1816 Milling machine invented to reduce hand filing of intricate shapes. (Simeon North, Harpers Ferry Armory)
"Later, in 1818, Whitney invented the first milling machine." From another source.
"A bit later in the year 1818 Eli Whitney (inventor of the cotton gin) invents a milling machine in New Haven Connecticut. Prior to the milling machine, a machinist's tools were primarily files and required a highly skilled operator. The milling machine allowed a less skilled operator to make the same quality of parts as the skilled operator with the file. This milling machine found use making rifles for the government.
The spindle of Eli Whitney's milling machine was moved from being horizontal to being vertical. This is commonly seen in the Bridgeport style knee-mill. The knee-mill is a vertical spindle milling machine that can move the workpiece in the x, y, and z directions by increments of 0.001" by turning the appropriate hand crank. " From yet another source.
1920 ca. Keller milling machine introduced: die-sinking for three-dimensional copying of template, used for large steel dies in automobile manufacturing.
The 1816 and 1920 dates are from:
The CNC (tape) machines started to show up around 1953
The MIT press has a book on the history of the milling machine.
It is strange that you would ask this question while I'm on a quest to get information on a Multi-axis milling machine that was used by the company I worked for in 1952. This machine was a wood milling machine made in England that was used in making patterns in a foundry. This machine had more axis than an octopus. The table had X-Y-Z, would rotate, tilt. All this motions were made by gear changes. The spindle head contained a gear head where the tool could be extended off the center line while running. If the spindle extension was set the gear head could rotate around the spindle axis while extending the tool bit. This machine generated so many wood chips that the floor around the pedestal was a grate with a vacuum pickup.