The “story” of zero is more than just a lesson in mathematics; it’s a centuries-long evolution that transformed a place-holder into a powerful mathematical tool (In mathematics, a placeholder is a symbol, letter (like 𝑥,𝑦,𝑧), or empty box used to temporarily represent an unknown, unspecified, or variable value. It acts as a structural marker in equations, formulas or numbers, holding a position until the final, specific value is determined or inserted).
Life before zero
In the absence of a mathematical zero, ancient civilizations relied on physical tools, descriptive language and clever notation to manage daily life and navigate commerce, construction and accounting:
Physical Tools: Merchants used the abacus or counting boards. If a column was empty, it meant “nothing” was there. The Incas used quipus (knotted strings), where a gap between knots acted as a placeholder.
Plain Language: Instead of writing “0,” people wrote words like “none” or “empty.” In ancient Egypt, they used a symbol for “beautiful” to show that a monthly account perfectly balanced out.
Smart Systems: Roman numerals (like VIII for 8) did not need a zero because they just added symbols together. If you had no “tens,” you simply did not write the letter “X.”
Symbols: The Bakhshali manuscript (3rd/4th century), an ancient Indian mathematical text,used a dot (called bindu or bindi) as a placeholder to represent empty places. Greek Astronomers used the letter omicron (ο), representing the Greek numeral for 70 but also functioning as a placeholder for null or zero
Blank Spaces: Early mathematicians in China often just left a space in their writing to show a missing value, relying on the reader to understand the context. Babylonian system used a blank space or, later, two slanted wedges to signify an empty place value (around 300 BC).
These symbols indicated “nothing” in a specific spot but were not treated as numbers in calculations until later in the 7th century, when Brahmagupta defined the rules for zero.
Origin of the concept
The concept of zero originated from the Sanskrit term “shunya”, which means “void” or “emptiness.” Unlike many Western philosophies that rejected the idea of “nothingness,” ancient Indian thought — spanning Hinduism and Buddhism —embraced shunya not merely as an absence of value, but as a source of limitless possibilities. In Hinduism, shunya embodies a complex paradox, simultaneously representing absolute void and the ultimate reality (Brahman), the wellspring of infinite potential. This unique cultural perspective facilitated the natural progression for Indian thinkers to treat “nothing” as a legitimate, tangible value within their systems of thought and mathematics.
The fifth century mathematician and astronomer, Aryabhata (also Aryabhatt), introduced the concept of zero in his 499 CE treatise, the Aryabhatiya. Though he did not actually use the modern “0” symbol. he perfected a decimal place-value system that relied on the inherent concept of zero. He used the Sanskrit word “kha” (meaning space or void) as a functional place-holder to denote the absence of a value in a specific column, which allowed him to perform incredibly precise astronomical calculations, such as determining the Earth’s circumference and the length of a solar year.
By treating “nothingness” as a structural necessity within his alphabetic numerical notation, he transformed zero from a mere philosophical idea into a powerful mathematical tool that defined a digit’s value based on its position. “Nothing” held a place that changed the value of other digits — turning a “1” into a “10”.
In 628 CE, another legendary mathematician-astrologer Brahmagupta went a step further by becoming the first person in history to treat zero not just as a place-holder, but as a number with its own identity. In his groundbreaking work, the Brahmasphutasiddhanta, he formalised the first written rules for arithmetic involving zero: 𝐴+0 = 𝐴; 𝐴−0 = 𝐴; and 𝐴×0 = 0, which he explained using the logic of fortune and debt:
- The Law of Identity: If you have five apples and I give you “nothing,” you still have five apples (5+0 = 5).
- The Law of Debt*: If you have zero and take away five, you are left with a “debt” of five (0−5 = −5)
- The Law of Erasure: If you multiply any fortune, no matter how vast, by zero, it vanishes into the void (5×0 = 0)
* This was his most radical move: using zero to define negative numbers.
The Indian numeral system was subsequently transmitted to the medieval Arab world through trade routes and the translation of scholarly texts. In the 9th century, the Persian mathematician Al-Khwarizmi recognised the superiority of the Indian place-value system and popularised it further through his influential book Kitāb al-ḥisāb al-hindī (On the Calculation with Hindu Numerals). He documented the use of the 10 numerals, including zero (which he called sifr, meaning ‘void’ or ’empty’), providing clear, procedural rules (algorithms) for performing arithmetic calculations using the decimal, place-value system.
This book was translated into Latin around 1126 CE, introducing the Hindu-Arabic numeral system to Europe. The Latin translation of his name, Al-Khwarizmi to Algoritmi, led directly to the English word “algorithm,” while the title of his other major work (Al-Kitab al-Mukhtasar fi Hisab al-Jabr wal-Muqabala, or al Jabr for short) gave us the word “algebra.”
Advocacy of the concept
A young Italian merchant-mathematician named Fibonacci (Leonardo Bonacci, 1170-1250) travelling around the Mediterranean learnt about the Hindu–Arabic numeral system from fellow merchants. In 1202, he wrote the Liber Abaci (Book of Abacus or The Book of Calculation), where he introduced the so-called modus Indorum (method of the Indians), today known as the Hindu–Arabic numeral system, with ten digits, including a zero and positional notation.
In Liber Abaci, Fibonacci did not just teach theory; he solved real-world ‘headaches’ of the 13th century to prove that Indian numerals (and zero) were superior to Roman ones. The book showed the practical use and value of applying the numerals to commercial bookkeeping, converting weights and measures, calculation of interest, money-changing and other applications.
Read ‘Fibonacci’s Formulas: The four problems that changed history’ in the box below.
Europeans, especially its religious leaders and governments, could not initially understand how a symbol for “nothing” could actually be “something.” It took nearly 300 years of underground use by merchants before the “magic” of zero was finally accepted. The perception shifted when the practical benefits outweighed concerns about adopting an alien concept:
Bookkeeping Revolution: Italian merchants realised that the Hindu-Arabic system allowed for double-entry book-keeping. It made balancing accounts (getting the total to reach zero) much faster than by using an abacus.
The Birth of Science: By the 17th century, philosophers like René Descartes used zero as the centre point (the origin) of his (Cartesian) coordinate system, establishing a central origin point (0,0) essential for mapping space, motion and physics (A Cartesian coordinate system is a grid/graph that uniquely locates points on a flat surface (or in space) by measuring their distance from a horizontal x-axis and a vertical y-axis, which intersect at a central point (0,0)).
The invention of calculus by Newton and Leibniz in the late 17th century relied entirely on zero. This field, which studies continuous change, depends on the mathematical concept of limits — values that approach zero infinitely closely.
Ultimately, the West went from banning zero as a “hollow symbol” to realising it was the foundation of modern logic.
China began using a specific symbol for zero systematically in the 13th century. The circular symbol ‘〇’ was introduced by the mathematician Qin Jiushao in his 1247 work Mathematical Treatise in Nine Sections. Before that, Chinese mathematicians used a decimal place-value system with counting rods where a blank space indicated the absence of a value in a specific position, effectively acting as a placeholder zero. The Indian symbol for zero (a dot or small circle) had been introduced earlier through Buddhist texts around the 8th century CE, but it was not widely adopted by Chinese mathematicians at that time.
How Zero Makes Our World Work
Over the years, the concept of zero transformed “nothing” into a tangible numerical tool, revolutionising mathematics and science by enabling advanced abstraction. Today, zero underpins much of the modern world, making life and technology possible in fundamental ways:
- Foundation of Arithmetic: Zero acts as a crucial placeholder, defining the difference between 1, 10 and 1,000. Without this place value system, tracking large numbers would be cumbersome, replacing inefficient systems like Roman numerals and making complex multiplication and division significantly easier for trade and science.
- Algebraic Necessity: Zero is essential for balancing accounts and solving equations. It formalised the use of negative numbers (representing debt in accounting or values below a baseline in science), which are vital in various applications.
- Scientific Measurement: Scientists use zero to establish essential baselines for measurement. This includes setting the origin point (0,0) for tracking motion on a map in coordinate systems and defining the coldest possible temperature in the universe (absolute zero) for thermodynamics and quantum mechanics (e.g., zero-point energy).
- Technological Bedrock: Every computer and smartphone runs on a simple code of just two numbers: 0s and 1s. While 1 represents the “on” switch, 0 represents the equally important “off” switch in the digital circuits. This binary system is the very foundation of modern computing, artificial intelligence and digital storage (bytes, terabytes).
Did you know?
- The Bakhshali Manuscript, an ancient Indian mathematical text, carbon-dated by Oxford University to the 3rd or 4th century, contains hundreds of zeros denoted as dots, marking the earliest known use of the symbol. Found in 1881 in the village of Bakhshali, Mardan (near Peshawar in present-day Pakistan, historical Gandhara), the text, written on birch bark, is perhaps “the oldest extant manuscript in Indian mathematics.”
- In Chaturbhuj Temple in Gwalior, India, an 876 CE inscription documenting a gift of land and flowers clearly displays the numbers “270” and “50”. This is one of the world’s oldest examples of zero written as the familiar circle we use today.
Image 1: A commemorative postage stamp released by India in 1975 to celebrate the launch of India’s first satellite from the Soviet Union. The satellite was named Aryabhata to honour the 5th-century Indian astronomer and mathematician.
Image 2: A special cover was released by India Post at Stamp Expo 2012 in Patna, Bihar, honouring Aryabhata (also Aryabhatt).
Image 3: Soviet Union (USSR) issued a postage stamp in 1983 to commemorate the 1200th anniversary of the birth of Muhammad ibn Musa al-Khwarizmi, the Persian polymath and astronomer. Image courtesy Wikimedia Commons.
Image 4: An Italian postage stamp issued in 2020 to commemorate the 850th anniversary of the birth of the mathematician Leonardo Fibonacci. For more information on the mathematician, visit The Fibonacci Association website: httpsW//mathstat.dal.ca/fibonacci/.
Image 5: A postage stamp issued by France in 1996 commemorating Rene Descartes, French Philosopher, mathematician and scientist.
Image 6: A 1926 German Reich postage stamp featuring a portrait of Gottfried Wilhelm Leibniz, German polymath, philosopher and mathematician.
Do visit abakus.com for more postage stamps on genius mathematicians from across the world.