Jordan algebras

Jordan algebras are mathematical structures that focus on operations resembling the “average” of two elements, using a symmetrical product. They originated in the study of quantum mechanics and help describe observables—a set of measurable properties. Unlike regular multiplication, Jordan algebras emphasize symmetry and commutativity, capturing the essence of certain algebraic systems where the order of operation isn’t as critical. They serve as a framework to explore complex mathematical and physical phenomena, bridging algebra, geometry, and theoretical physics in a coherent way.