India's oldest record for the concept of "zero" is in the Bakhshali birch bark manuscript and originally dated to the 9th century, but the University of Oxford just carbon dated it to the 3rd century, making it 500+ years older.
Since this book is remarkable fragile, it's likely are even older records that did not survive as well as it did. There are many other ancient civilizations responsible for building impressive architecture, making astronomical calculations, and so on.
This Bakhshali book was found by a farmer in 1881 and named after the Pakistani town, Bakhshali, it was found in.
A mathematician can really appreciate this book because it contains rules, illustrations, solutions, verifications, algebra, geometry, and more. Can you imagine finding an ancient textbook teaching how to run business, build computers, or drive a car?
The topics include fractions, square-root, arithmetical and geometrical progressions, income and expenditure, profit and loss, computation of gold, interest, rule of three, summation of certain complex series, simple equations, simultaneous linear equations, quadratic equations, indeterminate equations of the second degree of a particular type, mensuration, and miscellaneous problems.
The Bakhshali book predates a 9th-century inscription of zero on a temple wall in Gwalior, Madhya Pradesh, previously regarded as the oldest record a zero in India. Actually, parts of the book are even older than the rest, being from 224-383 CE.
“The zero symbol that we use today evolved from a dot that was used in ancient India and can be seen throughout the Bakhshali manuscript,” said University of Oxford Professor Marcus du Sautoy and co-authors.
“The dot was originally used as a ‘placeholder,’ meaning it was used to indicate orders of magnitude in a number system — for example, denoting 10, 100s and 1000s.”
The Bakhshali is written in a semi-sacred text: a hybrid of Sanskrit and Buddhist languages. This might be why the placeholder dot evolved to have a hollow center, thus representing the concept of emptiness found in Buddhism.
“Today we take it for granted that the concept of zero is used across the globe and is a key building block of the digital world. But the creation of zero as a number in its own right was one of the greatest breakthroughs in the history of mathematics,” Professor du Sautoy said.
“We now know that it was as early as the 3rd century that mathematicians in India planted the seed of the idea that would later become so fundamental to the modern world. The findings show how vibrant mathematics has been in the Indian sub-continent for centuries.”
“Determining the date of the Bakhshali manuscript is of vital importance to the history of mathematics and the study of early South Asian culture and these surprising research results testify to the subcontinent’s rich and longstanding scientific tradition,” said Richard Ovenden, Bodley’s Librarian.