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)
But Heaviside didn't care about "mathematical elegance." He was a telegraph engineer who wanted tools that worked. He famously said, "Vectors are a great help to a man who has any physics in him." He used this "new" vector algebra to condense Maxwell’s 20 original equations down to the 4 we use today. 4. Victory and the Modern Textbook Classical Vector Algebra (Textbooks in Mathemat...
They split quaternion multiplication into two distinct operations: Hamilton believed quaternions were the ultimate language of
The traditionalists were furious. , Hamilton’s successor, called Gibbs’s new algebra a "hermaphrodite monster." He believed that by removing the "quaternion" structure, Gibbs and Heaviside were destroying the mathematical soul of physics. Classical Vector Algebra (Textbooks in Mathemat...