Zero the number that multiplied the power of mathematics.

Until recently, the origin of zero, one of mankind’s greatest inventions, was not clear. The enigma was revealed throughout the 20th century, and a new archaeological dating leaves no room for doubt: zero was born in India. It was the Indian sages who first drew up a symbol to represent the zero, a digit that does not appear in Greek writings or among Roman numerals.

That simple symbol triggered the ability of mathematicians to operate with numbers as large as they wanted. But the great sages of the classical period of mathematics in India went much further. Not only did they use the zero as a simple number, with which to complete their positional number system, but they converted it into an independent number with its own entity, which they began to employ in arithmetic operations (addition, subtraction, multiplication and division). Based on this concept of zero, those outstanding mathematicians carried out during almost a thousand years (from the 4th to the 13th century) a quiet mathematical revolution.

Heirs of the Greeks, the Indians took up their baton in the history of mathematics to deepen arithmetic -separating it from geometry- and to lay the foundations of algebra (later developed by the Arabs). The most important were Aryabhata (6th century), Brahmagupta (7th century), Mahavira (9th century) and Bhaskara II (12th century). Around the year 500, Aryabhata devised a positional decimal numbering system, which he described in his treatise Aryabhatiya, a poem written in Sanskrit consisting of 121 verses. Although he does not yet propose a symbol for zero, he does write the word kha instead.

POSITIONAL NUMBERING

The positional decimal system with the inclusion of the zero – the one we use today – has the advantage of allowing any number to be written with only 10 different digits (0, 1, 2, 3, 4, 5, 6, 7, 8, 9), which makes it easier to operate with very large quantities, as opposed to, for example, the Roman numeral system (based on the letters I, V, X, L, C, D and M, which represent the numbers 1, 5, 10, 50, 100, 500 and 1,000).

In a positional system, the value of each digit depends on its position within the number. For whole numbers, starting from right to left, the first digit corresponds to units, the second to tens, the third to hundreds, and so on (for example 5,876 = 5,000+800+70+6). In non-positional systems (such as the Roman system) a symbol always has the same value, no matter what position it is in – which requires such a number of symbols for large numbers that it is impractical to perform operations with them (for example: in Roman numerals, 5.876 is MMMMDCCCLXXVI).

In the seventh century, the writings of mathematician Brahmagupta are the first known in which he considered the zero as a number (not just a placeholder digit) and explained how to operate with the zero. He defined it as the result of subtracting a number from itself and noted some properties of the new number: when zero is added or subtracted from a quantity, it remains unchanged. Brahmagupta also introduced negative numbers in his writings to indicate debts, while positive ones represented fortunes. So, for example, he explains that a debt minus zero is a debt, a fortune subtracted from zero is a debt or the product of two debts is a fortune.

THE APPEARANCE OF THE SYMBOL

The oldest known appearance of the symbol “0” – as we know it today – dates from the 9th century: it is on a stone inscription, which indicates the year 876. It explains that in the city of Gwalior (400 km south of Delhi) “gardens of 187 by 270 hectares (Indian measure equivalent to almost half a meter) were planted so that they could produce enough flowers to give 50 garlands a day to the employees of the Chaturbhuj temple”. Both the 270 and the 50 are written down almost as we would write them today, but the 0 is somewhat smaller and slightly raised, almost like a superscript.

However, that inscription alone does not prove the origin of the zero in India. Since there was already extensive commercial contact between the Arab, European and Asian worlds in the ninth century, the inscription is not old enough to prove that the figure was invented there. There is an earlier inscription – made in 683 in the Khmer language of Cambodia – which contains another similar symbol for zero, as the mathematician Amir Aczel explains in his book In Search of Zero.

These are earlier writings, such as those of Aryabhata and Brahmagupta, which point to an Indian origin. Pulling on that thread, we arrive at the Bakhshali manuscript, the oldest Indian mathematical text, which was found in 1881 and comprised many fragments written from the third to the tenth century. The most recent and accurate archaeological dating.

During the mathematical revolution that the Indian wise men carried out over several centuries, they also operated with the irrational roots of other numbers – such as √2 or √3 – in the same way, that they operated with rational numbers. Partly because their arithmetic was completely independent of geometry, unlike the Greeks, who did not conceive of irrational numbers as true numbers, since they could not be compared or measured by a ratio of whole numbers. Indian mathematicians, on the other hand, did not get to the bottom of this differentiation between commensurable and immeasurable magnitudes in Greek arithmetic. They also made progress in algebra. They used abbreviations of words and symbols to describe operations. For unknowns, when there was more than one, they used color names: black, blue and yellow.

Zero was born in India but was baptized in Europe. It was the Italian mathematician Fibonacci who popularized the Indian-born decimal system in the West and who began using the word zero to designate the symbol of nothingness. The term sifr, empty in Arabic, derived from the Latin zephyrum, which ended up becoming the Italian zephyr and contracted into the Venetian zero, which Fibonacci decided to name the “0”.