History of Quaternions - After Hamilton

After Hamilton

After Hamilton's death, his pupil Peter Tait, as well as Benjamin Peirce, continued advocating the use of quaternions. Topics in physics and geometry that would now be described using vectors, such as kinematics in space and Maxwell's equations, were described entirely in terms of quaternions. There was a professional research association which existed from 1899 to 1913, the Quaternion Society, exclusively devoted to the study of quaternions.

From the mid-1880s, quaternions began to be displaced by vector analysis, which had been developed by Josiah Willard Gibbs and Oliver Heaviside. Both were inspired by the quaternions as used in Maxwell's A Treatise on Electricity and Magnetism, but — according to Gibbs — found that "… the idea of the quaternion was quite foreign to the subject." Vector analysis described the same phenomena as quaternions, so it borrowed ideas and terms liberally from the classical quaternion literature. However, vector analysis was conceptually simpler and notationally cleaner, and eventually quaternions were relegated to a minor role in mathematics and physics. A side effect of this transition is that works on classical Hamiltonian quaternions are difficult to comprehend for many modern readers because they use familiar terms from vector analysis in unfamiliar and fundamentally different ways.