This essay summarises the development of zero, as both digit and number, from early to modern civilisations. More willing to accept the concept of void, the Eastern civilisations are credited with the invention of zero. The Western civilisations, on the other hand, struggled for almost two millennia to finally accept zero.
The history of zero from merely a placeholder in place value systems (digit) to finally becoming accepted as a number has a very long history in Western civilisations. This was mainly due to their strong rejection of the concept of void. The Eastern civilisations, fortunately, were never so fearful of the idea of void, which was in fact strongly intertwined in their religion (Seife, 2000, p. 65). It is therefore not surprising that zero was first invented in the East. From the 5th century BC, the Babylonians had used zero placeholder in their base-60 number system (Boyer, 1991, p. 31). In this system, diagonal double wedges were used to represent empty placeholder (see figure 1). Using their base-20 counting system, the Mayans were the first civilisation whose counting system started with zero, not one (Kaplan, 1999, p. 82). Unfortunately, their isolation from other civilisations meant that their more sensible system never spread outside Central America.
Figure 1. Babylonian base-60 number system with zero placeholder 1| 61| 3601|
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1x600| 1x601 + 1x 600| 1x602 + 0x601 + 1x600|
The Egyptians, Greeks and Romans, on the other hand, never used zero even as a digit, nor did they accept zero as a number. This, however, did not prevent them from creating sophisticated civilisations where the art of Geometry was invented. However, with the mindset appeared to be fixed in the dual properties of number and shape, their number systems were only capable of dealing with realistic objects such as triangles. Zero, however, represented void with no shape, hence could not be a number
Great admirers of the Egyptians, the Greeks had advanced Egyptian mathematics to the highest point in ancient times. Unlike the Egyptians who were of more practical bent, the Greeks were more willing to embrace the abstract and started to put maths into their philosophy. They were, however, still reluctant to accept zero. They had been aware of the use of zero placeholder, as they used the Babylonian number system to calculate astronomical tables. They were therefore fully aware of the easiness of the system in performing intricate calculations compared to their own. However, they would always translate the results back into their own number system - without zero (Seife, 2000, p. 59). This reluctance appeared to be more philosophical. The Greeks were always keen followers of Aristotle‘s universe, in which “There was no infinity, no void – just beautiful spheres that surrounded the earth, which was naturally placed at the centre of the universe” (Seife, 2000, p. 45).
Within a culture where maths and philosophy were strongly intertwined, naturally there would be a few Greek philosophers who started to question the concept of zero and infinity. Zeno of Elea was the first to come up with such concept (O’Connor and Robertson (1996)), while Archimedes was the first to find the practical use of zero and infinity while attempting to calculate the areas of section of a parabola (Seife, 2000, pp. 50). However, while starting to see the necessity of using zero to solve mathematical problems, Archimedes, like other philosophers of his time were still too torn between their strong support of Aristotle’s universe and their own invention - to openly accept zero (Seife, 2000, p. 51).
The fall of Greek civilisation in around 300 BC was quickly followed by the rise of Roman civilisation, during which little contribution was made to further development in mathematics. With the rise of Christianity throughout Europe and the fall of the Roman Empire, the Dark Ages in the Western...