Re: [HM] The Zero Story: a question

Kim Plofker (Kim_Plofker@Brown.edu)
Mon, 26 Apr 1999 19:49:14 -0400 (EDT)

>A colleague has asked me about the accuracy of what follows.
>Appreciate your help.

This is all so inaccurate and/or totally mistaken that I don't know
where to begin. I'll try to take it point-by-point, and I'll try to
concentrate only on major errors of fact and shaky assumptions rather
than on what can be considered allowable hyperbole for a general
audience. And I'll leave discussion of ancient Greek and Near Eastern
zero concepts for those more knowledgeable about them. It may spread out
over two postings...

Kim Plofker

Dept. of History of Mathematics
Brown University

> THE ZERO STORY:
> -----------------------------
> Source: Unknown, from the Siemens Network Magazine.
>
> A plural is possible only if there is a singular.
> A singular is possible, if there is nothing to begin
> with. And what is the number of nothingness? It was
> a subtle Indian mind, Aryabhata's, who bestowed a name
> and number upon a gap, the profound Shunya, Zero. He
> used the symbol of a circle with a dot within, perhaps
> to show the immense space captured within a mere circle.
> He knew the potential.

See R. C. Gupta, "Who Invented the Zero?", _Ganita Bharati_ 17,
1--4 (1995), 45--61, for a much more knowledgeable and informative
overview of the subject. This author's chief mistake seems to be
assuming that the three best-known Indian mathematicians---Aryabhata,
Brahmagupta, and Bhaskara II---are necessarily the inventors of
various developments. The Sanskrit word "sunya" (void, sky) for
a zero-marker is found in Pingala's Chandahsutra, probably no later
than 200 B.C. Certainly, Indian mathematicians were habitually using
a symbol and operations for zero long before Aryabhata in the 6th c. C.E.

[to be continued...]
>
> Indians became adept mathematicians around 3000BC, when
> the Mohenjadaro and Harappa civilizations flourished. Its
> usage became well known around the 6th century when
> Brahmagupta of Multan formulated the rules of operation of
> Aero in his treatise, Brahmasphutasiddantha, in which he
> treated Zero as just another number: A+0=A, A-0=A; Ax0=0
> A/0=0. He went wrong on the last count. Any quantity divided
> by zero is infinity. The mistake was corrected some centuries
> later when Bhaskara (AD 1114) of Bijapur wrote Leelavati.
> He claimed that the division of any quantity by zero is an
> infinity, or immutable god, a god who does not change when
> worlds are created or destroyed. Only the tangible changes;
> zero the intangible, immutable. For 400 years from the 6th
> century, India was foremost in maths and zero began its journey
> around the world. With the rise of trade among Arabs, Greeks
> and Indians, caravans carried more than goods to China, Arabia
> and Greece. Though Arabs used Indian numbers and Zero, it was
> the Arab mathematician Al-Khowarizmi, who popularised its use
> Shunya became al-sifr or sift, sifr became Zero. al-jabr into
> algebra.
>
> When the Arabs invaded Palestine, the putative Arabic origin of
> Indian numbers earned them the label of infidel Numbers.
> When Turks captured Constantinople in 1453, the city's scholars
> fled to distant parts of Europe, taking the 'zero' with them.
> By the end of 16th century, the zero was all over the world.