The Origin of Zero: Uncovering India's Forgotten Mathematical Legacy

In the intellectual and scientific evolution of human civilization, the invention of 'Zero' and the decimal place-value system is widely regarded as one of the most epoch-making events. The entire colossal framework of modern science, space mechanics, quantum physics, computer science, and artificial intelligence (AI) rests firmly upon this mathematical and binary foundation. Without the concept of zero, the technological marvels that define our modern world would simply cease to exist.

Recognizing the profound depth of India's ancient scientific heritage, there is a growing and vital movement to document these historical truths and integrate them into mainstream education. A highly commendable effort in this direction has been initiated by the NCERT, aligning with the vision of the National Education Policy (NEP 2020) and the Indian Knowledge Systems (IKS). For instance, the latest Class 9 mathematics curriculum introduces students to this rich legacy in one of its new curriculum texts' chapters titled 'The World of Numbers'.

However, a critical analysis of this conventional timeline reveals a deep-seated academic bias that still lingers within the standard modern narrative. Mainstream histories have systematically sidelined the Jain tradition, disproportionately focusing on Vedic mathematics and early Buddhist literature before making a convenient leap to classical, secular mathematicians like Aryabhata and Brahmagupta. This restrictive approach completely overlooks Jain Karnanuyog—one of the most ancient, structured, and historically robust foundations of mathematical thought. To truly uncover the unbiased, original source of zero and the decimal system, modern curricula must dismantle this systemic omission and acknowledge that the Jain mathematical legacy is not merely a 'missing link,' but a foundational genesis of Indian exact sciences.

Before the mathematical zero (as an independent operational digit and decimal place-value determinant) emerged in the Indian subcontinent, various ancient civilizations grappled with the concept of "nothingness" or empty space in their calculations. However, their symbols were largely restricted to being mere placeholders or philosophical concepts, never evolving into a fully functional mathematical number.

Here is a look at how other great early civilizations struggled with the void:

• Mesopotamia (Sumerians & Babylonians): Around 5,000 years ago, the Sumerians developed a base-60 (sexagesimal) system, which we still use today for measuring time and angles. Later, around 700 BCE, Babylonian mathematicians began using slanted double wedges (cuneiform) as a placeholder to indicate empty space between two non-zero digits. However, this system had severe limitations: the symbol was never placed at the end of a number, leading to ambiguity regarding the actual magnitude of the figures. Furthermore, it was never used in independent mathematical operations like addition, subtraction, or multiplication. It was strictly a space indicator, not a mathematical zero.

• Ancient Greeks & Romans: The Greeks, renowned for their exceptional contributions to geometry and logic, faced a deep ideological block when it came to zero. Great philosophers like Aristotle fundamentally rejected the idea of a "void" or "nothingness," arguing logically: "how can what is nothing be something?". Believing that nature abhors a vacuum (Horror vacui), the Greeks entirely excluded zero from their alphabet-based numerical system, limiting themselves only to positive integers. While astronomers like Ptolemy later used a small circle as a placeholder for calculating angles in degrees and minutes, it remained purely an astronomical indicator, not a part of mainstream mathematics. Similarly, the ancient Romans relied on the abacus and Latin terms for "none," but their Roman numerals (I, V, X, L, C, D, M) completely lacked a zero.

• The Mayan Civilization: Operating completely independently in Mesoamerica, the Mayans developed a sophisticated base-20 (vigesimal) system. By the 3rd and 4th centuries CE, they successfully used a shell-like symbol (or turtle shell) to represent zero, integrating it deeply into their complex Long Count calendar. While their conceptual use of zero was remarkably advanced, their severe geographical isolation—and the subsequent decline of their civilization—prevented this knowledge from spreading. Consequently, the Mayan zero had absolutely no direct influence on the global development of mathematics.

For decades, the global academic world and modern historians widely regarded the Bakhshali Manuscript as containing the oldest surviving written evidence of a zero symbol in India. In 2017, it was famously reported that Folio 16 of the manuscript—which contains a distinct dot-shaped symbol representing a positional zero—dated to the 3rd–4th century CE (224–383 CE).

However, a significant scientific revision has now changed this chronology. On October 14, 2024, researchers at the University of Oxford published a new radiocarbon-dating report based on additional analysis of the Bakhshali manuscript. The study examined five folios—15, 16, 23, 33, and 55—and revised the earlier dating of the manuscript material. The resulting radiocarbon evidence places the sampled folios within a substantially later period, and Oxford's phase modelling places the surviving manuscript material broadly between 799 CE and 1102 CE.

Most importantly, the specific Folio 16, which contains the famous dot-shaped zero, was redated from the earlier 224–383 CE range to approximately 931–1032 CE. Thus, the celebrated Bakhshali zero can no longer be securely presented as a 3rd-century CE example on the basis of the earlier radiocarbon result.

This revised dating places the surviving folio containing the zero several centuries after the monumental works of prominent Indian mathematicians like Aryabhata (499 CE) and Brahmagupta (628 CE).

This massive paradigm shift effectively shatters the previous mainstream narrative. It reopens the profound historical question: If the Bakhshali zero is from the 10th century, where is the true, oldest, and most authentic evidence of the decimal place-value system in the Indian subcontinent? The answer lies hidden in plain sight within the ancient scriptures of the Jain tradition.

According to Jain philosophy and ancient Indian knowledge traditions, the origin of systematic mathematics and scripts is directly attributed to the first Tirthankar, Bhagwan Rishabhdev (Adinath). During the cosmic time cycle's transition into Karmabhoomi—an era where human society required structured civilization, effort, and labor to survive—he established the foundational arts and sciences. As part of this monumental civilization-building, he imparted the knowledge of alphabets and scripts (Lipi Vidya) to his eldest daughter, Brahmi (after whom the historical Brahmi script is named), and bestowed the profound science of numbers and mathematics (Ank Vidya or Sankhyan) upon his second daughter, Princess Sundari. While this account belongs to Jain itihasa—a traditional and scripturally preserved historical memory distinct from direct archaeologically dated history—it carries deep epistemological significance for understanding how the Jain tradition itself conceived the origins of number and script.

This historical and philosophical event is not a mere mythological tale. The antiquity and pan-India presence of the 1st Tirthankar, Bhagwan Adinath, are supported by profound archaeological evidence, with many scholars drawing compelling parallels that trace his legacy as far back as the Indus Valley Civilization—representing the earliest dawn of Indian history. In Jain philosophy, mathematics was never seen merely as a tool for commercial trade, agricultural measurement, or daily transactions. Instead, it was mainly viewed as a vital scientific and philosophical instrument required to understand the ultimate reality. The Jain worldview posits that the universe is uncreated, eternal, and governed by extraordinarily strict, rational, and mathematical laws. Therefore, mastering Ank Vidya was an absolute philosophical necessity to accurately decode and measure the complex, quantized structures of space, time, and matter.

From the perspective of Jain epistemology, this mathematical knowledge is not a mere human invention but an eternal truth; in every descending time cycle (Avasarpini), the fundamental architecture of numbers and the concept of zero are systematically reintroduced at the dawn of Karmabhoomi by the first Tirthankar (Bhagwan Rishabhdev was the 1st Tirthankar of the current cycle). Even strictly within the boundaries of modern historical frameworks, the omniscient teachings of the 24th Tirthankar, Bhagwan Mahavira, firmly establish Karnanuyog as the most ancient and highly evolved mathematical tradition. Although these extremely complex doctrines of cosmic mathematics and karma calculus were formally codified into written texts like Kashay Pahud around the 1st century CE, they represent centuries of a meticulously preserved, unbroken oral tradition that was practically applied long before any other civilization.

From historical, academic, and archaeological perspectives, the most ancient, explicit, and undisputed written evidence of zero (0) and the decimal place-value system is not found in the works of mainstream secular mathematicians, but within the Jain Karnanuyog text, the Lok-Vibhag. Originally composed in Prakrit by Muni Sarvanandi in 458 CE, and later translated into Sanskrit by Simhasururshi, this document serves as a monumental milestone in the global history of mathematics.

While describing immense cosmic distances and the circumferences of celestial bodies (yojanas), the Lok-Vibhag systematically employs 'Shunya' (zero) not merely as a blank space or philosophical void, but as a fully functional mathematical digit with a precise decimal place value. This undeniable historical proof is perfectly preserved in the text's fourth section, specifically in Shloka 4/36:

Translated literally into digits, the words in the verse appear in the following sequence: 0 (Shunya), 9 (Nava), 1 (Ekam), 4 (Chatvari), 5 (Pancha), 3 (Trini), 3 (Trikam), 2 (Dvikam), 7 (Sapta), 0 (Shunya), and 2 (Dvikam).

To extract the actual mathematical value from this verse, Jain Acharyas applied the famous ancient Indian algorithmic rule: "Ankanam Vamato Gatih" (अंकानाम वामतो गतिः), which translates to "numbers go from right to left". By reading the sequence of digits in reverse order, we arrive at the incredibly precise 11-digit number: 20,723,354,190 (Over 20 billion, 72 crore). The text brilliantly uses this massive, exact figure to measure the outer circumference of a cosmic structure in yojanas.

The significance of this cannot be overstated. With a firmly established composition date of 458 CE, the Lok-Vibhag profoundly predates the works of Aryabhata (499 CE) and Brahmagupta (628 CE). Furthermore, it was written centuries before the Bakhshali Manuscript’s 'Folio 16', which modern carbon-dating has now proven belongs to the 10th–11th century. The Lok-Vibhag unequivocally and definitively establishes the Jain Karnanuyog tradition as the world's first recorded source of zero and the decimal system.

Apart from zero being formally codified for calculation, ancient Jain scholars had also developed extraordinarily advanced mathematical frameworks to measure and quantify the vastness of the cosmos. For them, numbers were not just tools for counting; they were the very architecture of the universe.

To understand cosmic scales, Karnanuyog texts classified numbers into 21 distinct categories, broadly categorized into Sankhyat (Enumerable), Asankhyat (Innumerable), and Anant (Infinite). Remarkably, their profound understanding that "infinities have different sizes" predates the famous German mathematician Georg Cantor’s Set Theory and his concept of transfinite numbers by nearly 2,000 years.

To calculate the extreme upper limits of enumerable numbers, ancient texts like the Tiloyapannati and Triloksaar utilized breathtaking thought experiments. The most famous is the Kund Prakriya (Method of Pits). This conceptual experiment involved imagining four massive cylindrical pits—each 100,000 yojanas wide and 1,000 yojanas deep—systematically filled and emptied with tiny mustard seeds (sarshap). This mind-bending process perfectly demonstrates the use of complex recursive algorithms and exponential mathematics centuries before modern computer science existed.

Furthermore, to manage these astronomically massive cosmic calculations, Jain Acharyas developed concepts like Ardhachheda (the process of continuously halving a number), which functionally serves as an early version of modern base-2 logarithms.

Because the sheer complexity of these cosmological algorithms, karma calculus, and infinite hierarchies is so profound, delving into their complete mathematical proofs goes beyond the scope of this article. We will explore the fascinating mechanics of the Kund Prakriya and Jain Set Theory in comprehensive detail in dedicated upcoming Vidyaaytan Prep blogs! (For a basic idea of Jain Mathematics of number and infinity following video can be referred to).

The profound mathematical knowledge preserved for centuries within the spiritual texts of Karnanuyog did not remain confined to religious literature. By the 5th and 6th centuries CE, this advanced numerical framework provided a remarkably strong conceptual foundation for Indian scholars like Aryabhata (499 CE) and Brahmagupta (628 CE). While Jain Acharyas utilized these complex numbers to calculate infinite cosmic scales and geography, it was Brahmagupta who took a monumental step for secular arithmetic. In his seminal 628 CE work, Brahmasphutasiddhanta, he formalized the world's first operational rules for the addition, subtraction, and multiplication of zero as a distinct numeral.

From the Indian subcontinent, this revolutionary mathematical system began its westward journey during the 8th century, traveling along the Silk Road to the Middle East. Through the influence of scholars at the Abbasid Caliphate's 'House of Wisdom' in Baghdad, Indian mathematical and astronomical texts were translated into Arabic. In the 9th century, the great Persian mathematician Al-Khwarizmi meticulously studied the Indian decimal place-value system and zero, authoring his highly influential book often translated as 'Arithmetic of the Indians'. In the Arabic tradition, this revolutionary digit was termed "Sifr", which translates to "empty" or "nothing". This rigorous study of Indian mathematics by Arab scholars laid the very foundation for modern algebra.

The final leg of Zero's global journey occurred as this knowledge flowed through Mediterranean maritime trade routes connecting North Africa and Spain to the rest of Europe. In 1202 CE, the Italian mathematician Leonardo Fibonacci, having learned the system from Arab merchants, published his groundbreaking book 'Liber Abaci'. This publication introduced the 1-9 Hindu-Arabic numerals, alongside zero, to the Western world, effectively replacing the cumbersome Roman numeral system for trade and science. Over time, the Arabic word "Sifr" was Latinized into "Zephirum", which ultimately evolved through Italian dialects into the modern English word we use today: "Zero".

A meticulous exploration of historical, philosophical, and textual evidence reveals a profound truth: the ancient Jain Acharyas played a foundational, yet often overlooked, role in elevating zero into a functional, independent mathematical digit. Driven by a deep spiritual and scientific necessity to quantify the infinite cosmos and the microscopic realms of karma, their insights heavily influenced the development of the advanced decimal place-value system we rely on today.

As India reshapes its academic landscape, supporting the visionary goals of the National Education Policy (NEP 2020) and the Indian Knowledge Systems (IKS) initiative becomes vital. To truly honor and reclaim the nation's complete scientific legacy, mainstream educational frameworks should integrate foundational Karnanuyog texts—such as the Lok-Vibhag and Tiloyapannati—into future academic curricula.

By bringing these unparalleled mathematical achievements into classrooms, we are not merely correcting historical oversights; we are empowering the next generation to reconnect with the authentic, diverse roots of global mathematics.