Well, as an amateur historian who almost became a professional historian, Ancient Times finish at the same time everywhere and that corresponds roughly to the fall of the Roman Empire in Europe, North Africa and the Middle East, the fall of the Gupta Empire in India. In other words "Medieval Times" by Western standard (mine) corresponds to the rise of Islam, the beginning of the Sui and Tang dynasties in China, the Yamato and Nara periods in Japan, of the decline of the Classic Maya period.
Sorry, I mistook when I said Maya above, so I have added it. There is little need including the smaller American and Middle Eastern civilisation in a poll for the greatest one... Anyway, I think it is better to avoid confusion by adding to many small civs or an option "Other", as people like you might think of later civilisations .