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 (
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. Classical Vector Algebra (Textbooks in Mathemat...
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) In 1843, the Irish mathematician was walking across
The history of isn’t just a dry sequence of formulas; it’s the story of a hundred-year "math war" over how to describe the physical world. 1. The Shadow of Hamilton (1840s) It allowed us to build bridges, fly planes,
They split quaternion multiplication into two distinct operations:
The (measuring how much vectors go in the same direction).