In the summer of 1881, near the village of Bakhshali, not far from the ruins of the ancient university town of Taxila in present-day Pakistan, a farmer was digging along a ruined stone enclosure when he unearthed an ancient-looking manuscript. There were about 70 leaves of birch bark, most of them falling apart with age and densely packed with inked writing. The fragile package was handed over to the authorities for examination and translation. Then came a stunning announcement.

The manuscript was essentially a handbook of mathematical rules, problems, and instructions, possibly for the use of merchants and traders, written in a language which included elements of what is called Buddhist Sanskrit, Prakrit, and Old Kashmiri. The problems were written in verse and the solutions laid out in carefully worded prose with elaborate explanations. The topics covered were fractions, profit and loss problems, mensuration, linear equations, square roots, and geometric progressions. The manuscript was believed to have belonged to the third or fourth century CE, making it the earliest Indian mathematical text ever found!

But there was more. Throughout the manuscript, scattered within large numbers – poised above and below fraction lines and included within long multiplication sums – were large dots.

They were symbols for zero, and it appeared that the Brahmana who originally wrote the manuscript, described as “the son of Chajaka … king of calculators for the use of Vasistha’s son Hasika”, was using zero quite confidently as a number for mathematical operations. These were the earliest written representations ever found of that all-important number – zero!

Numbers depicted in the manuscript. | Image credit: Augustus Hoernle / Public Domain.

Ganita-shastra, or mathematical science, has been a highly advanced subject in India since ancient times. Using a combination of philosophical concepts, advanced astrological knowledge, and smart number skills, ancient Indian mathematicians managed to formulate many of the fundamental concepts of mathematics that are still accepted today.

Going back all the way to Vedic times, numbers were not just numerals but were spoken of in tracts of verse. Brick altars for sacrifices were built with guidelines from the earliest manuals on geometry of the time. By the fifth century CE, the number notations we are familiar with had appeared, and the decimal system had been discovered that allowed the use of extremely large numbers based on the use of a decimal point. Indian mathematicians also invented the earliest forms of algebra. Among the many recorded accomplishments of the famous astronomer Aryabhata was a value of pi correct to four decimal places. In the Jain traditions, deep interest in the cosmos led to discussions on geometry and the arithmetic of large numbers.

And then there was zero.

No one really knows who invented zero or when. A pre-second century BCE Sanskrit text by Pingala uses a symbol he calls shunya, empty or void, which is possibly the earliest reference to the concept of nothing or zero. Texts written in the sixth and seventh centuries by astrologers and mathematicians like Varahamihira and Brahmagupta show they were already using the zero. Many of these texts were based on knowledge from much earlier times when scholars had memorised this knowledge and passed it on in spoken form until, finally, in some later period, someone decided to write it all down.

Other ancient civilisations, such as the Mesopotamians and the Mayans, understood the idea of using a symbol to denote “nothing” as a concept.

However, it was in India that the dot hollowed out into the circle, the widely accepted symbol for zero, and more importantly, where it was first used for independent mathematical operations. A number in its own right, in one stroke, the zero made large numbers easy to count and handle. From India, important mathematical ideas made their way to West Asia with Persian and Arab scholars and traders, carrying the concept of zero along with them. Today, it’s hard to imagine our world without zero.

What zero looked like in the manuscript. | Image credit: National Geographic / Public Domain

The Bakhshali manuscript now rests in the Bodleian Library at the University of Oxford, England. Its fragile pages are preserved in a special folio with transparent windows to view the manuscript without the need to physically handle it. There is some unresolved controversy over the age of the manuscript. Based on the language and script and the mathematical concepts discussed, some historians believe that the Bakshali manuscript could be a later copy of a more ancient text written around the fourth century CE. Scholars continue to research the language and script, scouring it for more information.

But for now, the Bakshshali manuscript is considered the earliest mathematical manuscript from India, one that provides written evidence of what is considered the greatest invention in the history of mathematics.

Excerpted with permission from A Children’s History of India in 100 Objects, Devika Cariapa, illustrated by Priyanka Tampi, Puffin India.