They provide an axiomatic geometry for complex numbers in three-dimensional space.  
Their discovery marked a break from the commutative property of multiplication. Their discoverer cut into the Brougham Bridge over Dublin's Royal Canal their fundamental formulas, those being I squared equals k squared equals j squared equals I times j times k equals negative one.  They provide an axiomatic geometry for complex numbers in three-dimensional space.  FTP, name these ordered quadruplets discovered by Sir William Rowan Hamilton.
Their discovery marked a break from the commutative property of multiplication.
Quaternions