Photo: National Geographic · Public domain
Manuscript · Radiocarbon dates between the 3rd and 10th centuries CE (2017; the dating is debated)

The Bakhshali manuscript

Found
Dug up by a farmer in 1881 at Bakhshali village, near Mardan (now in Khyber Pakhtunkhwa, Pakistan)
Kept at
Bodleian Library, Oxford (since 1902)

Seventy fragile leaves of birch bark holding a book of arithmetic in Sharada script, in which zero is written as a dot.

What it says

The work sets out rules, worked examples and their checks: square roots, linear equations, arithmetic progressions, problems of profit and loss. Numbers are written in the decimal place-value system, with a dot standing for zero in empty places. In 2017 the Bodleian’s radiocarbon tests of three leaves gave 224–383, 680–779 and 885–993 CE; some historians of mathematics hold that the leaves belong together and date from around the 8th–10th centuries.

What it proves

It is the oldest surviving manuscript of Indian mathematics and among the earliest written uses of zero as a sign.

Evidence for