Imagine a number so powerful it terrified the Greeks for two thousand years and yet was celebrated as divine in India from the very beginning. The Greeks, who saw the universe as a perfect harmony of numbers, could not fathom shunya (zero). Pythagora believed that “all was number” and everything in nature, music, geometry, and cosmic order could be expressed as integer ratios. But shunya defies this logic. A ratio involving shunya can destroy logic and put a hole in the Pythagorean order of the universe, and so could not be tolerated.
Even Archimedes, who put forward axioms asserting that any quantity added often enough must surpass any given magnitude, could not reconcile the concept of shunya into this framework. Shunya annihilates any number when multiplied, but does not change anything when summed.
Basically, shunya breaks the very foundations of the Greek understanding of numbers. To Greeks, shunya was not just puzzling; it was dangerous to their worldview. Their confusion is understandable as they inherited much of their mathematics from the Egyptians, who were more concerned with land measurement rather than abstract calculations. This early influence partly explains the Greeks’ fear of shunya. After all, how can nothing (shunya) explain something?
Meanwhile, in India, shunya was embraced and nurtured. The Nasadiya Sukta of the Rigveda contemplated that the universe was born from nothingness. The same idea appeared in the later Upanishadic inquiries. A thought-provoking hymn from the Isha
Upanishad says:
पूर्णमदः पूर्णमिदंपूर्णात्पूर्णमुदच्यते।
पूर्णस्य पूर्णमादाय पूर्णमेवावशिष्यते॥
That is Purna (shunya); This is also Purna; From Purna is manifested Purna. Taking Purna from Purna, Purna indeed remains.
Mathematically speaking, 0-0=0, but the hymn philosophically explores the cosmos. Over time, the idea evolved into practical numerals, with shunya becoming the key part of the Hindu numeral system. A more explicit use of shunya appeared in the Bakhshali manuscript, where a dot served as a placeholder for shunya, and in the Gwalior inscription of 876 CE, where the circular shunya was clearly inscribed. By the 7th century, Brahmagupta formalized the very first rules of arithmetic with shunya, though division by shunya remained undefined. What happens if a number is divided by shunya? In the 12th century, Bhaskara-II addressed this puzzle by invoking the idea of infinity (ananta). To him, anything divided by shunya revealed ananta. The creator has been discovered once more in nothingness.
In parallel with these mathematical developments, the philosophical exploration of shunya continued in India. Jain thinkers were quite fond of large numbers and naturally contemplated the opposite extreme, nothingness. Meanwhile, the Mahayana Buddhist philosopher Nagarjuna (2nd-3rd century CE) elevated shunyata (emptiness) to the state of nirvana.
Indians not only celebrated shunya in philosophy and mathematics, they also depicted it in an astonishing way. The cosmic form of Shiva, especially in the Chola bronze of Natraja, is an intriguing example. With the damru in one hand, Shiva embodies the rhythm of creation, while fire in the other hand signifies destruction. He is called Nishkala, literally “without parts”, the ultimate void and yet the creator of the universe. Unlike the medieval European universe, the Hindu cosmos is infinite, a continuous cycle of origin and dissolution. Shunya was never just a mathematical symbol. It was also a lived philosophy, celebrated as a source of creation and the ultimate goal of human existence.
Only the Babylonians and Mayans came close to using shunya like the Hindus. The Babylonians, working with a base-60 system, faced difficulty distinguishing numbers such as 1, 60, and 3600. They used empty space (later on slanted double wedges) between a double wedge to mark the difference. But here, shunya functioned only as a placeholder, not as a number in its own right. The Mayans faced similar challenges in distinguishing 1, 20, and 400 as they followed a base-20 system. They developed a distinct shell symbol for shunya and counted their days in cycles of 20, from 0 to 19. Yet even the Mayans used shunya as a placeholder. It was India where shunya was truly transformed into both a numeral and a number with its own arithmetic rules. The properties of the Hindu numeral system, including shunya, attracted Arabs in the 8th-9th century following the rise of Islam.
When Arab scholars came into contact with India, they encountered mathematical ideas unfamiliar to them. During the Abbasid Caliphate, a famous House of Wisdom was established in Baghdad, where numerous Hindu texts were translated into Arabic. Notably, Al-Khwarizmi, a Persian mathematician working there, wrote ‘On the Calculation with Hindu Numerals’, introducing the Hindu numeral system, including shunya, to the Arab world. Hindu numerals became very popular across the Islamic world, especially for accounting and calculation. But how did shunya travel further and become zero in Europe?
Leonardo of Pisa, better known as Fibonacci, was a young boy when he encountered the Hindu-Arabic numeral system. His father was stationed in North Africa for trade, and during one of these stays he took Fibonacci with him. Fibonacci studied mathematics there under Muslim scholars and learned the Hindu-Arabic numerals, including the use of shunya. Fibonacci later introduced this system to Europe in his famous book Liber Abaci (1202 CE). The Arabic word ‘sifr’ (meaning empty or shunya) became ‘zephirus’ in Latin, later evolving into the Italian cifra and into the English zero.
Europe, still steeped in Aristotle and Pythagorean thought, viewed zero as dangerous. However, Italian merchants, recognizing the practical advantages of the Hindu-Arabic numerals with zero, eagerly adopted them, freeing themselves from cumbersome and boring counting boards. The local government, including the Church, resisted, and in 1299 CE, Florence even banned Hindu-Arabic numerals due to philosophical or mystical ideas about nothingness that conflicted with religious doctrine, and to practical concerns that these numerals could be easily falsified in commercial records. Merchants, however, continued using the system, and eventually, zero overcame resistance, destroying the Aristotelian philosophy and reshaping European mathematics. Over time, the importance of zero grew so much that the word ‘cipher’ also came to mean ‘secret code’.
While zero was born out of necessity in Babylonian and Mayan civilizations, in India, it remained the subject of profound enquiry; it was nurtured, celebrated, and explored in countless ways. Entire philosophical systems grew around zero, and its mathematical power was deeply contemplated. In a true sense, the zero belongs to Indians, a concept both practical and divine, unlike anywhere else in the ancient world.
Author: Dr. Gaurav Tomar
