The ancient Indian Bakhshali manuscript about mathematics contains the oldest recorded use of the dot symbol for zero, according to new radiocarbon dating of the manuscript. Carbon dating by the University of Oxford and Bodleian Libraries places the Bakhshali manuscript in the 3rd or 4th centuries CE, specifically between 224-383 Common Era (CE). The previous dating placed the manuscript in the 9th century CE. This revised dating is an important finding for the history of mathematics because the revision moves the birth of the concept of a mathematical zero back 500 to 600 years earlier than currently thought.

Zero as a number in its own right

The Indian Bakhshali manuscript has the oldest known recorded dot symbol, and in India, the dot symbol later evolved into the number zero. Several cultures outside of India, including the Mayan and Babylonian cultures, used a dot symbol to indicate zero, just as the Indian Bakhshali manuscript does. But it was only in India that the dot symbol evolved to become a hollow circle representative of zero as a number in its own right.

During early usage in these ancient cultures, the dot symbol for zero was used as a "placeholder" for "nothing." A placeholder signifies "orders of magnitude in a number system — for example, denoting 10s, 100s and 1000s," as explained by Marcus du Sautoy, University Of Oxford Simonyi Professor for the Public Understanding of Science.

Bakhshali maths book of rules and examples

The Bakhshali manuscript, named for the field where it was unearthed, is a rule book for students of mathematics. Concepts in math are presented with examples given to illustrate math problems. Most examples include their solutions and the verification, just as modern textbooks do. Subjects covered are among those studied today: arithmetic, algebra and geometry.

Topics within these subjects are well known and include:

  • fractions and square roots
  • profit and loss and monetary interest
  • simultaneous linear equations and quadratic equations

Indian astronomer and mathematician Brahmagupta, 628 CE

It was in 628 CE that Indian mathematician and astronomer Brahmagupta wrote a treatise called Brahmasphutasiddhanta in which zero as a number in its own right was discussed.

For the first time on record, zero was discussed as a number instead of as a placeholder of numerical magnitude. Today zero helps run "the digital world" globally, as stated by Professor du Sautoy. He called the "creation of zero as a number" one of the "greatest breakthroughs" in the history of mathematics.

Found in Bakhshali field by a farmer in 1881

Found in 1881 by an Indian farmer in a field called Bakhshali and written in a "variant of Buddhist Hybrid Sanskrit," as explained by Du Sautoy and his study co-authors, the Bakhshali field manuscript is the oldest Indian mathematics document and informs the later discussion of zero as a number executed by Brahmagupta. The 70 leaves of birch bark the manuscript is written on are in a fragile state.

To preserve the birch bark leaves' integrity, Bodleian Libraries’ Weston Library, Oxford, houses the 70 leaves in a specially bound book having pages with "windows" through which both sides of the birch barks can be read. According to Du Sautoy, the 70 bark leaves of the manuscript show "how vibrant mathematics" has been in India from ancient times. The Bakhshali manuscript, found near Peshawar in modern-day Pakistan, now predates the "9th-century inscription of zero on the wall of a temple in Gwalior, Madhya Pradesh," previously held to be the oldest recorded instance of the dot symbol for zero, used in the Gwalior temple inscription as a placeholder.