India: 458 A.D. (debated)

The final independent invention of the zero was in India. However, the time and the independence of this invention has been debated. Some say that Babylonian astronomy, with its zero, was passed on to Hindu astronomers but there is no absolute proof of this, so most scholars give the Hindus credit for coming up with zero on their own.

The reason the date of the Hindu zero is in question is because of how it came to be.

Most existing ancient Indian mathematical texts are really copies that are at most a few hundred years old. And these copies are copies of copies of copies passed through the ages. But the transcriptions are error free...can you imagine copying a math book without making any errors? Were the Hindus very good proofreaders? They had a trick.

Math problems were written in verse and could be easily memorised, chanted, or sung. Each word in the verse corresponded to a number. For example,

Indian place notation moved from left to right with ones place coming first. So the phrase above translates to 4,230,000.

Using a vocabulary of symbolic words to note zero is known from the 458 AD cosmology text Lokavibhaga. But as a more traditional numeral--a dot or an open circle--there is no record until 628, though it is recorded as if well-understood at that time so it's likely zero as a symbol was used before 628.

Which it probably was, considering that 30 years previously, an inscription of a date using a zero symbol in the Hindu manner was made in Cambodia. The Hindus influenced the numeration of nearby locales, and introduced the zero to the Chinese and to the Arabs who developed the modern day shape of numerals and passed them, along with zero to the Europeans in the 12th century.

A striking note about the Hindu zero is that, unlike the Babylonian and Mayan zero, the Hindu zero symbol came to be understood as meaning "nothing." This is probably because of the use of number words that preceded the symbolic zero.