A new exhibit at the Oriental Institute in Chicago is called “Visible Language: Inventions of Writing in the Ancient Middle East and Beyond”; here is a discussion by The New York Times. According to the review,
The show demonstrates that, contrary to the long-held belief that writing spread from east to west, Sumerian cuneiform and its derivatives and Egyptian hieroglyphics evolved separately from each another. And those writing systems were but two of the ancient forms of writing that evolved independently. Over a span of two millenniums, two other powerful civilizations — the Chinese and Mayans — also identified and met a need for written communication. Writing came to China as early as around 1200 B.C. and to the Maya in Mesoamerica long before A.D. 500.