Geometric algebra as a basis for a [new] unified mathematical view of physics

Abstract

For years now, the mathematics used to property express the physical world has been evolving by leaps and bounds. Initially there was only the rather "primitive" Euclidean Algebra and Geometry. Then Newton and Leibnitz came with the Calculus; which has undoubtedly proved its powers by accurately describing the phenomena of science in a reasonably elegant way. Yet, even the Calculus has proved to be limited for an encompassing description of the physical world. Therefore, to help them in their neverending crusade of unravelling the secrets of the universe, physicists and mathematicians alike sought to discover new forms of mathematical systems.
Many distinct mathematical systems have been adapted or developed to express [many physical] relations and structures. Each of these has some significant advantage over the others in certain applications, yet not one of them provides an adequate mathematical structure of all purposes [in physics]. A unified theory of the physical world calls for a unified mathematical language to help develop and express it, and we think that geometric algebra can be a basis for that.