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Introduction

It can be said that the real quaternions were discovered (invented?) on October 16, 1843 by Sir William Rowan Hamilton (1805-1865), called Ireland's foremost mathematician. The story is well known and recounted in [1] and [2]. Indeed, a conference celebrating this historic event was held August 17 -20, 1993 in Dublin, Ireland.

The real numbers have an addition and a multiplication that satisfy the axioms of a field. In 1833, Hamilton showed that the two-dimensional space of ordered pairs of reals also has operations extending those of to yield the field of complex numbers. Could these operations be extended further into the space of real three-tuples or even to ? This was the problem troubling Hamilton when a brilliant spark of insight came upon him while walking along a canal in Dublin. The story goes that he was so excited, he took out his pocket knife and carved the defining relations in the stone of the Bourne Bridge then under construction. While we cannot condone this creative act of vandalism, we certainly empathize with the exuberance that a mathematician feels when the solution to a long standing problem is finally recognized.


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