Shunya: how India gave the world zero, and why it matters to Jyotish

Why we named the hub Shunya

Śūnya means "empty" or "void". In Indian mathematics it became the name of zero. We chose it for this knowledge hub because zero is one of the clearest examples of an idea that came out of the Vedic sciences, travelled the world and is now used by everyone. It also reminds us of a scholarly habit: to begin from an empty slate and build carefully.

Two kinds of zero

Historians distinguish two different achievements.

Zero as a placeholder. In a positional system the value of a digit depends on its place. Writing 205 requires a sign for "nothing in the tens place". Babylonian astronomers had a placeholder sign in their base-sixty system, and Maya calendar-keepers developed one independently.

Zero as a number. Treating zero as a quantity in its own right, something that can be added, subtracted and multiplied, with rules, is a further step. The earliest surviving systematic rules of this kind are Indian.

What India contributed was the combination: a decimal place-value system with nine digits and a zero, and a body of arithmetic that treated zero as a number. That combination is the one used across the world today.

The evidence, step by step

The word in metre. Pingala's Chandahsutra, a text on metre (Vedāṅga of chandas), uses the word shunya in a procedure for enumerating metres. Its date is uncertain, often placed in the last centuries BCE†, and whether "shunya" here already functions as a numerical zero is debated.

Place value in astronomy. By the fifth century CE astronomers were writing large numbers in word-numerals: each digit is replaced by a word for something that comes in that quantity (moon for 1, eyes for 2, and "sky" or "void" for 0), read from the lowest place upward. This system only works if place value and zero are understood. Aryabhata's Aryabhatiya (499 CE) uses its own alphabetic code for numbers and explains arithmetic operations that assume place value.

Zero as a number with rules. Brahmagupta's Brahmasphutasiddhanta (628 CE) states rules for computing with zero: a number plus zero is the number, a number minus itself is zero, a number times zero is zero. He also discusses negative numbers ("debts") alongside positive ones ("fortunes"). His rule for division by zero is not the one modern mathematics adopts, and later Indian mathematicians, including Bhaskara II, returned to the problem.

Zero in stone. An inscription in the Chaturbhuj temple at Gwalior, dated 876 CE, writes the numbers 270 and 50 with a small circle for zero. It is among the oldest dated examples of the modern zero symbol in India still in place.

The Bakhshali manuscript. This birch-bark mathematical manuscript, found in 1881 near Peshawar and now in the Bodleian Library, uses a dot for zero. Radiocarbon dating published in 2017 gave widely separated dates for different folios, some as early as the third or fourth century CE†. Scholars continue to debate how to interpret those results, so we mark the early date as uncertain.

How zero travelled

Indian numerals and arithmetic were taken up in Baghdad. Al-Khwarizmi wrote a treatise on Indian reckoning in the ninth century, and the Latin versions of it, together with Fibonacci's Liber Abaci (1202), carried the system into Europe. The Arabic word sifr, a translation of shunya, gives us both "cipher" and "zero".

Why zero matters to Jyotish

The connection to astronomy is not incidental. Indian mathematical astronomy works with very large numbers. The Sūrya Siddhānta counts revolutions of the planets over a mahayuga of 4,320,000 years: the Moon, for example, is given 57,753,336 revolutions in that period. To find a planet's mean position on a given day, an astronomer computes the number of days elapsed since the epoch, the ahargana, which can run to many millions, multiplies by the revolution number and divides by the days in the cycle. That arithmetic is laborious without place value and zero, and quick with them.

Zero also appears in the structure of the zodiac. Positions are written as sign, degree, minute and second, with the first sign counted from zero. A planet at "0 signs 15 degrees" is in the middle of Mesha. Computing a Tithi means taking the difference between the Moon's and Sun's longitudes and dividing by twelve degrees. Each of these steps is a place-value computation.

So the people who needed zero most urgently were the astronomers. Much of the early history of Indian mathematics survives inside astronomical texts: the mathematics chapters of the Aryabhatiya, the Brahmasphutasiddhanta and Bhaskara's Siddhanta Shiromani, whose arithmetic part, the Lilavati, became a textbook in its own right.

A note on sources

The history of Indian numerals has been surveyed by many scholars. David Pingree's catalogue of the exact sciences in Sanskrit remains the starting point for locating texts. K. S. Shukla and K. V. Sarma's critical edition of the Aryabhatiya (1976) is the standard text of Aryabhata. Claims made in popular writing about zero sometimes outrun the evidence; where a date is debated we say so.

Try it

Open the Calendar converter to see how a date moves between the Gregorian, Shaka and Vikram reckonings, a small exercise in exactly the arithmetic that zero made easy. The Panchang tool shows the tithi computed from the Sun–Moon difference.

Further reading

See the texts shelf for the Aryabhatiya, the Siddhanta Shiromani and the Lilavati.

† Marked dates or readings are debated among scholars or still being confirmed by our faculty.