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PT 55, the design that would later become FF Meta, was devised by Erik Spiekermann for the German Post Office (Deutsche Bundespost) in 1985. The Post Office, who was using Helvetica at that time, cancelled their commission at the last minute. Spiekermann's design went into hibernation. Interestingly enough, the post office did eventually change their corporate face—to Frutiger, which they still use today.
Around the same time as the founding of FontShop, Spiekermann and several of his colleagues revived their dormant design, creating FF Meta, whose first weights were released in 1991. Over the next 15 years, numerous more weights would be devised.
FF Meta is named after the studio which Spiekermann headed at the time, MetaDesign. Meta is proud of the face, calling it the Helvetica of the '90s (quote attributed to Robin Kinross). Meta was designed for use at smallish sizes, but became more widely used by designers looking for a workhorse typeface with range.
More history: How FF MetaPlus Became FF Meta
See also: FF Meta Serif