Who Invented Zero? The Story of Zero from India

Today we write numbers such as 10, 100 or 2026 with ease, but that became possible because of one small sign — zero. Without zero, large numbers could not be written easily, and computers would never have been built. The credit for inventing zero as a full number in its own right goes to the mathematicians of ancient India.

Zero's two roles

To understand the history of zero, two things must be kept apart. The first is the placeholder — a sign that shows an empty place, like the middle zero in 205, which tells us the tens place is empty. The second is zero as a number, which you can add, subtract and multiply with. The ancient Babylonians had the first, and the Maya of Central America also used a zero in their own way. But the ten-digit place-value system, and the rules that treat zero as a full number, were developed in India.

Zero's journey in India

Time	Where / who	What happened
About the 3rd–2nd century BCE	Pingala	The word "shunya" used in the study of metre
About the 3rd–4th century CE (some pages)	The Bakhshali manuscript	A dot (•) used for zero
499 CE	Aryabhata	Describes place value that grows tenfold
628 CE	Brahmagupta, "Brahmasphutasiddhanta"	The first rules for calculating with zero
876 CE	Gwalior, Chaturbhuj temple	A round "0" in an inscription

Brahmagupta's rules for zero

In 628 CE Brahmagupta, in his work "Brahmasphutasiddhanta", wrote down rules for calculating with zero for the first time:

Adding or subtracting zero leaves a number unchanged (5 + 0 = 5, 5 − 0 = 5).
Multiplying a number by zero gives zero (5 × 0 = 0).
Subtracting a number from itself gives zero (5 − 5 = 0).
He also gave rules for negative numbers ("debts") and positive numbers ("fortunes").

Brahmagupta's answer for dividing by zero does not match today's mathematics; later Bhaskaracharya (Bhaskara II) called it "khahara" — a quantity like infinity. In modern mathematics, dividing a number by zero is considered "undefined".

Did you know? In 2017 the University of Oxford had the Bakhshali manuscript carbon-dated, and some of its pages were found to be from the 3rd–4th century. The dot it uses for zero was counted among the oldest written evidence of zero, though scholars also debate its dates. The manuscript was found in 1881 in the village of Bakhshali, in today's Pakistan.

From India to the Arab world and Europe

Around the 9th century the Baghdad mathematician Muhammad ibn Musa al-Khwarizmi wrote a book on Indian numerals, which spread the system through the Arab world. In 1202 the Italian mathematician Fibonacci carried it to Europe through his book "Liber Abaci". That is why these digits are now called "Hindu–Arabic numerals". The Sanskrit "shunya" became "sifr" in Arabic, and from it came the English words "zero" and "cipher". The word "algorithm" also comes from al-Khwarizmi's name.

Today's world without zero

Roman numerals have no zero, so multiplying and dividing large numbers with them was very hard.
The language of computers, "binary", rests on just two digits, 0 and 1.
Algebra, calculus and modern science would not be possible without zero and place value.

Read about India's great mathematicians: Srinivasa Ramanujan and Mathematics personalities. More achievements of ancient India: Amazing facts about ancient India.

Key points

Treating zero as a full number with its own rules was developed in India.
Brahmagupta wrote rules for calculating with zero in 628 CE.
The Bakhshali manuscript uses a dot for zero.
An inscription at the Chaturbhuj temple in Gwalior (876 CE) has a round "0".
Indian numerals reached Europe through the Arab world and were called "Hindu–Arabic numerals".

Frequently asked questions