The Forgotten Quaternions

A quick glance through the Mathematics section of the 2004 Stanford University Bulletin reveals five courses devoted to complex analysis, but no courses even mentioning quaternions. How is it that complex analysis, a subject that has suffered through hundreds of years of skepticism and distrust, came to be so widely accepted today, while quaternionic analysis, a modern subject immediately accepted as a straight-forward extension to complex analysis, has fallen by the way-side? I contend that the modern lack of interest in quaternions exists because quaternions solved no problem that could not be solved more easily by another method. I will (briefly) argue that complex numbers were too useful to be ignored, and thus developed into their modern conception, and offer it as an example of a subject accepted and developed because of its utility. The bulk of the paper will then be devoted to showing that quaternions did not achieve a level of utility sufficient to warrant its development into a mainstream subject. I will argue that quaternions did not achieve this level of utility because they were eclipsed by a related field of vector analysis that eventually became modern Vector Calculus.