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The Number That Is an Absence

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The Number That Is an Absence

Zero is the youngest of the small numbers and the last to be accepted as a number at all. The Greeks and Romans counted without it, and their arithmetic managed by other means; a symbol for the empty place in positional notation appears in Babylonian and, independently, Maya practice, but treating zero as a quantity that can be added and multiplied is an Indian achievement. Brahmagupta, in the Brahmasphutasiddhanta of 628, was the first to set out rules for arithmetic with zero, including the troublesome case of division by it. The Sanskrit word is shunya, emptiness or void, the same term that carries the Buddhist idea of shunyata, and the sign travelled west through Arabic as sifr, from which come both cipher and zero. The number that stands for nothing is therefore a relatively late and quite specific invention, not a universal intuition.

Zero's reception in the medieval West was slower and more contested than its Indian and Arabic transmission suggests. Leonardo of Pisa, known as Fibonacci, set out the Hindu-Arabic numerals, zero among them, for a European readership in his Liber Abaci of 1202, having learned the system from Arabic-speaking merchants and mathematicians in North Africa; adoption was nonetheless slow and locally resisted, and a 1299 statute of the Arte del Cambio, the moneychangers' guild of Florence, is recorded as barring the new figures from ledger-keeping, requiring sums to be written out in Roman numerals or in words instead, partly from a fear that the new digits, zero included, were too easily altered or forged.

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