China: 718 A.D.

China was one of the four independent inventors of the place value system, but they didn't make the leap to zero until it was introduced to them by a Buddhist astronomer (by way of India) in 718.

Although it seems strange to image a place value system with no place holder for "nothing, " it's easy to understand why zero wasn't invented when you see the Chinese method for writing and calculating numbers.

The Chinese used an additive system to write their numbers. There was a symbol for 1 and a symbol for five and these symbols were added together to form symbols for other numbers up to 9. The numbers were actually rods arranged on a counting board which ran from left to right. Any missing places were left blank on the counting board.

After the introduction of the zero symbol, the counting board could be retired. Numbers could be written on paper without the need of rods. This same phenomenon is the reason the Europeans did not adopt the zero until the 12th century. They used counting boards until that time.