There is no simple, specific answer to the question of who invented printing. Since printing has been with us, in some form, for many centuries, the answer is best approached through highlighting noteworthy advances in printing throughout time.
The earliest instances of what could be considered printing began with the carving of wooden blocks. This technique could be described as sculpting, on the woodblock, a mirror image of what was intended to be printed. While there is no specific record of who invented printing in this manner, the earliest evidence points to China in the 2nd century.
A major advancement in printing was the invention of movable type in the year 1040. It is credited to Bi Sheng, who lived in China. Movable type is simply a process of arranging individual characters in a frame, as opposed to the creating the content of an entire page all on a single woodblock. The single characters of the movable type press were initially forged in clay, then wood, and then metal a few centuries later.
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