Project Gutenberg#OTD in 1843.
William Rowan Hamilton invents quaternions, a 3D system of complex numbers.
Important precursors to this work included Euler's four-square identity (1748) & Olinde Rodrigues' parameterization of general rotations by 4 parameters (1840), but neither of these writers treated the four-parameter rotations as an algebra. Carl Friedrich Gauss had discovered quaternions in 1819, but this work was not published until 1900.
https://en.wikipedia.org/wiki/Quaternion
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