Abstract: In the mid-19th century, mathematicians were just beginning to work with complex numbers and develop the idea we know today as a vector. It was during this time that an Irish mathematician by the name of Sir William Rowan Hamilton discovered "quaternions." Like complex numbers, the quaternions can act as both states and operators. It was also from quaternions that Hamilton coined the term "vector." Although vectors are preferred today, quaternions are still quite useful for rotations in three dimensions.