The credit for this goes to Indian mathematicians and the number zero first appears in a book about ‘arithmetic’ written by an Indian mathematician ‘Brahamagupta’. Zero signifies ‘nothing’ and the current definition calls it an ‘additive identity’.
Mathematically; x + 0 = x, i.e. 0 is a number which, when added to a number yields the same number.
When we go deeper, it becomes clearer that the things are much more complex. It wasn’t that somebody suddenly came up with the idea of the zero and the mathematicians throughout the world accepted it. Around 500 AD, Aryabhata, an Indian mathematician, devised a numbers system and the symbol he used for the number zero was also the number used to represent an unknown element (x). This system was confusing but the improvements continued and by 876 AD, the concept of zero was mostly understood and the symbol for it was ascertained.
The Indian mathematicians Bhaskara, Mahavira and Brahamagupta worked on this new number and they tried to explain its properties. Some were true and some were not. For example, Bhaskara correctly that stated 02 = 0 and 01/2 = 0 but he was wrong to have supposed that n/0 = Infinity. If n/0 = Infinity were to be true there would arise results which don’t make sense. One of them was 1 = 2 = 3 …….
The reason of this was that the Indian mathematicians could not conclude that no number could be divided by zero. The Maya people in present day Mexico knew and understood the concept of zero but because they were so much disconnected with the rest of the world civilizations, it had little impact on the rest of the world.
Source: http://www.thegeminigeek.com/who-invented-the-zero/