Hamilton's Discovery of the Quaternions and Creativity in Mathematics

Abstract

Creativity can be defined as the process of forming new patterns from pre-existing component parts. As an illustration, we explain how Hamilton's discovery of the quaternions, and Cayley and Graves's subsequent discoveries of the octonions, could have resulted from considering the properties of complex numbers and asking for each one, ``how might this be different?''. We give some general suggestions on differences to look for and explain why creativity can be much richer when people work in small groups rather than individually