"Quaternions came from Hamilton after his really good work had been done; and, though beautifully ingenious, have been an unmixed evil to those who have touched them in any way, including Clerk Maxwell." - Lord Kelvin, 1892.
Formulated by the Irish Mathematician Sir William Rowan Hamilton in 1843, the quaternions are an extension of complex numbers $z=a+ib$ into four dimensions to form $z=a+bi+cj+dk$ where $i^2=j^2=k^2=ijk=-1.$

Multiplication of quaternions does not necessarily commute - note that $ij=-ji$ . The algebra of Quaternions was one of the first non-commutative algebras to be devised.

For 13 years Hamilton had tried to find a way to extend the complex numbers into three dimensions, but every attempt to multiply triples (with associated division) failed. Finally he realised that the additional dimension would work. This final revelation occurring in a sudden moment of inspiration whilst on a walk along a canal in Dublin. A plaque now commemorates the location.