The quaternions were discovered by the Irish mathematician William Rowan Hamilton on October 16th, 1843.[2] During the eighteen hundreds, the complex numbers were a well researched topic in mathematics. Rules for addition, subtraction, multiplication, and division between two complex numbers were known. What wasn't known was how to multiply three numbers in the form (a + bi + cj) where a, b, and c are real numbers and
i2 = j2 = -1. This problem was what troubled Hamilton for over ten years. It was not until he was walking with his wife along the Royal Canal in Dublin, Ireland that the idea for the quaternions as a solution came to him. He was so estatic that he scratched the formula for the quaternions, i2 = j2 = k2 = ijk = -1, into the stonework of the Brougham Bridge.[3] What Hamilton had been missing for ten years was a fourth element in the form
(a + bi + cj + dk).