Grassmann’s legacy

In a previous conference honouring Hermann Grassmann’s profound intellectual con tributions [Schubring 1996a], I cast him as a central figure in the historical development of a universal geometric calculus for mathematics and physics [Hestenes 1996]. Six teen years later I am here to report that impressive new applications in this tradition are rapidly developing in computer science and robotics as well as physics and mathematics. Especially noteworthy is the emergence of Conformal Geometric Algebra as an ideal tool for computational geometry, as it fulfils at last one of Grassmann’s grandest goals and confirms the prescience of his mathematical insight. Geometric Calculus has finally reached sufficient maturity to serve as a comprehensive geometric language for the whole community of scientists, mathematicians and engineers. Moreover, its simplicity recommends it as a tool for reforming high-school mathematics and physics, as Grassmann had envisioned.