algebra. By the 10th century, the zero had entered the Arabic numeral system in a form resembling the oval shape we use today.

The zero continued to migrate for another few centuries before finally reaching Europe sometime around the 1100s. Thinkers like the Italian mathematician Fibonacci helped introduce zero to the mainstream, and it later figured prominently in the work of Rene Descartes along with Sir Isaac Newton and Gottfried Leibniz’s invention of calculus. Since then, the concept of “nothing” has continued to play a role in the development of everything from physics and economics to engineering and computing.

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Nothing matters: how the invention of zero helped create modern mathematics

Teaching Fellow, Department of Mathematics, University of Portsmouth

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Ittay Weiss does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.

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A small dot on an old piece of birch bark marks one of the biggest events in the history of mathematics. The bark is actually part of an ancient Indian mathematical document known as the Bakhshali manuscript. And the dot is the first known recorded use of the number zero. What’s more, researchers from the University of Oxford recently discovered the document is 500 years older than was previously estimated, dating to the third or fourth century – a breakthrough discovery.

Today, it’s difficult to imagine how you could have mathematics without zero. In a positional number system, such as the decimal system we use now, the location of a digit is really important. Indeed, the real difference between 100 and 1,000,000 is where the digit 1 is located, with the symbol 0 serving as a punctuation mark.

Yet for thousands of years we did without it. The Sumerians of 5,000BC employed a positional system but without a 0. In some rudimentary form , a symbol or a space was used to distinguish between, for example, 204 and 20000004. But that symbol was never used at the end of a number, so the difference between 5 and 500 had to be determined by context.

What’s more, 0 at the end of a number makes multiplying and dividing by 10 easy, as it does with adding numbers like 9 and 1 together. The invention of zero immensely simplified computations, freeing mathematicians to develop vital mathematical disciplines such as algebra and calculus, and eventually the basis for computers.

Zero’s late arrival was partly a reflection of the negative views some cultures held for the concept of nothing. Western philosophy is plagued with grave misconceptions about nothingness and the mystical powers of language. The fifth century BC Greek thinker Parmenides proclaimed that nothing cannot exist, since to speak of something is to speak of something that exists. This Parmenidean approach kept prominent historical figures busy for a long while.

After the advent of Christianity, religious leaders in Europe argued that since God is in everything that exists, anything that represents nothing must be satanic. In an attempt to save humanity from the devil, they promptly banished zero from existence, though merchants continued secretly to use it.

By contrast, in Buddhism the concept of nothingness is not only devoid of any demonic possessions but is actually a central idea worthy of much study en route to nirvana. With such a mindset , having a mathematical representation for nothing was, well, nothing to fret over. In fact, the English word “zero” is originally derived from the Hindi “sunyata”, which means nothingness and is a central concept in Buddhism.

So after zero finally emerged in ancient India, it took almost 1,000 years to set root in Europe, much longer than in China or the Middle East. In 1200 AD, the Italian mathematician Fibonacci, who brought the decimal system to Europe, wrote that :

The method of the Indians surpasses any known method to compute. It’s a marvellous method. They do their computations using nine figures and the symbol zero.

This superior method of computation, clearly reminiscent of our modern one, freed mathematicians from tediously simple calculations, and enabled them to tackle more complicated problems and study the general properties of numbers. For example, it led to the work of the seventh century Indian mathematician and astronomer Brahmagupta , considered to be the beginning of modern algebra.

Algorithms and calculus

The Indian method is so powerful because it means you can draw up simple rules for doing calculations. Just imagine trying to explain long addition without a symbol for zero. There would be too many exceptions to any rule. The ninth century Persian mathematician Al-Khwarizmi was the first to meticulously note and exploit these arithmetic instructions, which would eventually make the abacus obsolete.

Such mechanical sets of instructions illustrated that portions of mathematics could be automated. And this would eventually lead to the development of modern computers. In fact, the word “algorithm” to describe a set of simple instructions is derived from the name “Al-Khwarizmi”.

The invention of zero also created a new, more accurate way to describe fractions. Adding zeros at the end of a number increases its magnitude, with the help of a decimal point, adding zeros at the beginning decreases its magnitude. Placing infinitely many digits to the right of the decimal point corresponds to infinite precision . That kind of precision was exactly what 17th century thinkers Isaac Newton and Gottfried Leibniz needed to develop calculus, the study of continuous change.

And so algebra, algorithms, and calculus, three pillars of modern mathematics, are all the result of a notation for nothing. Mathematics is a science of invisible entities that we can only understand by writing them down. India, by adding zero to the positional number system, unleashed the true power of numbers, advancing mathematics from infancy to adolescence, and from rudimentary toward its current sophistication.

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A Number’s Journey: Uncovering Who Invented Zero

Zero, often seen as a simple circle, holds an extraordinary place in the annals of mathematics and human history. The question of who invented zero leads us into a fascinating exploration across ancient civilizations, each contributing uniquely to its development. From the early absence of zero in Roman numerals to its conceptual birth in India and independent emergence in the Mayan civilization, the story of zero is a journey of intellectual evolution, cultural exchange, and profound impact on modern science and technology.

Table of Contents

Who Invented Zero?

The invention of zero can be credited to ancient Indian mathematicians , particularly to those of the 5th century. While the concept of zero, or a placeholder for nothing, had been in use in several ancient civilizations for counting and positional notation, it was in India that zero was first conceptualized as a number with its own unique value and properties.

Early Numerical Systems Without Zero

In the absence of a zero digit, early numerical systems, including those of ancient civilizations, faced limitations in representing large numbers and performing complex operations like multiplying and dividing numbers. The Roman numeral system is a prime example, lacking a symbol for zero, which hindered mathematical progress in various fields.

READ MORE: Who Invented Math? The History of Mathematics and Who Invented Numbers? Unraveling the Origins of Numerical System

The Origin and History of Zero in India

The journey of zero in ancient India, a landmark in the annals of mathematics, is intertwined with the evolution of the concept of zero from a philosophical notion to a practical numeral. Indian mathematicians, delving into the realms of negative and positive numbers, recognized the necessity of a symbol that could represent an absence, an empty space, or ‘nothingness’ in their calculations. This recognition led to the birth of the mathematical zero digit, a concept that was both revolutionary and foundational for the development of modern mathematics.

Ancient Indian scrolls and texts, such as the “Bakhshali Manuscript,” dating back to as early as the third or fourth century AD, bear witness to this evolution. The manuscript, considered by many scholars as the oldest recorded example of the zero digit, features a dot symbol (which later evolved into the small circle we recognize as zero) used in a numerical context. This symbol signified more than just an empty column in counting; it represented a new, distinct quantity – a leap forward in the number system.

The real breakthrough, however, came with the works of Brahmagupta, a renowned Hindu astronomer and mathematician of the 7th century AD. Brahmagupta’s treatise “Brahmasphutasiddhanta” is a pivotal text in Indian mathematics, as it marks the first instance where zero is explicitly defined as a number in its own right. His work laid down rules for arithmetic operations involving zero, such as addition, subtraction, and even multiplication. This was a monumental step, as it transitioned zero from a mere placeholder to an integral part of arithmetic operations.

The philosophical and cultural factors in ancient India played a significant role in this development. The concept of ‘śūnya,’ or void in Sanskrit, permeated Indian philosophy and contemplations about the universe. This cultural backdrop facilitated the conceptual leap necessary to see zero not just as an absence but as a finite quantity, a concept that would have been considered a dangerous idea in other civilizations of the time.

Brahmagupta’s advancements in the field of Indian mathematics were not isolated developments. They were part of a broader tradition of mathematical inquiry that included other luminaries such as Aryabhata and Varahamihira. Their collective works contributed to a rich mathematical heritage that not only influenced contemporaneous philosophy but also paved the way for future generations of mathematicians and scientists.

The origin and history of zero in ancient India are a testament to the region’s intellectual prowess and its profound impact on the global understanding of mathematics. The journey of zero, from a philosophical abstraction on an ancient Indian scroll to a defined mathematical quantity by Brahmagupta, underscores the integral role of cultural and intellectual contexts in shaping scientific breakthroughs. This development in Indian mathematics laid the groundwork for modern arithmetic, calculus, and even the binary code used in most modern computers, underlining zero’s enduring legacy in shaping the world as we know it today.

Zero in the Americas

Parallel to developments in India, the concept of zero also emerged independently in the Americas, most notably within the Mayan civilization. The Mayans, around the 4th century AD, used zero in their elaborate calendar systems and astronomical calculations. Unlike the Indian zero, which was part of a decimal system, the Mayan zero was part of a vigesimal (base-20) system. This independent invention of zero by the Mayans illustrates the universal need and logical evolution of this mathematical concept in different cultures.

The Modern Zero Introduced in the Middle East

During the Islamic Golden Age , a period marked by significant advancements in science and culture, the concept of zero was introduced to the Middle East. This introduction was a direct result of the translation and study of Indian mathematical texts, which brought sophisticated mathematical concepts from the Indian subcontinent to the Islamic world. This era, spanning from the 8th to the 14th century, saw Islamic scholars and mathematicians not only assimilate knowledge from different cultures but also expand upon it.

A key figure in this process was the Persian mathematician Al-Khwarizmi , whose work in the 9th century played a pivotal role in the adoption and dissemination of the concept of zero. His famous text, “Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala” (The Compendious Book on Calculation by Completion and Balancing), is considered one of the foundational texts in algebra. In this work, Al-Khwarizmi systematically integrated the Indian numeral system, including the concept of zero, into Islamic mathematics. His work represented a significant advancement in numerical notation and calculation techniques.

The translation of these mathematical concepts into Arabic facilitated their spread throughout the Islamic world and later into Europe. The Arabic numeral system, which included the concept of zero, was far more efficient than the Roman numeral system used in Europe at the time, particularly for complex calculations. Islamic mathematicians’ work with zero enabled advancements in various fields of mathematics, including algebra , arithmetic, and trigonometry.

Moreover, the introduction of zero had practical implications beyond pure mathematics. It found applications in fields like astronomy, where it was used for more accurate calculations and predictions. It also played a role in the development of accounting and bookkeeping methods, improving the efficiency and accuracy of financial transactions.

Impact on Europe and the Western World

Zero’s journey to Europe was met with resistance and skepticism. Initially viewed with mistrust due to its association with foreign cultures and its challenging philosophical implications, zero eventually gained acceptance. The work of mathematicians like Fibonacci , who introduced Arabic numerals and zero through his book “Liber Abaci,” was pivotal. By the 17th century, zero had become an integral part of European mathematics, paving the way for scientific and technological advances during the Renaissance and beyond.

Where Did Zero Get Its Name From?

The word “zero” has a fascinating linguistic journey. Derived from the Arabic word “sifr,” which means empty or nothing, it was later translated into Latin as “zephirum.” This term evolved into the Italian “zero,” which then made its way into the English language. The naming of zero reflects not only its mathematical function but also its philosophical and cultural interpretations across different societies, symbolizing concepts of void, nothingness, and the infinite.

The Final Count: Zero’s Role in Shaping Modern Thought

Zero’s evolution from a mere placeholder in ancient counting systems to a fundamental element of modern mathematics is a testament to human ingenuity. Its historical journey across different civilizations highlights the interconnectedness of human knowledge and the cross-cultural development of ideas. Zero is not just a number; it represents the concept of nothingness, a crucial element in the understanding of our universe and the advancement of technology.

How to Cite this Article

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July 28, 2022

The Elusive Origin of Zero

Who decided that nothing should be something?

By Frank Swetz & Shaharir bin Mohamad Zain

A number of jewelry relics of Sriwijaya Kingdom are seen after being found by fishermen at Musi River in Palembang, South Sumatera province, Indonesia in November 2021.

Muhammad A.F./Anadolu Agency/Getty Images

Sūnya , nulla , ṣifr , zevero , zip and zilch are among the many names of the mathematical concept of nothingness. Historians, journalists and others have variously identified the symbol’s birthplace as the Andes mountains of South America, the flood plains of the Tigris and Euphrates Rivers, the surface of a calculating board in the Tang dynasty of China, a cast iron column and temple inscriptions in India, and most recently, a stone epigraphic inscription found in Cambodia.

The tracing of zero’s heritage has been elusive. For a country to be able to claim the number’s origin would provide a sense of ownership and determine a source of great nationalistic pride.

Throughout the 20th century, this ownership rested in India. That’s where an inscription was discovered, holding the number “0” in reference to land measurement inside a temple in the central Indian city of Gwalior. In 1883 the renowned German Indologist and philologist, Eugen Julius Theodor Hultzsch copied and translated the inscription into English, dating the text to the year C.E. 876. And this has been accepted as the oldest known date for the appearance of zero. However, a series of stones in what is now Sumatra, casts India’s ownership of nothingness in doubt, and several investigators agree that the first reference of zero was likely on a set of stones found on the island.

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In 1891 a French archaeological team uncovered a stone stele near the village of Sambor on the banks of the Mekong River, in what was then French Indochina, later to become Cambodia/Kampuchea. The stone bore a Khmer epigraphic inscription that included the date for the Khmer year 605, reckoned within the Hindu Saka system, a historical calendar based on the rule of the Indian emperor Shalivahana. The calendar’s reference year (zero) corresponds to the Julian year 78. Thus, the inscribed date is C.E. 685 .

Political upheavals precluded further scholarly examination of this stone, and it would not be until the 20th century that another Western scholar took up this task. Georges Cœdès, a Frenchman, who in 1918 became director of the National Library of Thailand, located the so-called Sambor stone, given the archaeological designation K–127 by the archaeological team that uncovered it. In 1931 Cœdès concluded that the numeration system used in the inscribed date, 605, was decimal in nature and positional in conception and that the central glyph was an empty placeholder, a zero. This assessment meant that 605, referencing a year, singled out the earliest known and documented zero. So, now the preeminent honor of claiming zero, the elusive and mathematically important entity, rested with Cambodia.

The claim earned little attention at the time; thus India maintained its status as the birthplace of zero. In the disruptions of World War II, people forgot about the Sambor stone, which was lost. Almost a century later, a popular science writer, Amir Aczel, tried to find the missing stone and authenticate its existence and significance. He found it in an archaeological warehouse, near the ancient Khmer ruins of Angkor Wat.

Aczel documented his quest and adventures in a book, Finding Zero , published in 2015. His testimony affirmed the existence of the zero and endowed its elusive heritage to Cambodia. Aczel’s suggestion that he had found the “ first zero ” was celebrated in the media. But perhaps such euphoria was premature.

Around 1918, Cœdès had postulated the existence of a dominant but previously unknown Old Malay empire in Southeast Asia, one that predated the Khmers. Named Sriwijaya, it was ruled by a maharaja, centered on the island of Sumatra in what is now Indonesia, and flourished in the period C.E. 650 to 1377.

Sriwijaya was a major trading and maritime power controlling the sea lanes from Madagascar, across the Indian ocean, the Straits of Malacca, the whole of the South China Sea and on to the islands of the Philippines. Sriwijaya was also an early center of Buddhist teaching and proselytizing.

Archaeological explorations have uncovered a rich trove of Sriwijayan artifacts and records. Dutch colonial officers discovered three dated ceremonial stones with the historical numerals 605, 606 and 608, marking the years as reckoned from the Hindu Saka–era calendar. Translated into our Common Era chronological systems, those numerals would be: 683, 684 and 686.

The stones are named after the places of their discovery: Keduan Bukit, Talang Tuwo and Kota Kapur. These stones were polished and inscribed and probably intended for use in a ceremonial ritual, perhaps ablution, suggesting they originated in the seventh century. If correct, the existence of zero in the stones’ inscriptions predates the findings of the Gwalior Indian claim by two centuries!

Researchers at the Center for Civilizational Dialogue at the University of Malaya in Kuala Lumpur have been investigating the history of early numeration systems of Southeast Asia. Their findings further strengthened Sumatra’s claim, to which we, the authors, agree. Acknowledging this state’s strong economic influence and mercantile activities, and the existence of three independent stone glyph inscriptions within its realm bearing a zero, this claim certainly has strong credibility. A 1995 article published in the Journal of the Malaysian Branch of the Royal Asiatic Society had also offered this conjecture.

In 1976, while on a research visit to Sumatra to examine the numeration systems of the region, one of us (Swetz) was impressed by the mathematical abilities of the traditional Batak people. In returning to Malaysia, he conveyed his impressions to Malaysian colleagues. A team at the Center for Civilizational Dialogue, headed by the other of us (Zain), then focused their attention on Sumatra and arrived at the conclusion that zero had an early presence in the region.

While the issue requires more deliberation and historical examination, this discovery of a possible nothingness symbol is intriguing. Could zero have been conceptually conceived of and utilized in an ancient and barely known Southeast Asian society? Was the Khmer zero actually influenced by the Sriwijayan culture? Did the use of zero spread from this region westward into India and finally into Europe? Is the credibility of the term “Hindu-Arabic” numerals under serious threat? These questions require further investigation, but, as we see, the history of mathematics offers many mysteries that can puzzle and amaze its disciples.

This is an opinion and analysis article, and the views expressed by the author or authors are not necessarily those of Scientific American.

Nothing matters: how the invention of zero helped create modern mathematics

Today, it’s difficult to imagine how you could have mathematics without zero. In a positional number system, such as the decimal system we use now, the location of a digit is really important. Indeed, the real difference between 100 and 1,000,000 is where the digit 1 is located, with the symbol 0 serving as a punctuation mark.

The method of the Indians surpasses any known method to compute. It’s a marvellous method. They do their computations using nine figures and the symbol zero.

Algorithms and calculus

Journey of Zero: How a simple number revolutionised the world from ancient India to our digital era

The number zero is a cornerstone of modern mathematics, technology, and the digital world. Its origins are rooted in the philosophical concepts of ancient South and Southeast Asia, and its journey to Western Europe is a fascinating tale of cultural exchange, scientific discovery, and technological advancement.  

This article explores the evolution of zero, charting its journey from its origins in Indian space to its dissemination through the Arab world and, eventually, its arrival in Europe, where it revolutionised Western mathematics and laid the foundation for modern science and technology. 

While there are other instances of the use of zero (see textbox below), our focus is on the direct lineage of zero from Asia , through the Mediterranean, to Europe, and beyond.

Zero across different numerical systems

The use of the number zero, while widely associated with the Indian numeral system, has evolved independently in various numerical systems over time. Here’s a chronological overview of its presence in different civilisations, though the exact years are approximations:

2,000 BC – The Babylonian numerical system : Rooted in the base-60 system, the Babylonian mathematical approach is the precursor to our modern method of measuring time, with 60 seconds in a minute and 60 minutes in an hour. While the Babylonians did employ a placeholder concept, it wasn’t quite the zero we recognise today. Some sources suggest that a closer semblance to the number zero might have emerged in their system around the 3rd century BC.

200 BC – The Han Dynasty’s mathematical : ’Nine Chapters on the Mathematical Art’ represents an early consolidation of Chinese mathematical thought. While a specific symbol for the number zero was absent, an empty position within a number essentially denoted zero, indicating its absence.

100 BC – The Maya mathematics : The Mayans introduced a glyph, resembling a shell, to symbolise zero. Notably, this glyph is evident on a stela found at the Chiapa de Corzo site in Mexico. Furthermore, the concept of zero was integral to the intricate Mayan Long Count calendar system.

This historical evolution underscores the universal need and recognition for a concept like zero, as societies grapple with mathematical and calendar challenges, leading to its independent inception in diverse parts of the world.

Zero in Ancient India

The concept of zero, termed ‘Shunya’ in Hindi, has deep roots in ancient Indian philosophical and religious traditions.  ‘Shunyata’, often translated as ’emptiness’ or ‘void’, holds significant importance in Buddhism.  The renowned philosopher Nagarjuna, active around the 2nd century CE, anchored Mahayana Buddhism on the principle of ’emptiness’, emphasising the interdependent existence of phenomena.

This philosophical understanding of ’emptiness’ or ‘void’ laid the groundwork for the mathematical adoption of the number zero. By the 6th century AD, prominent Indian mathematicians like Aryabhata and Brahmagupta had begun employing zero as a placeholder in their calculations.

To date, archaeological efforts have unveiled two significant artefacts in India that demonstrate the early use of the numeral zero:

The more ancient of the two is the stone known as K-127, dated to 683 CE. Discovered in the Hindu temple complex of Sambor near the Mekong River, this stone features the numeral zero depicted as a dot amidst other numbers. Presently, K-127 is housed in the National Museum in Phnom Penh, Cambodia.

Subsequent to this is the ‘Gwalior zero’, found inscribed in the Chaturbhuj Temple in Gwalior, India. This artefact, dating to 876 CE, showcases the use of the number zero in a manner akin to modern usage, specifically to document a land grant.

Birth of algebra in the Islamic Golden Age

In the 9th century, during the intellectual flourishing of the Islamic Golden Age, zero became fully integrated into mathematics. This critical development was spearheaded by the Persian scholar Muḥammad ibn Mūsā al-Khwārizmī, celebrated as the father of algebra. In the House of Wisdom in Baghdad, Al-Kwharizmi developed an Arabic numeric system with the number zero, called in Arabic ‘sifr’. 

The transmission of the zero concepts from India to Europe was expedited by the Latin translation of al-Khwarizmī’s seminal work, Algoritmo de Numero Indorum , in the 12th century. This translation served as a pivotal conduit, connecting the mathematical legacies of ancient India with the Arab world and, subsequently, with Europe. This served as the foundation for the zero concept’s wider adoption, which Arab traders also helped to facilitate.

Fibonacci and the spread of zero worldwide

The 13th century brought the next significant chapter in Zero’s odyssey. Italian mathematician Leonardo of Pisa, better known as Fibonacci, encountered the Hindu-Arabic decimal system, including the ‘0’, during his travels to North Africa. 

Recognising the immense potential of this system over the existing Roman numerals, Fibonacci introduced the ‘0’ to Europe through his book Liber Abaci (Book of Calculation) in 1202.

Zero in the digital era

The evolution of zero culminates in its central role in today’s digital world. In the binary system, which forms the basis of modern computing, digits 0 and 1 represent one bit. This seemingly simple binary language has led to the formation of bytes, kilobytes, megabytes, terabytes, and beyond, shaping the digital landscape we experience today.

Parting thoughts

The journey of zero is a testament to the power of cross-cultural exchange, human curiosity, and technological innovation. From its philosophical origins in ancient India to its mathematical maturity in the Arab world, and finally to its global adoption,

Zero has transformed human thought and society. Zero’s contributions to mathematics, physics, and digitalisation are fundamental and continue to resonate in our modern world, underscoring the profound importance of this seemingly simple number.

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Home — Essay Samples — Science — Invention — Abuela Inventions The Zero Analysis

Abuela Inventions The Zero Analysis

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Ancient Text Reveals New Clues to the Origin of Zero

New carbon dating provides insights on one of the most pivotal moments in the history of mathematics.

One of the biggest mathematical achievements in human history has to do with the origin of nothing—or zero, to be more specific.

Researchers at the University of Oxford's Bodleian Library recently conducted carbon dating on an ancient Indian text known as the Bakshali manuscript. They found that some pages in the manuscript date to the third or fourth century, five hundred years older than previously thought. That pushes back the origin of what would eventually become the zero symbol, 0, we use today.

The manuscript shows a series of Sanskrit numerals. In it, zero is represented by a small dot.

“This zero in India is the seed from which the concept of zero as a number in its own right represented by the same dot or circle will emerge some centuries later, something many regard as one of the of the great moments in the history of mathematics,” said lead researcher Marcus du Sautoy.

For mathematicians and historians like du Sautoy, the manuscript represents one of the most important clues to understanding a mathematical concept that would help fields such as calculus and physics flourish centuries later.

Origins of Zero

To understand the origin of zero and the debates that surround it, it’s important to first understand the distinction between what math historians refer to as a “placeholder zero” and what they refer to as zero as a numeral unto itself.

Placeholder zeros, or their equivalents, have been documented for thousands of years. Sumerians in Mesopotamia were the first to represent this concept 5,000 years ago, Harvard math professor Robert Kaplan wrote in Scientific American .

This concept of zero spread from ancient Mesopotamia into India and eventually China, Kaplan noted. Independently, the ancient Maya used placeholder zeros represented by turtle shells drawings.

The first documented use of zero came from the ancient astronomer and mathematician Brahmagupta, said Sautoy.

“Brahmagupta’s text Brahmasphutasiddhanta, written in 628 A.D., is the first text to talk of zero as a number in its own right and to include a discussion of the arithmetic of zero, including the dangerous act of dividing by zero,” he said.

Historians theorize that zero was spread from northern India by Arab traders along the Silk Road, an ancient trading route that connected Europe and Asia, and may have helped to develop more complex schools of mathematical thought.

Origins of the Bakhshali

A farmer unearthed the Bakhshali manuscript from a field in what is now Pakistan in 1881. It consists of 70 pages of birch bark, a common writing material before the advent of paper. Translations indicate that it may have been used by Silk Road merchants practicing arithmetic. In 1902, the manuscript was acquired by the University of Oxford, where it has been housed ever since.

For the past century, the manuscript’s date has been the subject of debate. Based on the writing style and mathematical content, scholars argued that it was created sometime between the eighth and twelfth centuries.

The Oxford researchers’ analysis revealed that parts of the manuscript contain birch bark from three different time periods, ranging from the third century to the 10th century.

Previously, the oldest known example of a zero symbol in ancient India came from a temple in Gwalior that was constructed in 876 A.D. If the carbon dating is correct, the Bakhshali manuscript could knock the Gwalior temple text into second place.

Why Does Zero Matter?

To conclusively prove evidence of zero as a number, Peter Gobets isn’t convinced unless he sees it used in an equation. Gobets is a leading member of ZerOrigIndia , or Project Zero, in the Netherlands, which partners with researchers in Mumbai to pinpoint the origin of zero.

He agreed with du Sautoy’s statement that Brahmagupta’s writings were the first to describe zero as a number in its own right, but the first use of zero in practical applications is unclear.

Gobets isn’t convinced that the Bakhshali manuscript itself could have led to the creation of zero—he and his team hope to independently study the document themselves—but he said it’s possible. Where and exactly how the number zero made the leap from a concept of nothingness to a circle factored into equations, he said, is still highly debated.

“Our biggest enemy is that there is very little evidence,” he said, with speculation but no documentation of exactly who began to use zero in equations and when.

What we do know, said Gobets, is that zero was crucial to the zero-to-nine decimal system upon which algebra developed in 9 th century Persia and was essential for physics principles documented by scientist Blaise Pascal in the 17 th century.

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The mind-bendy weirdness of the number zero, explained

We explain nothing.

by Brian Resnick

Additional reporting by Ellen Rolfes and Kimberly Mas

The computer you’re reading this article on right now runs on a binary — strings of zeros and ones. Without zero, modern electronics wouldn’t exist. Without zero, there’s no calculus, which means no modern engineering or automation. Without zero, much of our modern world literally falls apart.

Humanity’s discovery of zero was “a total game changer ... equivalent to us learning language,” says Andreas Nieder, a cognitive scientist at the University of Tübingen in Germany.

But for the vast majority of our history, humans didn’t understand the number zero. It’s not innate in us. We had to invent it. And we have to keep teaching it to the next generation.

Other animals, like monkeys, have evolved to understand the rudimentary concept of nothing. And scientists just reported that even tiny bee brains can compute zero . But it’s only humans that have seized zero and forged it into a tool.

So let’s not take zero for granted. Nothing is fascinating. Here’s why.

What is zero, anyway?

Our understanding of zero is profound when you consider this fact: We don’t often, or perhaps ever, encounter zero in nature.

Numbers like one, two, and three have a counterpart. We can see one light flash on. We can hear two beeps from a car horn. But zero? It requires us to recognize that the absence of something is a thing in and of itself.

“Z ero is in the mind, but not in the sensory world,” Robert Kaplan, a Harvard math professor and an author of a book on zero , says. Even in the empty reaches of space, if you can see stars, it means you’re being bathed in their electromagnetic radiation. In the darkest emptiness, there’s always something. Perhaps a true zero — meaning absolute nothingness — may have existed in the time before the Big Bang. But we can never know.

Nevertheless, zero doesn’t have to exist to be useful. In fact, we can use the concept of zero to derive all the other numbers in the universe.

Kaplan walked me through a thought exercise first described by the mathematician John von Neumann. It’s deceptively simple.

Imagine a box with nothing in it. Mathematicians call this empty box “the empty set.” It’s a physical representation of zero. What’s inside the empty box? Nothing.

Now take another empty box, and place it in the first one.

How many things are in the first box now?

There’s one object in it. Then, put another empty box inside the first two. How many objects does it contain now? Two. And that’s how “we derive all the counting numbers from zero … from nothing,” Kaplan says. This is the basis of our number system. Zero is an abstraction and a reality at the same time. “It’s the nothing that is,” as Kaplan said. (At this point in the story, you may want to take another hit on your bong.)

He then put it in more poetic terms. “Zero stands as the far horizon beckoning us on the way horizons do in paintings,” he says. “It unifies the entire picture. If you look at zero you see nothing. But if you look through it, you see the world. It’s the horizon.”

Once we had zero, we have negative numbers. Zero helps us understand that we can use math to think about things that have no counterpart in a physical lived experience; imaginary numbers don’t exist but are crucial to understanding electrical systems . Zero also helps us understand its antithesis, infinity, in all of its extreme weirdness. (Did you know that one infinity can be larger than another ?)

Why zero is so damn useful in math

Zero’s influence on our mathematics today is twofold. One: It’s an important placeholder digit in our number system. Two: It’s a useful number in its own right.

The first uses of zero in human history can be traced back to around 5,000 years ago, to ancient Mesopotamia. There, it was used to represent the absence of a digit in a string of numbers.

Here’s an example of what I mean: Think of the number 103. The zero in this case stands for “there’s nothing in the tens column.” It’s a placeholder, helping us understand that this number is one-hundred and three and not 13.

Okay, you might be thinking, “this is basic.” But the ancient Romans didn’t know this. Do you recall how Romans wrote out their numbers? 103 in Roman numerals is CIII. The number 99 is XCIX. You try adding CIII + XCIX. It’s absurd. Placeholder notation is what allows us to easily add, subtract, and otherwise manipulate numbers. Placeholder notation is what allows us to work out complicated math problems on a sheet of paper.

If zero had remained simply a placeholder digit, it would have been a profound tool on its own. But around 1,500 years ago (or perhaps even earlier ), in India , zero became its own number, signifying nothing. The ancient Mayans, in Central America, also independently developed zero in their number system around the dawn of the common era.

In the seventh century, the Indian mathematician Brahmagupta wrote down what’s recognized as the first written description of the arithmetic of zero:

When zero is added to a number or subtracted from a number, the number remains unchanged; and a number multiplied by zero becomes zero.

Zero slowly spread across the Middle East before reaching Europe, and the mind of the mathematician Fibonacci in the 1200s, who popularized the “Arabic” numeral system we all use today.

From there, the usefulness of zero exploded. Think of any graph that plots a mathematical function starting at 0,0. This now-ubiquitous method of graphing was only first invented in the 17th century after zero spread to Europe. That century also saw a whole new field of mathematics that depends on zero: calculus.

You may recall from high school or college math that the simplest function in calculus is taking a derivative. A derivative is simply the slope of a line that intersects with a single point on a graph.

To calculate the slope of a single point, you usually need a point of comparison: rise over run . What Isaac Newton and Gottfried Leibniz discovered when they invented calculus is that calculating that slope at a single point involves getting even closer, closer, and closer — but never actually — dividing by zero.

“All infinite processes [in math] pivot around, dance around, the notion of zero,” Robert Kaplan says. Whoa.

Why is zero so profound as a human idea?

We’re not born with an understanding of zero. We have to learn it, and it takes time.

Elizabeth Brannon is a neuroscientist at Duke University who studies how both humans and animals represent numbers in their minds. She explains that even when kids younger than 6 understand that the word “zero” means “nothing,” they still have a hard time grasping the underlying math. “When you ask [a child] which number is smaller, zero or one, they often think of one as the smallest number,” Brannon says. “It’s hard to learn that zero is smaller than one.”

In experiments, Brannon will often play a game with 4-year-olds. She’ll put out a pair of cards on a table or screen. And each card will have a number of objects on it. One card will have two dots, for instance. Another will have three. Here’s an example of what they might see.

She’ll simply ask the kids to pick the card with the fewest number of objects. When a card with nothing on it is paired with a card with one object on it, less than half the kids will get the answer right.

So what happens to make it all click?

Andreas Nieder , the cognitive scientist from Germany, hypothesizes there are four psychological steps to understand zero, and each step is more cognitively complicated than the one before it.

Many animals can get through the first three steps. But the last stage, the most difficult one, is “reserved for us humans,” Nieder says.

The first is a just having the simple sensory experience of stimulus going on and off. This is the simple ability to notice a light flickering on and off. Or a noise turning on and off.

The second is behavioral understanding. At this stage, not only can animals recognize a lack of a stimulus, they can react to it. When an individual has run out of food, they know to go and find more.

The third stage is recognizing that zero, or an empty container, is a value less than one. This is tricky, though a surprising number of animals, including honey bees and monkeys, can recognize this fact. It’s understanding “that nothing has a quantitative category,” Nieder says.

The fourth stage is taking the absence of a stimulus and treating as it as a symbol and a logical tool to solve problems. No animal outside of humans, he says, “no matter how smart,” understands that zero can be a symbol.

But even well-educated humans can still stumble a bit when thinking about zero. Studies have shown that adults take a few moments longer to recognize the number zero compared to other numerals. And when Brannon’s pick-the-lowest-number-card experiment is repeated with adults, they take slightly longer when deciding between zero and one, than when comparing zero to a larger number.

That suggests that zero, even for adults, takes an extra effort of brain power to process.

What else can understand nothing?

We may not be born with the ability to understand zero. But our capacity to learn it may have deep evolutionary roots, as some new science shows us.

The fourth step in thinking of zero — that is thinking of zero as a symbol — may be unique to humans. But a surprising number of animals can get to step three: recognizing that zero is less than one.

Even bees can do it.

Scarlett Howard, a PhD student at Royal Melbourne Institute of Technology, recently published an experiment in Science that’s almost identical to the one Brannon did with kids. The bees chose the blank page 60 to 70 percent of the time. And they were significantly better at discriminating a large number, like six, from zero, than they were in discriminating one from zero. Just like the kids.

This is impressive, considering that “we’ve got this big mammalian brain but bees have a brain that’s so small weighs less than a milligram,” Howard says. Her research group is hoping to understand how bees do these calculations in their minds, with the goal of one day using those insights to build more efficient computers.

In similar experiments, researchers have shown that monkeys can recognize the empty set (and are often better at it than 4-year-old humans). But the fact that bees can do it is kind of amazing, considering how far they are away from us on the evolutionary trees of life. “The last common ancestor between us and the bees lived about 600 million years ago, which is an eternity in evolutionary times,” Nieder says.

We humans might have only come to understand zero as a number 1,500 years ago. What the experiments on bees and monkeys show us is that it’s not just the work of our ingenuity. It’s also, perhaps, the culminating work of evolution.

There are still great mysteries about zero. For one, Nieder says “we hardly know anything” about how the brain physically processes it. And we don’t know how many animals can grasp the idea of nothing as a quantity.

But what mathematics has clearly shown us is that when we investigate nothing, we’re bound to find something.

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Published on August 30th, 2018 | by Harmonist staff

How India Gave Us the Zero

In Gwalior, a congested city in the centre of the India, an 8th-Century fort rises with medieval swagger on a plateau in the town’s heart. Gwalior Fort is one of India’s largest forts; but look among the soaring cupola-topped towers, intricate carvings and colourful frescoes and you’ll find a small, 9th-Century temple carved into its solid rock face.

Chaturbhuj Temple is much like many other ancient temples in India – except that this is ground zero for zero. It’s famous for being the oldest example of zero as a written digit: carved into the temple wall is a 9th-Century inscription that includes the clearly visible number ‘270’.

The invention of the zero was a hugely significant mathematical development, one that is fundamental to calculus, which made physics, engineering and much of modern technology possible. But what was it about Indian culture that gave rise to this creation that’s so important to modern India – and the modern world?

Nothing from nothing

I recalled a TED talk by renowned Indian mythologist Devdutt Pattanaik in which he tells a story about Alexander the Great’s visit to India. The world conqueror apparently met what he called a ‘gymnosophist’ – a naked, wise man, possibly a yogi – sitting on a rock and staring at the sky, and asked him, “What are you doing?”.

“I’m experiencing nothingness. What are you doing?” the gymnosophist replied.

“I am conquering the world,” Alexander said.

They both laughed; each one thought the other was a fool, and was wasting their life.

This story takes place long before that first zero was inscribed on Gwalior’s temple wall, but the gymnosophist meditating on nothingness does in fact have a connection to the digit’s invention. Indians, unlike people from many other cultures, were already philosophically open to the concept of nothingness. Systems such as yoga were developed to encourage meditation and the emptying of the mind, while both the Buddhist and Hindu religions embrace the concept of nothingness as part of their teachings.

Dr Peter Gobets, secretary of the Netherlands-based ZerOrigIndia Foundation , or the Zero Project, which researches the origins of the zero digit, noted in an article on the invention of zero that “Mathematical zero (‘shunya’ in Sanskrit) may have arisen from the contemporaneous philosophy of emptiness or Shunyata [a Buddhist doctrine of emptying one’s mind from impressions and thoughts]”.

In addition, the nation has long had a fascination with sophisticated mathematics. Early Indian mathematicians were obsessed with giant numbers, counting well into the trillions when the Ancient Greeks stopped at about 10,000. They even had different types of infinity.

Hindu astronomers and mathematicians Aryabhata, born in 476, and Brahmagupta, born in 598, are both popularly believed to have been the first to formally describe the modern decimal place value system and present rules governing the use of the zero symbol. Although Gwalior has long been thought to be the site of the first occurrence of the zero written as a circle, an ancient Indian scroll called the Bhakshali manuscript, which shows a placeholder dot symbol, was recently carbon dated to the 3rd or 4rd Centuries. It is now considered the earliest recorded occurrence of zero.

Marcus du Sautoy, professor of mathematics at the University of Oxford, is quoted on the university’s website as saying, “[T]he creation of zero as a number in its own right, which evolved from the placeholder dot symbol found in the Bakhshali manuscript, was one of the greatest breakthroughs in the history of mathematics. We now know that it was as early as the 3rd Century that mathematicians in India planted the seed of the idea that would later become so fundamental to the modern world. The findings show how vibrant mathematics have been in the Indian sub-continent for centuries.”

But equally interesting are the reasons as to why the zero wasn’t developed elsewhere. Although the Mayans and Babylonians (and many other civilisations) may have had a concept of zero as a placeholder, the idea is not known to have developed as a number to be used in mathematics anywhere else. One theory is that some cultures had a negative view of the concept of nothingness. For example, there was a time in the early days of Christianity in Europe when religious leaders banned the use of zero because they felt that, since God is in everything, a symbol that represented nothing must be satanic.

So maybe there is something to these connected ideas, to the spiritual wisdom of India that gave rise to meditation and the invention of zero. There’s another connected idea, too, which has had a profound effect on the modern world.

The concept of zero is essential to a system that’s at the basis of modern computing: binary numbers.

This article was originally published at BBC , and is partially reproduced here without the permission of the author, who is not affiliated with this website or its views.

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By Roger Highfield on 14 September 2017

Illuminating india: starring the oldest recorded origins of ‘zero’, the bakhshali manuscript.

The invention of zero, or rather the realisation that it was a number just like any other, was one of the greatest conceptual leaps in the history of mathematics, one that would spur the rise of modern science.

Today it was announced that the written record of zero, in the region which discovered this influential digit, dates back four centuries further than most scholars had thought, thanks to carbon dating of an ancient manuscript, written on 70 leaves of birch bark, held at the University of Oxford’s Bodleian Libraries.

Oxford’s dating project has been surprisingly revealing about the origins of the delicate and fragmented Bakhshali manuscript, one of the star objects in a forthcoming exhibition about Indian science and technology over the past five millennia, that will form part of the Museum’s Illuminating India season from October.

This carbon dating of the manuscript, shows that it is formed of leaves that are nearly 500 years apart in age, with some pages dating from as early as the 3rd to 4th century and others dating from the 8th and 10th centuries.

The field of mathematics provides the logical fabric of modern life – today’s society would falter without zero – so it is hard to imagine a time when zero was, well, zero and mathematics was expressed not by numerals but in verse.

When a written version of zero crystallised from verse in its birthplace in South Asia, it appeared in Sanskrit (not standard Sanskrit, but features of what is called Buddhist Hybrid Sanskrit), as well as other Middle-Indo Aryan languages (Prakrit and Apabhraṃśa) and Old Kashmiri.

Dots in a manuscript, found in a field in 1881 by a farmer in Bakhshali, located near modern Peshawar, Pakistan, mark the earliest written record in the location where zero was first incorporated into the system of numbers we know today, a remarkable moment in the history of mathematics and the development of modern thinking.

Not only is it the only known Indian document on mathematics from such an early period, it also shows all 10 decimal digits which included a dot for zero, and might have been used by Buddhist merchants in trading.

Other ancient peoples were by no means blank when it came to zero: the Babylonians and Mayans realised it was handy to have a placeholder to signal something was absent, using a double wedge or a shell shape.

But in India the symbol grew into a numeral that exists in its own right. You could add it, subtract it, multiply it. Division remains a bit trickier, but that challenge spurred the development of a gloriously strange field of mathematics as these mathematical pioneers wrestled with infinities. By comparison, zero happened with the Babylonian or Mayan placeholder zeroes.

“Why it is so exciting is that this zero in India is the seed from which the concept of zero as a number in its own right, represented by the same dot or circle, will emerge some centuries later, something many regard as one of the of the great moments in the history of mathematics,” comments Marcus du Sautoy, Professor of Mathematics at the University of Oxford.

The age of the Bakhshali manuscript, and thus the dot notation for zero, has been the subject of much scholarly debate. Before this new research, most would say that the manuscript dates back to somewhere between the 8th and 12th century, according to Camillo Formigatti, John Clay Sanskrit Librarian at the Bodleian.

Earlier this year the manuscript was carbon dated for the first time by a team including Formigatti; David Howell, Head of Heritage Science at the Bodleian Libraries; Gillian Evison, Head of the Bodleian Libraries Oriental Section; Virginia Llado-Buisan, Head of Conservation and Collection Care at the Bodleian Libraries and David Chivall, Chemistry Laboratory Manager at the Oxford Radiocarbon Accelerator Unit, which has worked on many significant projects, notably dating the Turin Shroud.

Each sample – between 1.4 mg and 1.8 mg of bark – was taken from an unmarked area of different birch folios. The team measured levels of radioactive carbon-14, compared to stable carbon-12 in each folio, which is continually produced in the upper atmosphere as cosmic rays strike the Earth. Plants and trees incorporate the radiocarbon, in the form of carbon dioxide via photosynthesis and lock up the carbon in their structures, for instance in the birch bark on which the manuscript was written, because radiocarbon decays with a half-life of 5,730 years, once the bark is formed, the amount of radiocarbon within it continually decreases, while the amount of stable carbon remains constant. In this way, the Oxford team could work out how long ago the bark was formed by measuring the ratio of radiocarbon to stable carbon.

The first surprise was that the results reveal that the three samples date from different centuries, one (Folio 33) dated from 885-993 CE, the expected date, but another (Folio 17) dated from 680-779 CE and another (Folio 16) dated from 224-383 CE. That was the biggest surprise of all.

Previous dating methods had been estimated based on the style of writing and the literary and mathematical content and, though a 3rd/4th century date was not totally unprecedented among some scholars, it had not been considered realistic by most of the academic community. The emergence of proto-zero in 200-400 BC comes a long time before the 7th Century, when the astronomer Brahmagupta became the driving force behind zero’s ascendance to greatness. His text, Brahmasphutasiddhanta, The Opening of the Universe, written in 628 CE, is the first to treat zero as a number in its own right and to include a discussion of the arithmetic of zero.

In fact, even more remarkable, the story of zero must date back even further than the Bakhshali manuscript since it is likely a recording of earlier manuscripts, which in turn were based on even earlier verbal representations of mathematics.

Around the time of Christ, scholars in south Asia probably realised the importance of zero and this makes sense because this abstraction thrived on local religious and spiritual beliefs. Jain mathematicians were not intimidated by the idea of the void, or of infinite space, unlike those in the West. The reason is that zero echoed ‘Sunyata’, a Buddhist concept of emptiness.

There was a democratic dimension to this number too: zero gave people power as they could do calculations without the need for an abacus. The story goes that when they did their sums in the sand, early mathematicians came to realise that as they removed stones that represented something, they left a hole behind, which is how we ended up with an empty circle as a zero.

From South Asia, zero migrated into the Middle East, where it was championed by Islamic scholars. In the 8th century the great Arab mathematician al-Khawarizmi adopted it. If only the sixth-century monk, Dionysius Exiguus (“Dennis the Short” from what today is Dobruja, in Romania and Bulgaria), had known about zero when he devised Anno Domini, year of the Lord. By his reasoning, 1 CE immediately followed 1 BC, and his omission of zero would cause much confusion.

Eventually zero arrived in Europe, where it exerted an extraordinary influence. For example, it allowed Isaac Newton in the mid-17th century to invent calculus, which charts change by focusing on “instantaneous” change, changes over tiny intervals that, effectively, are zero.

That is how Newton found that acceleration could be modelled by simple laws of motion. The rise of calculus helped to drive the rise of modern science which in turn has been applied through myriad technologies and generated even more unsettling insights into the nature of zero, not least the ultimate zero, the Big Bang, which saw the birth of space, time and the universe 13.8 billion years ago.

‘The Bakhshali manuscript helps to illustrate how vibrant mathematics has been in India and the east for centuries,’ says Prof du Sautoy. ‘It is also testament to the way mathematics crosses cultural, historical and political boundaries.’

The Professor of Mathematics adds that it is ‘deeply moving to see this dot on an ancient piece of birch bark and recognise how much I have to thank those mathematicians of the past who built the mathematical edifice I now stand on top of.’

Written by Roger Highfield and Matt Kimberley, curator of Illuminating India: 5000 Years of Science and Innovation.

A folio from the Bakhshali manuscript will go on public display at the Science Museum as a centrepiece of the major exhibition Illuminating India: 5000 Years of Science and Innovation , opening 4 October 2017.

Zero—a Tangible Representation of Nonexistence: Implications for Modern Science and the Fundamental

• Published: 06 September 2021
• Volume 60 , pages 655–676, ( 2021 )

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A defining characteristic of modern science is its ability to make immensely successful predictions of natural phenomena without invoking a putative god or a supernatural being. Here, we argue that this intellectual discipline would not acquire such an ability without the mathematical zero. We insist that zero and its basic operations were likely conceived in India based on a philosophy of nothing , and classify nothing into four categories— balance , absence , emptiness and nonexistence . We argue that zero is a tangible representation of nonexistence and constitutes all nonzero numbers, which together represent existence. It appears that zero’s journey out of India somewhat separated its mathematical and philosophical aspects, with the former being more valued by some cultures and the latter by others. The European culture, in which modern science grew, largely ignores a philosophy of nothing due to a deep-rooted Greek philosophical base, although this science relies on the notion of nonexistence through zero. Consequently, zero is a mere number of convenience without its foundational philosophy in science, and techniques to circumvent zero are developed. We insist that, while such techniques contribute to the progress of science and mathematics within the current framework, a tendency to avoid zero and its philosophy leads to approximations and may hinder a deeper understanding. Finally, we argue that nonexistence may notionally constitute existence, and hence may be the fundamental. This implies that, if a supernatural being exists , it is not the fundamental. The independence of modern science from a supernatural being is consistent with this.

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Ideas Magazine | Feature

The Invention of Nothing

The history of zero, shunya , and creation ex nihilo

In the beginning God created the heavens and the earth. And the earth was without form, and void; and darkness was on the face of the deep. And the Spirit of God was hovering over the face of the waters.

So opens the account of Creation in the King James Bible, a poetic evocation of the obscure relationship between absence and presence, nothing and everything. This is difficult, slippery territory. In working to understand the nature of this relationship, we are drawn to the very limits of language and conceptual thought.

The Hebrew word tohu —here translated as “without form”—occurs nineteen times in the Bible, rendered in varying contexts as wasteland, wilderness, an empty place, nothingness, vanity, and confusion. Bohu (“void”) appears only three times: once in Genesis 1:2 (above), once again in Isaiah 34:11 (there translated as “emptiness”), and a third time in Jeremiah 4:23, in direct reference to Genesis and so preserving the translation as “void.”

These are rarely used, fearful words. According to a note in the Oxford Annotated Bible, the formless void that somehow precedes or underlies Creation is associated with an ancient belief that the world originated from “a watery chaos, personified as a dragon in the Babylonian creation epic.” This “dragon” is the Leviathan referred to in Job and the Psalms, a fire-spitting, serpentine creature with fangs and claws—a graphic embodiment of our primal terror in the face of an abyss of nothingness undefined by time or space, an impenetrable, ungraspable, fathomless black hole out of which we emerge and into which we inevitably return.

This ancient story of the universe emerging ex nihilo (“from nothing”) resonates with a mythopoetic authority that has captivated the imagination of generations of commentators who struggled to come to terms with their own fears of what cannot, by its nature, be known. Like his Hebrew predecessors, the Greek philosopher Aristotle (384–322 BCE) found any reference to absolute nothingness troubling. For Aristotle, the problem was not so much poetic or psychological as rational. In his Physics he maintained that matter could have no beginning, as a beginning would itself have to begin, and that second beginning would in turn have to begin, implying an infinite regress and therefore a logical fallacy. One might wonder what exactly is the difference between an endless regress of beginnings and no beginning at all.

Aristotle’s opinion was enormously influential and more or less prevailed for centuries (even though it clearly rejected the biblical account of the creation) until Sa’adiah ben Yosef  Gaon (882–942)—a Jewish theologian writing in Arabic—composed his masterwork, The Book of Beliefs and Opinions , in which he countered Aristotle’s fear of infinite regress with a rigorous, systematic defense of the idea of creation from nothing. Over time, his arguments were refined by Muslim scholars, who carried them across the Middle East into North Africa and from there into Moorish Spain, where they caught the attention of the 12th-century Sephardic philosopher Maimonides and influenced his efforts to harmonize Aristotelian reason with the teachings of the Bible.

Carried forward by Jewish philosopher-mystics and Christian apophatic theologians, the doctrine of creation from nothing increasingly gained prestige until, at long last, it became respectable for Christian intellectuals to conceive of a nothing out of which everything is born. In 1215, at the fourth Lateran Council, Pope Innocent III certified creatio ex nihilo as the official doctrine of the Roman Catholic Church. After a thousand years the conflict between Aristotle and the Leviathan was resolved. The serpent prevailed.

B ut how is it that Sa’adiah ben Yosef Gaon’s ideas gained so much traction among European intellectuals, both Jewish and Christian? Even the most creative mind does not operate in a cultural vacuum. Where did he derive the inspiration for his radically new understanding of the relationship between absence and presence? While there may well be no single answer to these questions, history provides some tantalizing clues.

Rabbi Sa’adiah Gaon was born in Egypt, but he lived and worked for eleven years in Baghdad under the Abbasid Caliphate, during what is often considered the Golden Age of Islam. Arabs had conquered Persia in 651 CE, incorporating it into a vast Islamic empire that stretched from Spain to the frontiers of South Asia. During the 7th and 8th centuries, foreign ideas flowing west out of India into Persia exerted a profound influence on Muslim intellectuals,who in turn passed these ideas along to Europe. Among them was the ten-digit Indian numerical system, incorporating the concept of a number that is, in itself, nothing. This system was described in 825 CE by the Persian mathematician Muhammad Ibn Musa al-Khwarizmi (ca. 780–850) in a work synthesizing Greek and Indian thought. The Sanskrit name for this mysterious number was shunya . The phonetically similar Arabic word sifr (“empty”) was adopted as a translation for Sanskrit shunya , which was represented by a small, open circle.

By the early 9th century the Moors had conquered Spain and Sicily, bringing with them this revolutionary mathematical concept; al-Khwarizmi’s book was translated into Latin in 1145 and was, for the next four centuries, the principal mathematical textbook in European universities (the English word algorithm is derived from his name). In Italy, sifr became zefiro , zefro , or zevero , corresponding to the French zéro , which—minus the accent—made its way into English.

Though Sa’adiah Gaon was born some thirty years after al-Khwarismi’s death and does not appear to have directly referred in his writing to the concept of zero, it is difficult to believe he would not have been familiar with al-Khwarizmi’s work. In any case, Sa’adiah Gaon’s defense of creation ex nihilo and al-Khwarizmi’s explication of the mathematical concept of zero moved together from Persia through the Middle East, across North Africa and into Moorish Spain, where both were simultaneously diffused into European culture.

Z ero is the symbol for a number that is at once both nothing and something. In his book The Nothing That Is: A Natural History of Zero , Robert Kaplan nicely captures the paradoxical nature of zero: “Names belong to things, but zero belongs to nothing. It counts the totality of what isn’t there.”

Zero as a placeholder—used, for example, in a base ten system to mark the difference between one (1) and ten (10)—was common in the ancient world. But for the ancients a placeholder was not itself a number. Numbers have computational properties: they are used to count things; numbers don’t apply where there’s nothing to count. All of this was turned on its head by Indian mathematicians, who conceived, for the first time, of zero as having computational properties, though admittedly unlike the properties of any other number. First of all, addition and subtraction with zero changes nothing: add zero to any number—including itself—and the sum is that same number; subtract zero from any number and once again the number remains unchanged. But multiplication and division yield even more startling results. Multiply any number by zero and the product is zero; divide by zero and no matter what the dividend the quotient is infinity —which mathematicians still regard not as a number but rather as an exceedingly odd “concept.” As Charles Seife writes in Zero: The Biography of a Dangerous Idea , “Zero is powerful because it is infinity’s twin. They are equal and opposite, yin and yang. They are equally paradoxical and troubling.” In other words, zero is where nothing meets and mingles not just with some particular thing but with everything . As a mathematical concept, zero locates the interface between absence and presence, and in this respect it defies the law of noncontradiction, which states that contradictory propositions cannot both be true in the same sense at the same time. Considered to be one of the “laws of thought” and a cornerstone of reason, the law of noncontradiction finds its classical source in Aristotle’s metaphysics. And so, as Seife has it, “Zero conflicted with the fundamental philosophical beliefs of the West, for contained within zero are two ideas that were poisonous to Western doctrine. Indeed, these concepts would eventually destroy Aristotelian philosophy after its long reign. These dangerous ideas were the void and the infinite.”

No one knows exactly where the idea of “zero” as a placeholder first emerged, but historians agree that regardless of where it originated, India was where zero was transformed from mere placeholder to a legitimate number in its own right. And it was this transformation—a prodigious feat of imagination—that gave zero its mysterious power to absorb and defy all contradictions.

The earliest known reference to mathematical zero appears in the Chandah Shastra , a text on Sanskrit prosody attributed to an otherwise unknown author named Pingala and dated to sometime in the first few centuries BCE. The text unfortunately does not include any example of symbolic notation, but Pingala explicitly uses the Sanskrit word shunya to refer to the result of subtracting a number from itself. The oldest recorded use of symbolic notation for zero as a number is found in a birchbark text known as the Bakhshali manuscript, which has been radiocarbon dated to as early as the 3rd century CE and seems to have been intended for use by merchants as a practical manual on arithmetic. Here zero is indicated by a solid dot.

India was where zero was transformed from mere placeholder to a legitimate number in its own right. And it was this transformation—a prodigious feat of imagination—that gave zero its mysterious power to absorb and defy all contradictions.

By the end of the 5th century the same word shunya appears in another text, the Aryabhatiya , in the context of a fully developed system of decimal place-value notation. In a 7th-century commentary on the Aryabhatiya , the mathematician Bhaskara used a circle to represent shunya , which is the earliest recorded instance of the notation that has now become virtually universal. At that time, however, the circle was perhaps not yet standardized, since a mathematician by the name of Brahmagupta, a contemporary of Bhaskara’s, used the same solid dot that occurs in the Bakhshali manuscript. In his Brahmasphuta Siddhanta , composed around 650 CE, Brahmagupta referred to the dot as shunya or, alternatively, kha —literally a cavity, hollow, or empty space, and by extension, the Sanskrit word for “sky.” Nevertheless, the use of shunya seems at this point to have become more or less fixed. Brahmagupta’s treatise is unprecedented, however, in its meticulous analysis of zero in the context of negative numbers and corresponding algebraic operations. His work leaves no question that by the 7th century, Indian mathematicians had fully conceptualized the role of mathematical zero in the sense familiar to us now.

As it happens, however, this is only half the story of zero’s Indian history. In ancient India, zero was not only a mathematical concept.

T he Sanskrit word shunya is routinely used in Mahayana Buddhist texts dating back to the first few centuries BCE; which is to say, its appearance both as a revolutionary mathematical term and as the expression of a profound, intuitive understanding of the nature of reality—the mark of “transcendent, liberating wisdom” ( prajna-paramita )—seems to have occurred simultaneously in India. The paradoxical characteristic of mathematical zero—as a nothing that is not only something but everything—features in the Buddhist notion of shunya , but its implications are no longer merely abstract or computational. In the scriptures on perfect wisdom, shunya is presented as a fundamental truth of all existence, a truth fully appreciated by spiritual beings known as bodhisattvas, who have achieved this profound insight only as the result of long study and contemplative practice. The famous Heart Sutra opens by telling us that the bodhisattva Avalokiteshvara, “moving in the stream of perfect wisdom,” looked down over the world and saw that “zero-ness” ( shunya-ta ) is the essential nature of every element of experience—everything that makes up our mental and physical reality.

Here… form is zero-ness and zero-ness itself is form; zero-ness does not differ from form, and form does not differ from zero-ness. Whatever is form, that is zero-ness; whatever is zero-ness, that is form. The same is true of feelings, perceptions, impulses, and consciousness.

Nor is the ancient notion of zero as a placeholder marginalized in this literature. In the scriptures on perfect wisdom, this characteristic of zero is an integral component of its status as both absence and presence simultaneously. To say that every element of experience—every dharma —is zero is to say that, like zero, the appearance of individual, self-sufficient things is nothing more than appearance; there is no actual “thing,” no individual physical or mental object that truly exists as it appears. The mental or physical object that seems to exist separately from other such things in fact exists only as a placeholder. Which is to say, the individual exists only in relation to what it is not, and what it is not is literally everything else—an infinitude of other apparently individual things. This is the sense in which dharmas are said to be “devoid of essential nature,” which is the same as saying that their essential nature is zero-ness.

And so in the Perfection of Wisdom in Eight Thousand Lines —perhaps the oldest surviving text of this genre—we are asked, rhetorically: “To what dharma could I point and say that ‘it exists’ or ‘it doesn’t exist?’”

It is precisely through their essential nature that dharmas are not a thing. Their essential nature is no-nature, and their no-nature is their essential nature. All dharmas have only one characteristic, which is no characteristic at all.

“‘All things are no-things,’ taught the Tathagata [the Buddha], ‘therefore they are things.’” Perfect wisdom, then, is a deep understanding that breaks free of our normal habits of thinking and speaking, habits that compel us to both conceive and perceive individual things literally as either existing or not existing, as either this or that. Rather, as seen through the eye of perfect wisdom, things are not things, and not things are things, which means that they only seem to arise and pass away. This is true, according to the Diamond Sutra , for living beings as well, who merely appear to be self-contained individuals subject to birth and death: “‘Beings, beings’… the Tathagata has taught that they are all no-beings. In this way has he spoken of ‘all living beings.’” Nothing whatsoever is exempted: “This entire universe the Tathagata has taught as no-universe. In this sense it is called a ‘universe.’”

Therefore, Shariputra, in zero-ness there is no form, nor feeling, nor perception, nor impulse, nor consciousness; no eye, ear, nose, tongue, body, mind; no forms, sounds, smells, tastes, tactile objects, or objects of mind.… There is no ignorance, no extinction of ignorance … no decay and death and no end to decay and death. There is no suffering, no origin, no cessation, no spiritual path. There is nothing to realize, nothing to attain.

“It is on account of this,” explains the Perfection of Wisdom in Eight Thousand Lines , “that the Tathagata does not fully know the character of any dharma.” What is literal or concrete can be fully known or grasped, its character can—at least in principle—be understood empirically, rationally analyzed and explained; what is metaphorical is “as if,” and “as if” can only be intuited.

Consider, in this context, what Robert Kaplan has to say about zero as the interface of nothing and everything:

It is as if there were a layer behind appearances that had no qualities, but took on the character of its surroundings, accommodating itself to our interpretations, as ambergris acquires and retains fugitive fragrances, giving us perfume. Shunya isn’t so much vacancy, then, as receptivity, a womb-like hollow ready to swell—and indeed it comes from the root shvi , meaning swelling. Its companion kha derives from the verb “to dig,” and so carries the sense of “hole”: something to be filled. . . . This is the zero of the counting board: a column already there, but with no counters yet in it. This is the zero of the place-holder notation, having no value itself but giving value by its presence to other numerals. These same qualities belong to the variable, the unknown: a potential which the different circumstances of the equations it lies in will differently realize. The background shift is from counters taking their value from being in different places, to a single, receptive place whose circumstances will reveal its hidden value.

The concept of shunya evokes the ambiguous, ungraspable nature of what only appears to be literal, concrete truth or reality. The Indian mathematician Bhaskara acknowledges as much when, in a discussion of mathematical zero, he writes: “The arithmetic of known quantity . . . is founded on that of unknown quantity; and . . . questions to be solved can hardly be understood by any, and not at all by such as have dull apprehensions, without the application of unknown quantity.” Perhaps the most eloquent classical passage on this aspect of the zero-ness of things comes from the Diamond Sutra :

A phantom’s mask, a shooting star, a guttering flame. A sorcerer’s trick, a bubble swept On a swiftly moving stream. A flash of lightning among dark clouds. A drop of dew, A dream. So should one view all conditioned things.

This article is adapted from the essay “Absence and Presence” in the posthumous collection   What I Don’t Know About Death: Reflections on Buddhism and Mortality  by C. W. Huntington Jr., ©2021. Reprinted by permission of Wisdom Publications.

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Who invented Zero?

The concept of zero has not always been around, however, the introduction of zero brought a lot of changes not only in math but also in the general life of people. Zero has so many different names, for example, ‘null’, ‘nil’, ‘0’ as a digit, ‘sunya’ in Sanskrit, and so on. It is fascinating how the origin of zero bought changed and now it is used as a prime digit in mathematics. Before learning about the modern zero, let’s learn about the origin of zero in India.

Who Invented Zero? Aryabhatta

Table of Content

Origin of Zero in India

History of zero in india, modern zero, who actually invented zero, how zero got named, journey of origin of zero, early concepts of empty space, ancient indian contributions, transmission to the islamic world, incorporation into western mathematics, zero as a conceptual breakthrough, conclusion – who invented zero, faqs on who invented zero.

The invention of zero is one of the most significant milestones in the history of mathematics. Zero is not just a numeral but a concept that has revolutionized mathematics, science, and engineering. Its introduction allowed for the development of the decimal system, algebra, calculus, and more. Understanding the origins of zero helps us appreciate its profound impact on human knowledge and technological advancement.

The origin of zero in India came from a well-known astronomer and mathematician of his time, Aryabhatta. The well-known scientist used zero as a placeholder number. In the 5th century, Aryabhatta introduced zero in the decimal number system and introduced it in mathematics. After Aryabhatta, Brahmagupta described rules for zero in the 7th century. The most evident proof of the origin of zero in mathematics is mentioned in the oldest manuscript of India known as the ‘Bakshali manuscript’, zero was used as a dot in the book.

The history of zero in India goes back to the 5th century. In the 5th century, a well-known mathematician and astronomer named Aryabhatta introduced zero in India.

Earlier, zero was represented as a dot in mathematics and later when it reached Arab, an oval shape was given to the number that we today know as the ‘0’ digit. This is the reason why zero belongs to the Hindu-Arabic numeral system. After Aryabhatta, Bramhaputra is credited for zero, in the 7th century, Bramhaputra started using zero in mathematical operations.

The modern zero was later introduced when zero reached China from India and later reached the Middle East.

In around 773 AD, the mathematician Mohammad ibn-Musa al-Khowarizmi studied and synthesized Indian arithmetic and showed how zero functioned in the system of formulas he called ‘al-jabr’—today known as algebra.

Around 1200 AD, Italian mathematician Fibonacci introduced zero in Europe. Initially, zero was called ‘Sunya’ in India, it was called ‘Sifr’ in the middle east when it reached Italy, it was named ‘Zefero’ and later in English, it was called ‘Zero’.

The specific individual credited with the invention of zero is not known. The development of zero as a mathematical concept was likely a gradual process that involved contributions from multiple cultures and mathematicians over centuries.

It is difficult to attribute the invention of zero to a single person because it emerged as a result of the collective efforts and advancements in various civilizations.

When zero was introduced in India, it was called ‘Sunya’ which is a Sanskrit term for zero. Later when it reached the middle east, it was named ‘Sifr’, after the Arabs, when zero was introduced by Italians, they named it ‘Zefero’ which was later transformed to ‘Zer’o’ in French, the modern zero is also inspired by the same term. Today Zero is universally used.

The discovery and origin of the concept of zero mark a crucial milestone in the history of mathematics and human thought. The journey of zero’s discovery and its evolution into a fundamental mathematical concept spans millennia and traverses different cultures and civilizations.

The concept of zero, or the idea of nothingness, has intrigued thinkers since ancient times. Early civilizations such as the Babylonians and the Maya developed placeholder symbols to denote empty spaces in numerical systems, but these symbols did not necessarily represent the abstract notion of zero as a number in its own right.

One of the most significant developments in zero’s history occurred in ancient India. The earliest recorded use of a symbol for zero as a numerical digit dates back to the 9th century CE in the Indian subcontinent.

The Indian mathematician and astronomer Brahmagupta, in his seminal work “Brahmasphutasiddhanta,” discussed the properties of zero and its role as a placeholder and as a number in mathematical operations.

The concept of zero spread from India to the Islamic world, where scholars further developed its mathematical significance. Mathematicians such as Al-Khwarizmi and Al-Kindi played pivotal roles in transmitting Indian mathematical knowledge, including the concept of zero, to the Arabic-speaking world.

The introduction of zero into Western mathematics occurred through the translation of Arabic texts into Latin during the Middle Ages. Fibonacci, an Italian mathematician, encountered the Hindu-Arabic numeral system, which included zero, during his travels to North Africa and the Middle East. His influential book “Liber Abaci” helped popularize the use of Hindu-Arabic numerals, including zero, in Europe.

The recognition of zero as a numerical digit and as a placeholder revolutionized mathematics and laid the groundwork for advanced mathematical concepts such as place value, decimal notation, and the development of algebra and calculus. Zero’s inclusion in numerical systems provided a powerful tool for computation, measurement, and abstraction, enabling advancements in fields ranging from astronomy and physics to economics and engineering.

Zero is a basic idea in mathematics that has important applications in many other fields. It is an essential part of the decimal numbering system and acts as a placeholder, signifying the lack of a quantity or value. In arithmetic operations like addition, subtraction, multiplication, and division, zero is essential because it frequently acts as a neutral element or identity. Additionally, it makes it possible to represent negative integers and fractions, which broadens the range of possible mathematical expressions and computations. Beyond mathematics, zero has deep philosophical and cultural meaning as a symbol of nothingness, emptiness, and the void.

What is the Origin of Zero in India?

Aryabhata, a great astronomer of the classic age of India was the one who invented the digit “0” (zero) for which he became immortal but later on is given to Brahmagupta who lived around a century later 22, another ancient Indian mathematician. The first numeral zero comes from a Hindu astronomer and mathematician Brahmagupta in 628. The symbol to represent  the numeral was a dot underneath a number.

How Zero got named?

Zero was called ‘Sunya’ in India, it was called ‘Sifr’ in the middle east, when it reached Italy, it was named ‘Zefero’ and later in English, it was called ‘Zero’.

Who invented zero, Aryabhatta or Brahmagupta?

Aryabhatta is credited for using zero in the decimal system and introducing zero in mathematics. Brahmagupta, an astronomer and mathematician from India used zero in mathematical operations like addition and subtraction. Aryabhatta introduced zero in 5th century and Brahmagupta introduced zero in calculations in around 628 AD. Therefore, it can be said that Aryabhatta invented zero.

When did Zero came to Europe?

Zero came to Europe during the Middle Ages, notably through the translation of Arabic mathematical texts into Latin, with Fibonacci’s “Liber Abaci” contributing significantly to its adoption and popularization in Western mathematics.

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You Can Visit the World’s Oldest Zero at a Temple in India

Indian mathematicians were the first to treat zero as an equal

Colin Schultz

The idea of zero was born,  says journalist Alex Bellos , from “the idea of nirvana, the transcendent state of “nothingness”, when you are liberated from suffering and desires.” And about 1,500 years ago, someone invented a symbol for that idea: 0.

The circle we know as “zero”  was invented in India , and on the walls of a temple in  Gwalior , you can find the oldest known representation of the circular symbol for nothing.  Bellos , while working on  a documentary  about the ancient 0, traveled to Gwalior to see it. At some point, a couple of professors explained, the idea of “nothingness” became a mathematical concept:

In fact, the word used in philosophical texts to mean nothing, or the void, is “shunya”, the same word later used to mean zero….”Shunya means a sort of salvation,”  said. “When all our desires are nullified, then we go to nirvana or shunya or total salvation…. For George Gheverghese Joseph, a maths historian at the University of Manchester, the invention of zero happened when an unknown Indian mathematician about two thousand years realized that “this philosophical and cultural concept would also be useful in a mathematical sense.”

Other cultures, says Bellos, had markers to help indicate numbers above 9, but the Indian mathematicians were the first to treat zero as an equal, as a number in its own right.

Right in the center of this image the characters “270″ stand out, surprisingly modern numerals etched in an ancient temple in Gwalior. Photo:  ccarlstead

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Colin Schultz is a freelance science writer and editor based in Toronto, Canada. He blogs for Smart News and contributes to the American Geophysical Union. He has a B.Sc. in physical science and philosophy, and a M.A. in journalism.