Origins of Geometric Algebra

Abstract

There is a tendency among physicists to take mathematics for granted, to regard the development of mathematics as the business of mathematicians. However, history shows that most mathematics of use in physics has origins in successful attacks on physical problems. The advance of physics has gone hand in hand with the development of a mathematical language to express and exploit the theory. Mathematics today is an immense and imposing subject, but there is no reason to suppose that the evolution of a mathematical language for physics is complete. The task of improving the language of physics requires intimate knowledge of how the language is to be used and how it refers to the physical world, so it involves more than mathematics. It is one of the fundamental tasks of theoretical physics.