The Tragic Downfall and Peculiar Revival of Quaternions

Danail Brezov ()
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Danail Brezov: Deptartment of Mathematics, University of Architecture, Civil Engineering and Geodesy, 1 Hristo Smirnenski Blvd., 1164 Sofia, Bulgaria

Mathematics, 2025, vol. 13, issue 4, 1-15

Abstract: On October 16th 1843, the prominent Irish mathematician Sir William Rowan Hamilton, in an inspired act of vandalism, carved his famous i 2 = j 2 = k 2 = i j k = − 1 on the Brougham Bridge in Dublin, thus starting a major clash of ideas with the potential to change the course of history. Quaternions, as he called his invention, were quite useful in describing Newtonian mechanics, and as it turned out later—also quantum and relativistic phenomena, which were yet to be discovered in the next century. However, the scientific community did not embrace this new approach with enthusiasm: there was a battle to be fought and Hamilton failed to make a compelling case probably because he was standing alone at the time. Although Quaternions were soon to find useful applications in geometry and physics (with the works of Clifford, Cayley, Maxwell, Einstein, Pauli, and Dirac), the battle seemed lost a few decades after Hamilton’s death. But, a century later computer algorithms turned the tides, and nowadays we are witnessing a revived interest in the subject, prompted by technology.

Keywords: quaternions; geometric algebra; spatial kinematics; relativity; robotics; computer vision (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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