In 1843, the Irish mathematician was walking across a bridge in Dublin when he had a "eureka" moment. He carved the formula for Quaternions into the stone. Quaternions were four-dimensional numbers (
By the early 1900s, the battle was over. In 1901, , a student of Gibbs, published Vector Analysis . This was the first true textbook in the modern sense. It standardized the notation we use in every physics and engineering classroom today ( Classical Vector Algebra (Textbooks in Mathemat...
Enter two rebels: (an American) and Oliver Heaviside (an Englishman). Independently, they decided to "vandalize" Hamilton’s work. They took the quaternion, chopped off the "real" part ( ), and focused only on the components. In 1843, the Irish mathematician was walking across
Classical Vector Algebra became the "gold standard" because it was practical. It allowed us to build bridges, fly planes, and understand electricity without the overhead of 4D hyper-complex numbers. In 1901, , a student of Gibbs, published Vector Analysis
Hamilton believed quaternions were the ultimate language of the universe. However, they were incredibly difficult to use. To do simple physics, you had to drag around a complicated four-part number when you really only cared about three-dimensional space. 2. The Great Schism (1880s)