Free Finding Zero by Amir D. Aczel Page A

to find the earliest known zero in India. This inscription certainly existed.
    Before leaving Jaipur, I went to visit the Jantar Mantar (observatory; literally “instrument formula”) in this city—in which some prominent Indian mathematicians had worked many centuries ago. The Jantar Mantar of Jaipur is now used as a museum to explain early astronomy to the people of India and to visitors. I studied the sophisticated instruments on display. These devices predated telescopes, so no lenses were used, but they were remarkably advanced and could estimate with good accuracy the various angles to heavenly bodies; some were tracking instruments that could follow the movements of planets, the moon, and the sun over the entire year. I inspected the numerals shown on these instruments. What was on display here were the later devices used at this observatory, from the sixteenth and seventeenth centuries. Therefore, all the numerals were our modern ones, and included a zero.
    The earliest view that our numbers, with zero, came from India appears to have been proposed in a scholarly publication by the renowned German historian of science Moritz Cantor. In a publication of 1891, Cantor says, “This kind of conscious juggling with the notions of positional arithmetic with the zero is most easily explained in the home of these notions, which home for us is India and this we may affirm even if there is question of a second home. We mean if both notions were born in Babylon, of which there is great probability, and were carried over into India in a very undeveloped state.” 3
    Louis C. Karpinski of the University of Michigan quoted Cantor’s groundbreaking passage on the putative origin of numbers in his article in Science on June 21, 1912. He had translated Cantor’s German into English. 4 Then his own article went on to discredit any notion that the numbers may have originated in Babylonia, in any form, because the Babylonians used a sexagesimal system, building their numbers using a very large base: 60. He pointed out that the Babylonians did not use any place-holding zero. His conclusion was that the numbers had to have originated in India. But what was the evidence that the numbers—and especially the all-important zero—were invented in India?
    Neither Cantor nor Karpinski presented any such definitive proof. Karpinski said in his article that “[an] early document referring to the Hindu numerals has been published. This document is of prime importance because, being written in 662 A.D., it antedates by more than two centuries the earliest known appearance in the ninth century of the numerals in Europe.” 5 Surprisingly—for an article in the prestigious journal Science —Karpinski doesn’t tell us what this document is. In fact, if such a document existed today—and if one could prove definitively that it was written in the seventh century—it would be one of the most important documents in the history of science. Equally surprising is his statement that the numerals arrived in Europe in the ninth century, again without any proof.
    So in the meantime, lacking convincing evidence that the numbers including zero were of Indian origin, many scholars in Europe remained as skeptical as ever about any Eastern origins whatsoever—some claiming, as we will see, that the numbers andthe zero were either invented by the Europeans themselves or by the Arabs.
    Perhaps Karpinski was alluding to the famous Bakhshali manuscript. This mathematical document, written on birch bark, was discovered in the 1800s in the ground near the village of Bakhshali, not far from Peshawar in present-day Pakistan. It clearly is very ancient, and the bark on which it was written, 70 leaves of it, is so fragile that no one has been allowed to touch it for fear it will disintegrate. Today this ancient document is on display at the Bodleian Library at Oxford. Because the Bakhshali cannot be touched, no