History of zero
The use of zero as a number should be distinguished from its use as a placeholder numeral in place-value systems. Many ancient texts used zero. Babylonians and Egyptian texts used it. Egyptians used the word nfr to denote zero balance in double entry accounting entries. Indian texts used a Sanskrit word Shunya to refer to the concept of void; in mathematics texts this word would often be used to refer to the number zero.
Records show that the Ancient Greeks seemed unsure about the status of zero as a number: they asked themselves "how can 'nothing' be something?" leading to interesting philosophical and, by the Medieval period, religious arguments about the nature and existence of zero and the vacuum. The paradoxes of Zeno of Elea depend in large part on the uncertain interpretation of zero. (The ancient Greeks even questioned if 1 was a number.)
The late Olmec people of south-central Mexico began to use a true zero (a shell glyph) in the New World possibly by the 4th century BC but certainly by 40 BC, which became an integral part of Maya numerals and the Maya calendar. Mayan arithmetic used base 4 and base 5 written as base 20. Sanchez in 1961 reported a base 4, base 5 'finger' abacus.
By 130, Ptolemy, influenced by Hipparchus and the Babylonians, was using a symbol for zero (a small circle with a long overbar) within a sexagesimal numeral system otherwise using alphabetic Greek numerals. Because it was used alone, not as just a placeholder, this Hellenistic zero was the first documented use of a true zero in the Old World. In later Byzantine manuscripts of his Syntaxis Mathematica (Almagest), the Hellenistic zero had morphed into the Greek letter omicron (otherwise meaning 70).
Another true zero was used in tables alongside Roman numerals by 525 (first known use by Dionysius Exiguus), but as a word, nulla meaning nothing, not as a symbol. When division produced zero as a remainder, nihil, also meaning nothing, was used. These medieval zeros were used by all future medieval computists (calculators of Easter). An isolated use of their initial, N, was used in a table of Roman numerals by Bede or a colleague about 725, a true zero symbol.
An early documented use of the zero by Brahmagupta (in the Brahmasphutasiddhanta) dates to 628. He treated zero as a number and discussed operations involving it, including division. By this time (7th century) the concept had clearly reached Cambodia, and documentation shows the idea later spreading to China and the Islamic world.
