Classical Vector Algebra (textbooks In Mathemat... -

By the late 19th century, scientists were frustrated. had written his famous equations for electromagnetism using quaternions, but they were so dense that almost no one could solve them.

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) Classical Vector Algebra (Textbooks in Mathemat...

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 late 19th century, scientists were frustrated

The (measuring how much vectors go in the same direction). However, they were incredibly difficult to use

In modern high-level physics (like General Relativity or Quantum Mechanics), we’ve actually circled back to more complex structures like Tensors and Spinors that look a lot more like those "monstrous" quaternions than Hamilton ever could have dreamed.

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.

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 (