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By Root 714 0

the best way to calculate could be properly exploited using written symbols. Zero would enhance mathematics in other ways too, by leading to the ‘invention’ of negative numbers and decimal fractions – concepts we learn effortlessly at school and are intrinsic to our needs in daily life, but which were in no way self-evident. The Greeks made fantastic mathematical discoveries without a zero, negative numbers or decimal fractions. This was because they had an essentially spatial understanding of mathematics. To them it was nonsensical that nothing could be ‘something’. Pythagoras was no more able to imagine a negative number than a negative triangle.

Evolution of modern numerals.

Of all the innovative ways that numbers were treated in ancient India, perhaps none was more curious than the vocabulary used to describe the numbers from zero to nine. Rather than each digit having a unique name, there was a colourful lexicon of synonyms. Zero, for example, was shunya, but it was also ‘ether’, ‘dot’, ‘hole’ or the ‘serpent of eternity’. One could be ‘earth’, ‘moon’, ‘the pole star’ or ‘curdled milk’. Two was interchangeable with ‘arms’, three with ‘fire’ and four with ‘vulva’. The names that were chosen depended on context and conformed to Sanskrit’s strict rules of versification and prosody. For example, the following verse is a piece of number-crunching from an ancient astrological text:

The apsides of the moon in a yuga

Fire. Vacuum. Horsemen. Vasu*. Serpent. Ocean, and of its waning node

Vasu. Fire. Primordial Couple. Horsemen. Fire. Twins.

The translation is:

[The number of revolutions] of the apsides of the moon in a [cosmic cycle is]

Three. Zero. Two. Eight. Eight. Four, [or 488,203] and of its waning node

Eight. Three. Two. Two. Three. Two. [or 232,238]

While at first it might seem confusing to have flowery alternatives for each digit, it actually makes perfect sense. During a period in history when manuscripts were flimsy and easily spoiled, astronomers and astrologers needed a backup method to remember significant numbers accurately. Strings of digits were more easily memorized when described in verse with varied names, rather than when using the same number names repeatedly.

Another reason why numbers were passed down orally was that the numerals that were emerging in different regions of India for the numbers from one to nine (zero, I will come to later) were not the same. Two people who did not understand each other’s number symbols could at least communicate numbers using words. By 500 CE, however, there was greater uniformity in the numerals used, and India had the three elements that were required for a modern decimal number system: ten numerals, place value, and an all-singing, all-dancing zero.

Owing to its ease of use, the Indian method spread to the Middle East, where it was embraced by the Islamic world, which accounts for why the numerals have come to be known, erroneously, as Arabic. From there they were brought to Europe by an enterprising Italian, Leonardo Fibonacci, his last name meaning ‘son of Bonacci’. Fibonacci was first exposed to the Indian numerals while growing up in what is now the Algerian city of Béjaïa, where his father was a Pisan customs official. Realizing that they were much better than Roman ones, Fibonacci wrote a book about the decimal place-value system called the Liber Abaci, published in 1202. It opens with the happy news:

The nine Indian figures are:

9 8 7 6 5 4 3 2 1

With these nine figures, and with the sign 0, which the Arabs call zephyr, any number whatsoever is written, as will be demonstrated.

More than any other book, the Liber Abaci introduced the Indian system to the West. In it Fibonacci demonstrated ways to do arithmetic that were quicker, easier and more elegant than the methods the Europeans had been using. Long multiplication and long division might seem dreary to us now, but at the beginning of the thirteenth century they were the latest technological novelty.

Not everyone, however, was convinced to switch immediately.